A Game Theoretic Framework for Surplus Food Distribution in Smart Cities and Beyond
Surja Sanyal, Vikash Kumar Singh, Fatos Xhafa, Banhi Sanyal, Sajal Mukhopadhyay
aa r X i v : . [ c s . G T ] F e b RESEARCH ARTICLE
A Game Theoretic Framework for Surplus Food Distribution inSmart Cities and Beyond
Surja Sanyal a , Vikash Kumar Singh b , Fatos Xhafa c , Banhi Sanyal d , and SajalMukhopadhyay e a National Institute of Technology, Durgapur, West Bengal, India; b School of ComputerScience and Engineering, VIT-AP University, Amaravati, Andhra Pradesh, India; c Universitat Polit`ecnica de Catalunya, Barcelona, Spain; d National Institute of Technology,Rourkela, Odisha, India; e National Institute of Technology, Durgapur, West Bengal, India
ARTICLE HISTORY
Compiled February 10, 2021
ABSTRACT
Food waste is a major challenge for the present world. It is the precursor to severalsocioeconomic problems that are plaguing the modern society. To counter the sameand to, simultaneously, stand by the undernourished, surplus food redistribution hassurfaced as a viable solution. Information and Communications Technology (ICT)-mediated food redistribution is a highly scalable approach and it percolates intothe masses far better. Even if ICT is not brought into the picture, the presence offood surplus redistribution in developing countries like India is scarce and is limitedto only a few of the major cities. The discussion of a surplus food redistributionframework under strategic settings is a less discussed topic around the globe. Thispaper aims at addressing a surplus food redistribution framework under strategicsettings, thereby facilitating a smoother exchange of surplus food in the smart citiesof developing countries, and beyond. As ICT is seamlessly available in smart cities,the paper aims to focus the framework in these cities. However, this can be extendedbeyond the smart cities to places with greater human involvement.
Abbreviations:
CA-DTB: Chronological Acceptance using Double Tie Breaking;CTFU: Classification and TriFurcation of Users;FDRM-CA: Food Donor to Receiver Matching with Chronological Acceptance;FSSAI: Food Safety and Standards Authority of India;GPS: Global Positioning System;ICT: Information and Communications Technology;IFSA: Indian Food Sharing Alliance;NGO: Non Government Organizations;NUIR: New User Interrupt Routine;P2P: Peer-To-Peer;UT: Union Territory
KEYWORDS
Food surplus; Food redistribution; Food recovery; Food waste; Food sharing; Foodwaste management; Smart cities; ICT-mediation; Game theory; Double-sidedmarket; Sustainability; Scalability
CONTACT Surja Sanyal. Email: [email protected] Vikash Kumar Singh. Email: [email protected] Fatos Xhafa. Email: [email protected] Banhi Sanyal. Email: [email protected] Sajal Mukhopadhyay. Email: [email protected] . Introduction
For the last couple of years, food waste has been a major contributor to-wards several socioeconomic problems (Harvey, Smith, Goulding, & Illodo, 2020;Ganglbauer, Fitzpatrick, & Molzer, 2012), including, but not limited to, global warm-ing, greenhouse gas emissions, water wastage, soil degradation, farmer suicides, pricefluctuations, black marketing, and hoarding. On a global scale, more than 30% of alledible products ends up as waste (Shi, Yuan, Lo, Lizarondo, & Fang, 2020). Each yearthis wastage amounts to billions of tons of food, out of which near 60% is avoidable(Zhong, Xu, & Wang, 2017). One of the solutions that can deal with this underrated,yet malicious, problem of food wastage is surplus food redistribution. Distributingfood from the surplus to the deficit hits the generation of food waste at the surplusend and hunger at the deficit end. While this may not be a solution to the wholesituation, it targets the 60% avoidable food waste into a win-win scenario for the soci-ety as well as the economy of the land. Information and Communications Technology(ICT) has taken this a step further (Ciaghi & Villafiorita, 2016, September) and madethe redistribution activity smoother by connecting the donors with the receivers, andthe available volunteers, by minimizing human interference as far as possible. The useof ICT brings the very desirable properties of sustainability and, more importantly,scalability to the table. ICT-mediation in food redistribution is the buzz of the day(Weymes & Davies, 2018) and is gaining fast popularity around the world due to itsnumerous upsides. In the smart cities of developing countries like India, however, a lotremains to be done as the presence of food redistribution movements mediated by ICTis scarce and only limited to a few major cities. The discussion of a surplus food redis-tribution framework under strategic settings is a less discussed topic around the globe.This paper aims at addressing a surplus food redistribution framework under strategicsettings, thereby facilitating a smoother exchange of surplus food in the smart citiesof developing countries, and beyond. As ICT is seamlessly available in smart cities,the paper aims to focus the framework in these cities. However, this can be extendedbeyond the smart cities to places with greater human involvement.
Figure 1 presents an overview of the model. The donation that the donors makeis transported by the volunteers, who are available on the fly or as planned, to thereceivers for the matching assignment made by the algorithm, as shown by the brownarrows . The movement of information used by the app for match generation hasbeen denoted by blue arrows , and the generated match information flow has beenrepresented with green arrows . Notice the magenta arrows that indicate thatdonors and receivers can also volunteer for transportation, while being a donor or areceiver, simultaneously.The rest of the paper is organized into the following sections. Section 2 presentsthe related work in this field; Section 3 presents the method followed in presentingthe solution to our problem. The system model has been discussed in Section 4. Themechanism used is discussed in Section 6 followed by its analysis and simulation inSection 7. Conclusion and future work is presented in Section 8.
2. Related Work
The foundation of our work already exists in the form of establishing food redistribu-tion as one of the leading solutions of dealing food wastage, and ICT-mediation as agreat add-on to boost the surplus movement. However, work on the algorithms used2 onorsVolunteersReceivers
FOOD | DONATIONFOOD | RECEIPT
DonorsVolunteersReceivers FDRM-DALocationFood TypeFood AmountPackagingPreperation/ExpiryFood ImagePickup DateTime RangePreferred ReceiversRouteTransport TypePayloadTransport AC Status
Availability DateTime Range
LocationFood TypeFood AmountDropo ff DateTime RangePreferred Donors
VOLUNTEERINGVOLUNTEERING
DonationRequestVolunteeringRequestReceiptRequest
MatchedUsers
Receivers
Figure 1.
Overview of the Model to match the donors with the receivers remains elusive and is the main agenda of ourpaper.
A study (Spring & Biddulph, 2020) has identified the rapid global growth of surplusfood redistribution initiatives relying on volunteer activities mediated by ICT-basedplatforms. The involvements and contributions of cultures, organisational facts andinternal experiences has also been explored by another study (Rut, Davies, & Ng,2020). Reduction of food waste production as an approach towards mitigating cli-mate change (Nikravech, Kwan, Dobernig, Wilhelm-Rechmann, & Langen, 2020) at-tempted by grassroots initiatives aim to prevent avoidable food waste and redistributesurplus food for consumption. These low budget initiatives rely heavily on volunteersto curb their costs. Another study (Bergstr¨om, Malefors, Strid, Hanssen, & Eriksson,2020) suggests that environmental sustainability is best supported by an approachcalled the
Social Supermarket in which a body for handling the surplus of a cityworks with several food distributors gets its surplus either directly from the donorsor through a government charitable body and redistributes it to the needy. A uniquestudy (Koivunen et al., 2020, June) reports an attempt at the tricky task of reduc-ing consumer food waste at cafeterias using the combo of ICTs and IoTs. Lunchlines containing sensors that track food wastage which is later showed in each con-sumer’s mobile via an app revealed an average 3% food wasted by the customers. An-other study (Spicer, Patel, Bodurtha, & Maslen, 2020) worked to create surplus fooddata of market value and assess the prevailing practices of surplus food management.As mentioned, partnering with a food sharing app
OLIO ( https://olioex.com/ ),one study (Harvey, Smith, Goulding, & Illodo, 2020) presents an analysis of the so-cial network of the app. It reveals the formation of new relationships that divertfrom the expected donor-receiver ones. This may prove pivotal for policymakerswho aim to analyse and encourage ICT-assisted food redistribution. Recent studies(Eriksson, Giovannini, & Ghosh, 2020; Davies, Cretella, & Franck, 2019) discuss the3egislation policies affecting food wastage directly or indirectly in the European Union.They point out that the food policies of the land affect proper food redistribution andfood waste prevention.A study (Weymes & Davies, 2019) points out that the use of ICT speeds-up theredistribution process, provides high scalability of the operations and also attractsbetter quality surplus food. Research (Berns & Rossitto, 2019) also documents thecomplexities and opportunities involved in food redistribution locally. It also highlightsthe practices that can transform the way surplus food is perceived and revalued. Therealso has been research (Durr & Lotz-Sistika, 2019) on a specific South African mobileapp named Food for Us ( http://foodforus.co.za/ ). This app works on providingfood to the under-provided and allowing small-scale producers to get their produce tomarkets. This paper reveals the need for developing a strong social networked systembuild around technological platforms such as this app, to help find alternate marketsfor unsold farm produce. Another study (Spring, Adams, & Hardman, 2019) providesvaluable learning by contrasting images between different food handling practices.It ponders on the need of knowing and paying attention to the details that thathelp differentiate between food and waste. One study (Arcuri, 2019) portrays foodredistribution as a double-sided sword to fight against food insecurity and food waste.It discusses the efficacy of the anti-waste/pro-donation law of Italy in addressing bothfood waste and insecurity. It points out that its effectiveness lies in bringing togetherthe different actors in the food management process for tackling the food insecurityissue. Another study (King, 2019) focuses on the concept of a peer-to-peer (P2P) foodsharing system based on high internet usage and people interested in food sharing. Thisstudy acts as a base to identify future P2P food collection and redistribution zonesand the actors they can attract. A different study (Light & Miskelly, 2019) analyzesthe creation and accumulation of networks of sharing individuals, and how digitalplatforms can aid in the scaling of such an approach keeping in mind the sustainabilityof such initiatives. One study (Davies & Evans, 2019) has directly assessed the scenarioof sharing food in cities and has viewed it as a field of experimentation and innovation.It has been recognised (El Bilali & Allahyari, 2018) that ICTs do contribute to-wards a smoother transformation to sustainable food systems by increasing resourceproductivity, reducing inefficiencies, decreasing management costs, and improving foodchain coordination. As a matter of fact, a study (Davies & Weymes, 2018) observesthe contribution of ICT in the redistribution of surplus prepared or cooked food whichhas a very short window of recoverability before it spoils. One study (Rut & Davies,2018) terms food sharing practices as “messy” pointing out that it includes diverseranges of participants and practices that also vary over space and time and get con-nected via both physical and virtual platforms (ICTs). As noted previously, a study(Weymes & Davies, 2018) points out that ICT intervention resulted in the recoveryof surplus food at all stages of food production. However, maximum recovery wasnoted in the retail stage. Research (Facchini, Iacovidou, Gronow, & Voulvoulis, 2018)finds production beyond need, poor management, and bad consumer behaviours asthe reasons that give birth to the difficult challenge that is food wastage on a globalscale. One study (Frigo & Lucchini, 2018) explores how food donation facilitates thetransition towards a circular economy and bring together the diverse players of theprocess. It draws an important conclusion that multi-agent collaborations are the keytowards a circular economy. A thesis (Rombach, 2018) presents the different motivesand interactions of the different actors involved in the act of food distribution. Anotherstudy (Davies & Legg, 2018) summarizes the food redistribution initiatives taken byindividuals across more than ninety countries. It evaluates these initiatives in terms4f sustainability and creates a database that depicts the transformation of the societytowards sustainability.Research (Davies et al., 2017) acknowledges the positive impact of ICT in food re-distribution and also creates a database of such food sharing activities across severalcities, countries and continents in order to facilitate the identification and analysisof repetitive patterns and temporal trends in ICT-mediated surplus redistribution.Food sharing, coupled with structural changes along the production line and betterconsumer habits, has been deemed (Falcone & Imbert, 2017) as a potential solution to-wards reducing food waste. A study (Mousa & Freeland-Graves, 2017) establishes thefact that more than one out of eight people in the United States is affected with foodinsecurity in spite of around one thirds of all food production going into landfills. It ac-knowledges that food redistribution organizations do mitigate this insecurity, althoughmore in some states of the country than in others. Another study (Vittuari et al., 2017)recognizes the positive impacts of food redistribution on the environment, economy,and the society in Italy. A different study (Berry & Acheson, 2017) acknowledges thecontrasting challenges of food waste and food insecurity in the US. Based on the anal-ysis of K–12 school system in Maine, it points out that very little is known about thestrategies that schools use to handle the considerable amount of food waste that theyproduce. A study (Ananprakrit & Esbj¨ornsson, 2017) studied the prevailing traceabil-ity practices of Stockholm’s Stadsmission food bank. Although the current practicesproved to be sufficient to provide food safety and quality, potential for systematicerrors was also detected. A study (Philip, Hod-Ovadia, & Troen, 2017) observes theworking of an Israeli food bank using a different logistical model from the other foodbanks. They have nonprofit organizations (NPOs) as intermediaries that add fresh pro-duce to the surplus thereby improving the food value of the redistribution. One study(Fleming, 2017) contrasts the environmental impact of food redistribution from dona-tion to consumption against that of alternative options like landfilling and composting.Although the facts favoured composting, a better optimized food redistribution, uti-lizing benefits of using the other alternative options in the process, seems like thewin-win solution of the future.A study (Jurgilevich et al., 2016) accepts that the unwise and inefficient use of foodresources has rendered us in need for a transition towards sustainable practices. An-other study (Mourad, 2016) highlights the three phases of handling surplus food waste,namely, prevention, recovery, and recycling. This takes the utilization of surplus foodwaste to beyond human consumption. As already stated, the results of ICT appli-cation to the various stages of food wastage has been studied (Ciaghi & Villafiorita,2016, September). ICT-based solutions have also been identified (Svenfelt & Zapico,2016, August) for efficiency through monitoring and assessment of environmental im-pact, enhanced transparency and traceability in the food system, creation of a net-work between actors in the food chains, and to influence and change food practices.A study (Garrone, Melacini, Perego, & Sert, 2016) explores multiple case studies toprovide available surplus management options and the factors that make these optionsattractive and applicable. Another study (Gram-Hanssen et al., 2016) finds out andsuggests certain recommendations for the improvement of food redistribution. A re-search (Persson, 2016) contrasts a food redistribution environment with and withouta food bank into the picture and evaluates the effects of a food bank on the environ-ment and the finance of the participants of the activity. Another research (Anselmo,2016) studies Re-Food ( ), a Portuguese food redistrib-utor, and finds out that logistic related issues stop it from fully eliminating food waste.It also notes that the firm brings together people from different stages of the redis-5ribution activity to adhere to a common cause that is the local elimination of foodwaste and hunger issues. There is research (Orgut, Ivy, Uzsoy, & Wilson, 2016) onmathematical models of the food circulation by food banks to analyze and optimizethe effective and equitable distribution of food, i.e., food distributed to each servicearea should be proportional to the demand of food in that service area.One study (Vlaholias, Thompson, Every, & Dawson, 2015) puts forward the con-cept of food redistribution and the principles that follow it, and analyse the foodredistribution activities on that basis. A Norwegian study (Capodistrias, 2015) takesthe solution of food waste generation to beyond human redistribution and consump-tion. It includes approaches like fodder for animal, biogas generation, and even com-post, stretching the utility of surplus beyond the human edible window. One study(Silvennoinen & Katajajuuri, 2015) carried out in Finland calculates the number ofcooked meals at up to 10,000 a year, and that of redistributed food bags as up to270,000 bags a year by one organization, from surplus donated or redistributed food.Another study (Neff, Kanter, & Vandevijvere, 2015) analyzes government policies withrespect to handling food waste generation and overall people welfare and categorizesthem into policies those help achieve a relationship between both the above goals andthose which help achieve one of them while degrading the situation for the other.Food rescue has been highlighted (Lindberg, Lawrence, Gold, & Friel, 2014) asan initiative in the emergency food sector internationally as an attempt to re-duce food waste and to improve supplies to providers and consumers. A study(Caraher, Cavicchi, Garrone, Melacini, & Perego, 2014) brings into light the stepsthrough which food producers recover and donate their surplus food for redistribu-tion to the food banks. It provides valuable insight on the visceral operations of foodorganizations that relate to their tax savings, waste management, and society rap-port. While accepting surplus food redistribution as a key solution to food wastereduction, another study (Garrone, Melacini, & Perego, 2014) takes one step aheadby also suggesting a model for surplus food generation and management. A study(Downing, Kennedy, & Fell, 2014) notes that although food banks are a successfulconcept in the food management process, the government does not track its usage.Research (Kim, 2014) exists on the food redistribution systems that existed in Chinaat around 200 BC. It notes the redistribution by the emperor to the commoners in needand noted a bias towards saving physically capable farmers rather than addressing tothe needs of the economically endangered ones. It also sheds light on an exceptionalmethod of redistribution used by the rulers to feed people of inferior status throughfeast leftovers. Another study (Giuseppe, Mario, & Cinzia, 2014) proposes a model tomaximize the economical benefits of food redistribution for the retail donor organiza-tions. The model suggests optimal time for withdrawing food items from shelves forredistribution and also donation quantities for human and livestock consumption suchthat retailer profit is maximized. To understand the surplus redistribution frameworks in operation, we need to an-alyze the models used by various food sharing communities. According to
FoodTank ( https://foodtank.com/ ) (Furbank, 2016), there are several such food shar-ing communities that are already in operation globally. Some of the leadingnames amongst them include
412 Food Rescue ( http://412foodrescue.org/ ; cour-tesy: Ariel Procaccia and group) operating in Pittsburgh, Pennsylvania, United6tates;
Copia ( ) operating in San Francisco, Califor-nia, United States; Community Food Rescue ( https://communityfoodrescue.org/ )operating in Montgomery County, Maryland, United States; Food Cowboy ( ) operating in Bethesda, Maryland, United Statesand FoodLoop ( ) operating in Cologne, Germany.In India, a developing country, some notable presences include Feeding India ( ), operating in Kolkata, West Bengal, and 16 othercities in other states; Robin Hood Army ( https://robinhoodarmy.com ), operatingin Kolkata, West Bengal, and 8 other cities in other states; Roti Bank by Dab-bawalas ( https://rotibankfoundation.org ), operating in Mumbai, Maharashtra; Mera Parivar ( ), operating in Gurugram, Haryana;and Shelter Don Bosco ( ), operating in Mumbai, Maha-rashtra.Although, some communities use ICT platforms to match donors and receivers (like Copia: ), most others use ICT in much simpler forms likeapps for volunteer organization or social media for receivers to connect with the donors.This lack of complexity of the usage of the ICT platform renders available a wide gapof possibilities that can be addressed to smoothen the surplus food redistributionprocess further. With a more complex use of ICT, the communities can go acrossborders, redistribute faster, communicate seamlessly, reach a wider audience, trackfood quality and movement, and exploit higher scalability, just to name a few. To sumup, these, and several other such, communities have already been using ICT-mediatedmethods successfully to move surplus food from parties, organizations, individuals etc.to people with food deficit. Although, when it comes to developing countries like India,as the facts point out, their presence in several of the smart cities, not including theupcoming smart ones, is very limited.
ICT, with time, is gaining popularity in bridging the gap between the surplus andthe deficit. It is also evident that ICT is playing an important role as a medi-ator in achieving the goal of a sustainable food future. As stated previously, astudy (Davies & Weymes, 2018) points out that food is wasted at various stepswhile it reaches the ultimate consumers. However, with the intervention of ICT,the majority of the surplus recovery happened at the retail stage.
Foodsharing ( https://foodsharing.de/ ) pitches food sharing as a charitable practice. However,modern food sharing is mostly fueled from social and economic standpoints, often me-diated by ICT. As mentioned, another research (Ganglbauer, Fitzpatrick, & Molzer,2012) conducted in the US, pointed out that maximum food wastage occurs in thehouseholds. The use of ICT can attack this problem by attempting behavioural modifi-cation through the culture of good, long term food handling practices. ICT is pointedout as valuable tool capable of engaging consumers in cultivating better practiceswhile consuming less of their time. Results of ICT application to the various stagesof food wastage, as mentioned before, are documented as well (Ciaghi & Villafiorita,2016, September). The popularity of ICT platforms - web, social media and handhelddevice apps - in redistributing surplus food with leading initiatives like Food Runners , Copia , RePlate and
Food Recovery Network that exploit the benefits of the technologyplatforms, as already stated (Weymes & Davies, 2019), reveals our gaping scope ofresearch. It was also observed that using technology for food redistribution attracted7etter quality surplus food and increased the scalability of the operation. It notedthat redistribution, without the use of ICT, enforced limits like communication gaps,distribution delays and physical distances, on the operation of communities. The useof ICT led to higher satisfaction in the redistribution process, greater recoverability offood, lesser landfills, faster movement of food, better scalability and an overall betterquality of the surplus.
3. Method
An app will be used as an ICT-based mediator for surplus food distribution. Onstartup, the app will have options for registration and login. Then it will allow Users(hereafter interchangeably referred to as
Agents ) to raise food requests as donors, re-ceivers or volunteers. The app will take other required information like location, sur-plus food types, their expiry dates (packaged food items), preparation times (cookedfood items), pickup, drop, donation, receipt related information, etc. as input as well.Just before the request submission, the agent will be able to set preferences for do-nation, pickup, or volunteering, as applicable. Under the hood, the app will be usingdouble-sided market based game-theoretic algorithms to map donors with receiversand volunteers, if available, taking into account their preferences and location settingsalong with the timing windows for which they have opted.
4. Notations and Problem Formulation
Our model has three main agents: • The d Donors , D = { D , D , .., D d } , • The r Receivers , R = { R , R , .., R r } , • The v Volunteers , V = { V , V , .., V v } .All agents mentioned here, and henceforth, are representatives of the agents’ fooddonation/requirement/transportation requests. One agent can have multiple requestsrepresented by different Request IDs at the same time as we will see later in thepaper. Here, nothing is assumed regarding the relation between the number of donors( d ), that of the receivers ( r ), and that of the volunteer requests ( v ). However, underthe current scenarios prevailing in developing countries like India, it is fair to assumethat d < r . Also, the number of volunteer requests ( v ) is expected to fluctuate wildlydepending on several real-time parameters. Each agent submits/allows, as applicable, the details presented in
Table 1. Information Gathered at the time of registration/app usage. Allthe three agents are abstracted into three classes and an object is instantiated foreach agent involved. All the above details of each agent are accessible via functionsdefined in the respective object classes. Details on each piece of information havebeen discussed later in this paper. This information collected from the agents areonly displayed to other agents involved in a match generated by the algorithm. This8 able 1.
Information Gathered
Donors Receivers Volunteers
Location Location RouteType of food to donate Type of food required Type of transport (motored or not)Amount of food to donate Amount of food required Payload capacityPackaging of the food items - Air-conditioning status of the transportPreparation/Expiry time for food - -Image of the food to be donated - -Pickup date and time range Requirement date and time range Availability date and time rangePreferred receivers, if any Preferred donors, if any Receivers, if any
Table 2.
Bifurcation of Food Requests
All Food RequestsPerishable Non-PerishableDonations Receipts Donations Receipts
The Perishable FoodDonors (
PFD ) The Perishable Food Re-ceivers (
PFR ) The Non-Perishable FoodDonors (
NPFD ) The Non-Perishable FoodReceivers (
NPFR ) means that donors can know the details of the receiver who will receive the donor’sdonation and the volunteer who will be doing the transportation. This goes all ways,that is, receivers also can view the donor and the volunteer details upon a matchproduced by the algorithm, as can the volunteers view the other two agents’ details. There will be a list P , maintained at the server-end, defining types of food as belongingto Perishable or Non-Perishable categories, with mixed food type donors/receiversdefaulted to the
Perishable category. Another list C , also maintained at the server-end, grows by adding to itself new agents who have active/unmatched requests (notjust logged into it). A list M , created by the mechanism itself, is to store and updatethe matching outcomes of the mechanism and display the same to the involved agents.Classified on the basis of the type of food field detail of the donors and the receivers, fourlists further bifurcate the matching task into those of perishable and non-perishablefood items. This is shown in Table 2. Bifurcation of Food Requests . All theselists are used by a centralized website/server to carry out the matching process basedon the agent details. It then displays the matched details to the agents involved in therespective matching.
We have d donation requests D = { D , D , .., D d } to donate surplus food, and r re-quirement requests R = { R , R , .., R r } to receive these donations. Also, v volunteerrequests V = { V , V , .., V v } are to mediate the transportation of these donations. Thechallenge here is to suggest a proper matching between these requests to make thisprocess execute with minimum manual intervention. The simplified process to achievethe same is shown in Figure 2. Process Flow .Certain assumptions and constraints have been imposed on the system to make itsimple. When tweaked, they change the environment of work for the model. Theseassumptions and constraints frequently take the face of a few thresholds or param-eters used throughout the algorithm and often represent manageable, minimum, or9 tartInput agent requestsCheck if both sides of the market existExists?Sort agents by event end timingsCheck for volunteer availability duringdonation timing of each donorAvailable?Assign available volunteer to donormaximizing surplus transport distanceCalculate eligible donor list of eachreceiver based on event timings Extract receiver preferenceorder for eligible donorsCalculate position of receiver in thepreference list of each eligible donorAssign the donor with the highestpreference for the receiverBreak ties in favour of:1. Earlier event time2. Earlier request timeCheck for clearance of oneside of the marketClear?
Iterations= 2 ? EndYesYes YesYesNoNo NoNoUpdate agent preferences to account for incompletepreference lists
Figure 2.
Process Flow maximum acceptable quantities for the system. These are defined as follows: • T o minutes is the minimum overlap time between a donor and a volunteer for thelater to be assigned to the former. This threshold provides the volunteer timeto reach the donor and can be set based on the traffic conditions of the city ofoperation. • T l % is the off routing threshold for the volunteers. In simpler terms, it is expectedthat volunteers can manage going off their route by T l % of their travel distanceto address the transportation requests of donors. It can be argued that themaximum total off-routing percentage (Γ%) for one meal transportation underthis setting will always be less than equal to 4 × T l % of the volunteer routedistance (proof included in Section 7). • T m grams is the threshold for a healthy meal size. This ensures proper nutritionof the meal consumer. • T a % of the donation weight is the threshold extra payload capacity of any vol-unteer’s transportation over and above the capacity of the donation weight tobe able to comfortably transport the donation with its packaging. This extra ca-pacity is to allow for a smooth transportation of the food items without causingdamage to them. • T nmP kilometers is the threshold distance that perishable food can travel withoutspoiling in a non-AC and non-motored transportation when no volunteer hasbeen assigned for the transportation. • T mP kilometers is the threshold distance that perishable food can travel withoutspoiling in a non-AC and motored transportation when no volunteer has been10 able 3. Variables Extracted for Processing
Donors Receivers Volunteers
Location Location RouteType of food to donate Type of food required Type of transport (motored or not)Amount of food to donate Amount of food required Payload capacity- - Air-conditioning status of the transportPickup date and time range Requirement date and time range Availability date and time rangePreferred receivers, if any Preferred donors, if any Receivers, if any Td Donation AvailabilityVolunteer AvailabilityTransportation Assignment WindowVolunteerAssigned
Time → VolunteerSearch Td Overlap Time ≥ To Figure 3.
Volunteer Assignment Chronology assigned for the transportation. • T NP kilometers is the threshold distance for non-perishable food to travel ina non-motored transportation in case no volunteer has been assigned for thetransportation. • T d minutes is the threshold time before the donation start and end timings duringwhich the donation request is considered available for matching and transporta-tion assignment. This threshold is to account for real-time delays in the matchingprocess and the volunteer arrival at the donor locations. • T r minutes is the threshold time before the requirement start and end timingsduring which the requirement is considered available for donation search process.This threshold is to account for real-time delays in the matching process, thefood donations from the donors, and transportation of the same by the volunteersto the receiver locations. • T w minutes is the threshold beyond which a displayed match will be automat-ically cancelled when kept unaccepted by any of the involved agents and allrequests involved in it will be considered for the next matching iteration.All requests are raised by the agents ( D ∪ R ∪ V ) in the mobile app and are first queuedinto a list C for processing. The variables (agent details) extracted for the matchingprocess are mentioned in Table 3. Variables Extracted for Processing . To facil-itate the matching of perishable food requests before the non-perishable ones, all foodrequests are classified as already in
Table 2. Bifurcation of Food Requests .Matching of food items are done internal to these groups. An additional volunteergroup, which is involved in the transportation of both perishable and non-perishablefood items, is also present to classify the volunteer requests. Volunteer assignmentfor each donation request is done T d minutes before donation availability and withdonor-volunteer pairs having at least T o minutes of availability overlap to accountfor real-time delays as shown in Figure 3. Volunteer Assignment Chronology .Similarly, receivers are considered for matching T r minutes before their requirementstart time.Let us now follow a donation request from a donor to a receiver via a volunteer. Say,11 llReceivers T l VolunteerRoute Start VolunteerRoute EndDonorVicinity EligibleReceivers T l T l T l VolunteerRouteDonorNeighbourhood
Figure 4.
Receiver Eligibility Through Priority Modification the i th donor wants to donate some food from the j th location, and is offering foodof the k th type. The ICT-based platform splits this request into several requests ofmeal size T m . Let us, for the time being, track the movement of this donor’s l th meal.Therefore, we are now effectively tracking the l th meal, of the k th food type, donatedby the i th donor, from the j th location. Let this donation request be our virtual donor D ijkl . We are now in search of a volunteer for this donation. So, we now shortlist allvolunteers in this location who have a minimum T o minutes of availability overlap withthis virtual donor. We narrow down this list further by selecting only those volunteerswho have D ijkl in a radius of T l % of their travel distance, from their start location. Thisis shown in Figure 4. Receiver Eligibility Through Priority Modification . Wechoose the volunteer V m who maximizes the distance to which this donation D ijkl canbe transported subject to certain restrictions. This distance V icinity , that determinesthe donor neighbourhood, is lower bound by T P for perishable food, and T NP for non-perishable ones. Volunteers are only considered if the payload capacity of the volunteeris T a % more than the donation weight of D ijkl . The AC status of the transportationand whether the vehicle is motored or not are also factors in choosing the volunteer.This determines how far the surplus can be sent for consumption before it spoils. Incase we did not have any volunteer to assign to this donor, we would still proceed toreceiver assignment process bypassing the volunteer assignment step. However, in thatcase, the V icinity would be scaled down to its lower bound ( T nmP /T mP /T NP ) for thetype of food being donated and whether the transport is motored or not, to make thetransportation feasible for the agents. If the agents can predict volunteer unavailabilityin advance, they can themselves submit a volunteering request, in parallel, to aid thetransportation themselves. This volunteering request then needs to have the receiveras its only entry in the volunteer’s receiver list.We now have our volunteer V m assigned to the virtual donor12 onation Availability Receiver: R Time → Receiver: R Figure 5.
End Time Based Sorting for Receivers
Time → D D D D D R R R R R Donors Sorted onDonation Start TimeReceivers Sorted onRequirement End Time
Eligibility: R : D , D R : D , D , D R : D , D , D , D R : D , D , D , D , D R : D , D , D , D , D Figure 6.
Donor Eligibility per Receiver D ijkl and ready for receiver assignment. Let us now observe Figure 5. End Time Based Sorting for Receivers , wherein one donor wantsto donate two meals and two receivers want to receive one meal each. We assumevolunteer availability for this donation. The two receivers have timing such thatthe donation is available before their requirement start times. However, the receiverwith a later requirement start time ( R ) has a very short availability. We can nowaddress requirement requests starting with the earliest requirement start time or theearliest requirement end time. Assuming that we start with the earliest requirement start time, by the time the volunteer delivers a meal to R who has the earlierrequirement start time, R ’s requirement might end. Instead, if we start addressingthe requirement requests starting with the earliest requirement end time, we cancater to the request of R first, followed by R who has a longer request availabilitytime, thereby attending to both the receivers. Thus, we opt for addressing therequirements in an earliest end time first fashion. Receivers can only receive food thathas already been donated, that is, the donation end time of a donor has to be beforethe requirement end time of a receiver. Figure 6. Donor Eligibility per Receiver clearly depicts the same and also states the donors eligible for each receiver. Thepriority order of the eligible donors is extracted from the receiver’s preference list.For donors not in the receiver’s priority list, they are assigned the minimum priorityeach as in
Table 4. Priority Extraction and Augmentation for receiver R n .Let us now get back to our virtual donor D ijkl to whom volunteer V m was as-signed and was ready for receiver assignment. We now start the process from thereceivers’ end and reach this donor of ours as a match. Let, for our tracking pur- Table 4.
Priority Extraction and Augmentation
Eligibility List Original Preference Extraction & Augmentation R n : D p , D q , D r , D s R n : D q ≻ D t ≻ D p R n : D q ≻ D p [ ≻ D r = D s ] able 5. Donor to Receiver Assignment
Donor Preferences D p : R ≻ R ≻ R ≻ R ≻ R n ≻ .. D q : R ≻ R n ≻ R ≻ R ≻ R ≻ .. D r : R ≻ R n ≻ R ≻ R ≻ R ≻ .. D s : R ≻ R ≻ R ≻ R n ≻ R ≻ .. Updated Preferences Preference Positions Best Match R n : D q ≻ D p [ ≻ D r = D s ] R n : D p . , D q . , D r . , D s . R n ⇐⇒ D q AllReceivers
VolunteerRoute Start VolunteerRoute EndDonor AssignedReceiver OriginalRouteUpdatedRouteEligibleReceivers
Figure 7.
Food Movement Through Volunteer poses, our donor D ijkl be matched to the receiver R n , in the future. Then R n surelyhas D ijkl in its extracted and augmented preference list. But to be matched toeach other, D ijkl also needs to have the highest preference for R n , compared toall other eligible donors for this receiver, in its extracted and augmented prefer-ence list prepared. This list is prepared, similar to what was done for the receiverpreference ( Table 4. Priority Extraction and Augmentation ), from the donor’ssubmitted preference list and the receivers in the donor’s neighbourhood determinedby the calculated
V icinity . The assignment process is shown with an example in
Table 5. Donor to Receiver Assignment for the receiver R n . In case of ties inpreferences as introduced by the augmentation of priorities, the agent with the earliestrequest submit time is favoured. In addition to that, for the facilitation of the trans-portation, R n also needs to be in a location that is at a maximum perpendicular dis-tance of T l % of the assigned volunteer V m ’s route distance, from the route itself. Thisis as shown in Figure 4. Receiver Eligibility Through Priority Modification .Post matching, food transportation from the donor D ijkl to the receiver R n via the vol-unteer V m is as shown in Figure 7. Food Movement Through Volunteer . How-ever, if any of the agents involved in a match reject the same, or do not accept itwithin T w minutes of the match generation, the match is cancelled and all agent re-quests involved are rescheduled for matching.14 . The Model Operations To understand how the model operates, we will warm-up with the simplestpossible view of it and then gradually up-shift gears towards more com-plex views of the same. An overview of the model is already presented in
Figure 1. Overview of the Model . Before we get into the analysis of complex scenarios, let us first handle the registrationand the login processes. As an agent registers with the agent’s personal details, contactinformation, email information, and a password, a specific Agent ID gets generatedwhich is essentially a sequence number, and is to be used for logging into the app.
Let us now log into the app and take a tour of the same via the different possibleroutes that an agent can take. While, for volunteer activity, a start and an end loca-tion for route determination is prompted, for donors and receivers only one location isaccepted on app login. Locations can either be provided using the GPS or manually.Hereafter, different agents are directed through markedly different routes while usingthe app, although the location acceptance step had already started to differentiatebetween the volunteers and the other agents. Volunteers will be prompted for thetype of transport, whether motored or not, the air-conditioning status of this trans-port, and the payload capacity that can be transported by them. These three detailsare later used to calculate the maximum distance to which food can be transportedwithout spoiling it, especially for perishable food. Availability date and time range isalso requested which defaults to the current date and time, if left missing. At last, anoptional prompt for choosing receivers to deliver the food is provided. This is helpfulfor those donor-receiver matching pairs who do not receive any volunteer due to avail-ability issues. If this choice is taken by the volunteers, and this receivers’ list is notempty then these volunteers only receive those transportation requests that involvethe receivers in this volunteer’s receivers’ list. Otherwise, when this list is empty, allreceivers are considered for this volunteer.Next, we follow the receivers’ route through the app. Post entering the locationas described above, a receiver needs to select the type of food that is required, interms of freshly cooked , frozen uncooked , frozen cooked , packaged solid , packaged liquid , fresh produce , fruits and vegetables , etc. This is later on used for classification intoperishable and non-perishable food requirements. The amount of food required is alsofed in along with the requirement start and end date and time. For all calculations,the requirement start and end date and time are considered as the event start and enddate and time . At last, an optional prompt for choosing preferred donors is provided.When this list is empty, all donors are considered with equal priority. Otherwise, thislist, along with the donors left out from this list with lowest priority assigned to themare considered at the time of generating a match.Lastly, we have the donors. They, similar to the receivers, need to select the typeof food that they want to donate along with the weight of the food to be donated.For this, the same list as that for the receivers is prompted to the donors. This is alsoused for classifying the donation as that of perishable or non-perishable food. However,15onors get additional prompts to mention about the packaging of the food item andto upload an image of the food to be donated. The former relates to the container tocarry cooked food items and is an essential factor in retaining high recoverability ofthe same, and the latter is meant for being a visual clue of the current condition ofthe surplus. Recoverability also depends on the preparation date and time, for cookedfood items, or the expiry date, for uncooked ones, and these are the next details thatthe donors need to provide.The time elapsed from the preparation date and time to the pickup time of the food,food cooked items, or the time that remains between the pickup date and the expirydate is a major determining factor for safe recovery and reuse of the surplus. Thus,the donors need to provide a date and time range for the pickup. For all calculations,the donation/pickup start and end date and time are considered as the event startand end date and time . Similar to the receivers, the donors also receive an optionalprompt for choosing their preferred receivers. This list of preferred receivers, if empty,defaults to the neighbourhood of the respective donors. Otherwise, it is consideredafter amalgamation with the donor’s neighbourhood.Now, for donors, the app chops up the donation amount in meal chunks of a thresh-old of T m grams and creates separate requests for the same donor by adding a sequencenumber to the donor identifier, the arrival date and time, and the request date andtime of the donor. This accounts for the difference in the requested amounts and thedonated amounts. However, all this processing is abstracted from all the agents unlessthe involved agents in different matching triplets of the different requests of the samedonor, are different. This is further reinforced by the app clubbing together differentmatching assignments into one, if the involved agents are the same. It is to be notedthat event start/end date and time for donors refer to the food donation start/enddate and time , and that for the receivers refer to the food requirement start/end dateand time . This is to mark the earliest availability of food for donation and the latestusability of the donated food at the extreme ends of the process. This information islater used to sort the donors and the receivers for matching so as to promote maximumsurplus food movement.All requests have a request identifier associated with it, and is formed by a requestsequence number, initiated to 1 at agent registration, appended to the agent identifierwhich is also a sequence number assigned to the agent at registration. This requestsequence number runs independently for each agent. After each matching iteration,the assignments made in each iteration of the FDRM-CA mechanism are displayed tothe involved agents via deferred notifications in their respective devices. To facilitatequick request submissions, the app will cache the last used agent data for each typeof request amongst donor, receiver, and volunteer requests, raised by the agent. Theseare later auto-filled in the input spaces when this agent chooses a similar path throughthe app. Of course, some fields are never auto-filled, like the image for surplus fooddonation. Let us start with the initial scenario where all the donors, the receivers and the vol-unteers are new to the app and submit no preferences. In this case, volunteers areassigned as per availability. Based on the type and air-conditioning status of the vol-unteer transport, the neighbourhood of each donor is computed in terms of receivers.Out of them, the receivers in the volunteer’s route and T l % of the route distance16round the route are then treated as the donor’s preference. Receiver preferences arenot computed, and all donors donating before the requirement start time are consid-ered with equal priority for the receivers having no donor preference. Then, the donorsare matched with the receivers as per the computed donor preferences. A slightly dif-ferent situation occurs when donors provide their preferences and receivers do not.The operation is identical to the previous one except that receivers in this prefer-ence list who are present in the neighbourhood, are prioritized over the ones who arenot present. If receivers also provide preferences, then chronologically available donorspresent in this priority list get preferred over those absent in the list. A more complicated situation arises when both donors and receivers, after using theapp for some time, provide preferences of their own. It then resembles the extendedmode of operation of the app. As before, volunteers are assigned as per availability,and based on the type and air-conditioning status of the volunteer transport, theneighbourhood for each donor, in terms of receivers, is calculated and then sorted byfood requirement end time. Out of them, the receivers in the volunteer’s route and T l %of the route distance around the route are treated as the donor’s preference. All donorsdonating before the requirement start time are considered for the receiver’s preferencelist. All such eligible donors absent in the receiver’s preference are appended to thesame with lowest preference. At last, the donors are matched with the receivers as perthe computed donor and receiver preferences.It is practical to assume that volunteer availability will fluctuate wildly with re-spect to the time of the day, the day of the week, the season, the weather, the ongoingoccasions, and such other parameters. Let us now analyse a case where a donor isnot assigned a volunteer due to unavailability. This situation is handled in a two foldway. Firstly, the V icinity of this donor is set in such a way that the transportationdistance becomes trivial. Secondly, if the receivers can predict, considering practicalsituations, that volunteers may be unavailable, they can enroll their own volunteersto do the transportation themselves. In this case, these volunteers provide only thisreceiver in their receivers’ list. When donors mapped to these volunteers are assignedreceivers, the volunteers’ receiver list is checked before the assignment is made. Thisalso holds true when the receivers are shown a mapping that has no volunteers as-signed to it, making the receivers take charge of transportation of the surplus. Es-sentially, both donors and receivers can be volunteers, simultaneously, as shown in
Figure 1. Overview of the Model . There will be scenarios where the amount thata donor wants to donate does not match with the amount that a receiver wants to re-ceive or with the amount that a volunteer can transport. All these probable scenarios,with donation amounts greater than a threshold of T m grams, are handled by choppingdown all donor requests into multiple requests, each with a meal size of T m grams. Incase food items are not divisible perfectly into a T m grams meal size (for packagedfood), the least number of units making the meal size over T m grams is acceptable asa meal. While doing this for each such donor, each meal is treated as a separate do-nation request and different sequence numbers are augmented at the end of the donoridentifier to generate different request numbers for each such chopped request. Thissame sequence number is also added to both the food donation/requirement time andthe arrival time of this donor request to uphold the tie breaking conditions.The handling of these donations with amount more than T m grams is handled at17he app’s client end where it is chopped down to create multiple requests from thesame donor using sequence numbers to distinguish them from each other. Similarly,when the agents (donor, receiver, and, if assigned, volunteer) are the same tripletfor multiple matched requests, with differences only in the sequence numbers usedto disambiguate the requests, they are clubbed and displayed as a single request tothe agents. Therefore, the granularity of the slicing and dicing of agent requests arekept abstracted from the agents as much as possible until the involved agents aredifferent for different matching requests. This abstraction is enforced both duringthe placement of requests by donors and during the display of the generated matchto the involved agents. Thus, each donor can have multiple volunteers and receiversassigned to the donor. Receivers, more often than not, will have multiple donors and/orvolunteers assigned to them. Note that receiver requests are not chopped into meals.Rather, these requests are treated as a single unit with an Amount property alongwith a
RemainingAmount method that returns the unfulfilled requirement amountwhen called via a
Receiver class object. A similar method,
RemainingPayload , of the
Volunteer class returns the payload capacity that remains unused for a volunteer. Notethat when multiple requests of the same donor are generated by the app as a resultof request slicing and dicing, they are listed one after the other, making a volunteer,chosen as the optimal transporter for the previous request from this donor and stillhaving unused payload capacity, be assigned to the same donor’s successive pickuprequests until the volunteer’s payload capacity is exhausted. This takes us to the nextcase where some, or all, of the agents involved in a mapping, reject the same. The appwill then automatically reject the complete matching and add the involved agents tothe global list of active agent requests, C , for matching in the upcoming rounds. Theaddition of these agents in the list ensures that the agent requests are made availableagain for proper processing in the next iteration of the mechanism.
6. Mechanism
The Food Donor to Receiver Matching with Chronological Acceptance (FDRM-CA)mechanism is proposed for matching donors to receivers, if possible, via volunteers.This section is to discuss the mechanism and its sub-processes in detail in a breadth-first travel of the main algorithm.
The FDRM-CA mechanism actuates itself via the following three steps. These stepsare repeated for a very large number of times to handle all incoming requests.(1) Constant and parallel check for unaddressed agent requests using the New UserInterrupt Routine (NUIR),(2) Classification and TriFurcation of Users (CTFU) into Perishable, Non-Perishable, and Volunteer categories, and(3) Chronological Acceptance, inspired by Roughgarden’s lecture on
Stable Matching and Gale & Shapley’s algorithm (Roughgarden, 2016; Gale & Shapley, 2013),using Double Tie Breaking (CA-DTB), for the donor-receiver matching.The detailed mechanism is as provided in
Algorithm 1: The FDRM-CA Mechanism .After initializing all the lists (line 1), a parallel process for queuing unaddressed18 lgorithm 1:
FDRM-CA() C , V , PFD , PFR , NPFD , NPFR ← φ // Initiate all lists do parallel // Execute in parallel NUIR( C ) // Add unaddressed requests to the list do parallel // Execute in parallel for i ← to n do // Handle all requests in n → iterations C , V , PFR , NPFR , PFD , NPFD ← CTFU( C , V , PFD , PFR , NPFD , NPFR ) // Classify requests M P , PFD , PFR , V ← CA-DTB(
PFD , PFR , V , F ood ← P ERISHABLE ) // Match perishable food // Display each match to involved agents foreach M j ∈ M P do M j → M j .M atchedAgents M NP , NPFD , NPFR , V ← CA-DTB(
NPFD , NPFR , V , F ood ← N ON P ERISHABLE ) // Match non-perishable food // Display each match to involved agents foreach M j ∈ M NP do M j → M j .M atchedAgents agent requests, the NUIR sub-process, starts (line 3). These lists are emptied ofelements that have completed all processing on themselves, in each iteration of themechanism, with the exception of agents who have not yet received a match. Toavoid clutter, this emptying has not been explicitly stated in the algorithm. While thequeuing of unattended agent requests continues for a very large number of iterations,it need not stop for the agents to be classified into Perishable, Non-Perishable andVolunteer groups (line 6), as it modifies a global list in parallel to the main mechanismprogram flow. The Perishable and Non-Perishable groups help prioritize the matchingof perishable food items over the non-perishable ones, while the Volunteer groupfacilitates the movement of the surplus food from the donors to the receivers. Thisis followed by matching donors with receivers, if possible, via volunteers (lines 7and 10), and then displaying each match to the involved agents (lines 9 and 12).The preferences of the donors and the receivers are taken into consideration whilegenerating the matching. As already mentioned, the donors who wish to donateperishable food and receivers who wish to receive perishables, are the first ones to bematched.It is worth mentioning that not all donors/receivers may get a match in their veryfirst matching iteration through the mechanism. Some may be left over for the nextiteration of this process destined for better matches as per their own preferences. Asthis process completes, the matches that were generated, are displayed to the involvedagents (lines 9 and 12). Note that, to promote maximum recoverability of perishablefood items, the generated matches for perishable food items ( M P ) is displayed (line 9)even before the matching for non-perishable food items can start (line 12). These matchdisplays are non-blocking, that is, they do not stop the execution of the FDRM-CAmechanism to wait for the matched agents to accept the match. The classification andmatching processes are repeated for a very large number of iterations. Each repetitioninvolves new sets of donation, receipt, and volunteering requests or such unmatchedrequests from previous iterations. Note that these are not new sets of agents, since thesame agents can have multiple requests on the same/different day(s). Instead, theseare new sets of requests. Also, old and unmatched requests, as well as requests whose19atches have been rejected by the involved agents, are forced to be processed again.The generated matches are displayed in a non-blocking way via device notifications. The detailed NUIR mechanism is as given in
Algorithm 2: The NUIR Process .As n → (line 2), the algorithm captures all agent requests. This is a simple,interrupt driven mechanism to queue new agent requests for the subsequent itera-tion of classification and matching (lines 5 to 8), and re-queue old agent requestsfrom unaccepted/rejected matches (lines 10 to 12). At each agent request submission,an interrupt ( N ewU serRequestInterrupt ) is generated that triggers this routine toadd the agent request to the list of active agent requests after processing for requestsplitting for multiple meals as per the donation amount (lines 5 to 8). Also, at therejection of a matching by any of the involved agents or by partial (not by all agentsinvolved in a match) acceptance by T w minutes of match generation, another interrupt( M appingRejectionInterrupt ) is generated that triggers this routine to fetch all ofthe involved agents of this rejected mapping and add them to the same list (lines 10to 12) for being matched in the next iteration of the matching process. This processruns in parallel with the main process without halting it, and modifies a global list C of active agent requests (line 1) for consumption in the next iteration of FDRM-CA.Thus, while the matching process is ongoing in the main program body, this process,in parallel, works on readying the requests that will be processed by the next iterationof the matching process. Algorithm 2:
NUIR( C ) global C // Agent requests available to other parallel processes for i ← to n do // Handle all requests in n → iterations if Interrupt then // Check for interrupts from the app // New agent request if Interrupt = N ewU serRequestInterrupt then A ← Interrupt.GetRequest if A .RequestT ype = D .U serT ype ∪ A .Amount ≥ × T m then C .AddRequest ( A .SplitIntoM eals ( T m )) // Split intomeals // Unmatched agent requests if Interrupt = M appingRejectionInterrupt then foreach A ∈ Interrupt.GetRequest do C .AddRequest ( A ) // Add request to list The detailed mechanism is as follows. The CTFU process checks for perishable fooditem requests and classifies the agent request into perishable/non-perishable categoriesfor donors/receivers (lines 2 to 9). It also classifies agents as volunteers (line 10). Itupdates five lists - V , PFR , NPFR , PFD , and
NPFD - for consumption by the CA-DTB20ub-process that follows it. Do note that these lists may have unconsumed agents fromthe previous round of CA-DTB, before the current round of CTFU may start. At theend, the algorithm returns the list C and the updated lists to the main body of theprocess (line 11) for consumption by the subsequent iterations of CA-DTB. Algorithm 3:
CTFU( C , V , PFD , PFR , NPFD , NPFR ) foreach A ∈ C do // Classify all requests if A .U serT ype = RECEIV ER then // Receivers if A .T ypeOf F ood = P ERISHABLE then // Perishable food PFR .AddT oList ( A ) else NPFR .AddT oList ( A ) // Non-perishable food else if A .U serT ype = DON OR then // Donors if A .T ypeOf F ood = P ERISHABLE then // Perishable food PFD .AddT oList ( A ) else NPFD .AddT oList ( A ) // Non-perishable food else V .AddT oList ( A ) // Volunteers return C , V , PFR , NPFR , PFD , NPFD // Return all lists
Algorithm 4: The CA-DTB Process works on the current agent requests, donorswith donations to be available in T d minutes and receivers with requirements starting in T r minutes (lines 2 and 3). Next, it gets the volunteers available for each such donor D i on the basis of donor-volunteer availability overlap time of at least T o minutes (line 5),volunteer transport type, and transport payload availability and its air-conditioningstatus (lines 10 to 15). Then, it matches the volunteer who maximizes the surplustransportation distance (lines 16 and 20). Next, receiver preferences are updated byextracting from it all chronologically available donors, appending donors with theminimum preference each, when required (line 23). This is followed by updating donorpreferences by extracting and augmenting, as before, receivers from around the donorinside and on the circle with radius V icinity and around the assigned volunteer route(line 25). To determine the neighbourhood of each donor D i , on the basis of relevantreceivers, the radius of the neighbourhood is calculated on the basis of a rough estimateof the spoiling time of the food items and the available transportation details. Forperishable food items, this radius, the V icinity , gets defaulted to T nmP for non-motored,and to T mP for motored transports. For non-perishable food items this V icinity getsa default value of T NP . A volunteer de-route percentage threshold T l has also beenused that symbolizes the percentage of the actual route distance of the volunteerthat is a manageable diversion from the actual route of the volunteer for the surpluspickup. Post this, each receiver R i is assigned to the eligible donor who has the highestpreference for R i (lines 26 to 31).Ties are broken first with food donation start/requirement end timings, and nextwith request arrival timings. The last donation that is required to match the re-quirement, even if it overshoots the requirement amount slightly, is accepted anyway( P mj =1 D j .Amount − ǫ = R i .Amount, ǫ → donationstart/requirement end date and time . However, to avoid duplicates in the values of re-quest arrival date and time, precautions have been taken. Firstly, they are not actualtimestamps, but are sequence numbers generated by a sequencer maintained by theserver. Also, these sequences maintain a total order in the system and therefore cannothave duplicate values. This is essential in the functioning of the algorithm since this isthe supreme tie breaking condition that is checked for donors/receivers having equalpriorities for an agent and having the same donation start/requirement end date andtime . The generated match is stored in the list M in each iteration of the mechanismand is displayed to the involved agents.
7. Analysis
In this section we discuss the correctness , strategyproofness , Pareto-optimality , and (polynomial) running time properties of the FDRM-CA algorithm. We follow this upwith the simulation results and their analysis.
Lemma 7.1.1.
FDRM-CA works correctly.
Proof:
We prove this using the loop invariant technique(Cormen, Leiserson, Rivest, & Stein, 2009). We start our proof with the mainFDRM-CA algorithm and then we go into the detailing of the inner sub-processes.FDRM-CA consists of three sub-processes, namely, NUIR, CTFU and the CA-DTB.In this proof, along with the main mechanism of FDRM-CA, the sub-processes aretaken into account as well, so that, we can prove that as a whole, FDRM-CA workscorrectly. • The Main Routine of FDRM-CA.
For this algorithm we use the following loop invariant:At the start of the i th iteration of the for loop of lines 5-13, eachreceiver R j processed in the prior ( i −
1) iterations have their bestavailable donors allocated, respecting the eligible donors’ preferencelists.
Initialization:
Prior to the first iteration of the loop, i = 1. There are noreceivers processed and no matching exists. This trivially satisfies the invariant. Maintenance:
At any iteration i of the loop, each receiver R j processed isclassified into either perishable or non-perishable category. Thereafter, for eachdonor in the priority list of R j , the donor’s ranking of R j is retrieved. The donor D k with the highest ranking for R j is assigned to R j . Furthermore, incriminating i for the next iteration of the for loop maintains the invariant.Of course, the correctness of the above step depends on the correctness of theinner sub-parts which is what has been proven later in this section.22 lgorithm 4: CA-DTB( D , R , V , F ood ) M ← φ // Initialize the matching R ′ ← { R k | N ow () ∈ [ R k .RequirementStartDateT ime − T r , R k .RequirementEndDateT ime − T r ], R k ∈ R } // Current receivers D ′ ← { D k | N ow () ∈ [ D k .RequirementStartDateT ime − T d , D k .RequirementEndDateT ime − T d ], D k ∈ D } // Current donors foreach D i ∈ { D l | D l ∈ D ′ , N ow () ∈ [ D l .DonationStartDateT ime − T d , D l .DonationEndDateT ime − T d ] } do // Available volunteers V ′ ← { V j | V j ∈ V , V j .RemainingP ayload ≥ (1 + T a %) × D i .Amount , V j .Route.Start ± T l % × V j .Route.Distance ≥ D i .Location , T o ≤ V j .AvailabilityDateT imeRange ∩ D k .DonationDateT imeRange ,( V j .Receivers = φ ) ∪ ( D i ∈ V j .Receivers ) } if V ′ = φ then // Defaults for no available volunteer if F ood = P ERISHABLE then D i .V icinity ← T nmP else D i .V icinity ← T NP else // Volunteers available foreach V ′ j ∈ V ′ do // Optimize volunteer assignment if F ood = P ERISHABLE ∪ V ′ j .ACStatus = AC then V icinity ← V ′ j .Route.Destination − D i .Location else if V ′ j .T ransportT ype = M OT ORED then
V icinity ← T mP else V icinity ← T nmP if V icinity > D i .V icinity then // Upgrade volunteer D i .V icinity ← V icinity if D i / ∈ M then M .AddM atching ( D i , V ′ j ) else M .U pdateM atching ( M .GetM atching ( D i ), V ′ j ) V ← V − M .GetM atching ( D i ) // Remove volunteer from market foreach A ∈ R ′ ∪ D ′ do // Update agent preferences if A .RequestT ype = R .U serT ype then // Receivers A .P ref erence ← [ { A .P ref erence ∩ A .EligibleDonors ( D ′ ) } ∪{ A .EligibleDonors ( D ′ ) − A .P ref erence } ] else // Donors A .P ref erence ← [ A .P ref erence ∩ { ( A .Location ± A .V icinity ) ∩ R ′ .All.Location ∩ ( M .GetM atching ( A ) .V olunteer.Route ± T l × M .GetM atching ( A ) .V olunteer.Route.Distance ) } ] foreach R i ∈ { R k | R k .Amount > , R k ∈ R ′ } do // Match receivers while R i .RemainingAmount > do // Meals per requirement R i .P ref erence ← R i .P ref erence ∩ D D j ← R i .P ref erence.P ref erredDonor ( min ( R i .P ref erence.P riorityP osition ( R i ))) M .U pdateM atching ( M .GetM atching ( D j ), R i )) // Agents matched D − D j // Remove donor from market return M , D , R , V // Return all updated lists ermination: At termination, when i = n + 1, each receiver R j processedin the prior n iterations have their best available donors allocated, respectingthe eligible donors’ preference lists. This proves that the FDRM-CA algorithmworks correctly. To reinforce the maintenance step of this proof, following arethe additional proofs of correctness of the sub-processes of this algorithm. • The NUIR Sub-Process.
This can be proved along similar lines as the above. • The CTFU Sub-Process.
For this algorithm we use the following loop invariant:At the start of the i th iteration of the foreach loop of lines 1-13,the first ( i −
1) agent requests from C , processed in the prior ( i − V , PFD , NPFD , PFR , NPFR . Initialization:
Prior to the first iteration of the foreach loop, there are noagent requests processed, and this trivially satisfies the invariant.
Maintenance:
In the i th iteration, the i th agent request is taken upfor processing from the list C . If this agent request is a volunteer re-quest, it is appended to the list V . If not, it is classified and appendedto one of the four food request lists ( PFD , NPFD , PFR , NPFR ) as per
Table 2. Bifurcation of Food Requests . Observe that, prior to this itera-tion, all the five lists, namely, V , PFD , NPFD , PFR , NPFR , already had a total of( i −
1) agent requests from C classified and appended to them from the ( i − foreach loop picks up the next agent request from C forthe next iteration, the loop invariant is reestablished. Termination:
At termination, the list C is empty and all agent re-quests have been classified and appended to one of the five lists, namely, V , PFD , NPFD , PFR , NPFR . Thus, the invariant is maintained. This proves thatthe CTFU process works correctly. • The CA-DTB Sub-Process.
This can be proved along similar lines as the above.By having proven the correctness of all its sub-parts, this concludes our proof ofcorrectness of the FDRM-CA mechanism.
Lemma 7.1.2.
FDRM-CA is strategyproof for donors and receivers.
Proof:
While there can be many places in FDRM-CA for donors to misreport, how-ever, they can never gain from the same.Firstly, say a donor D i misreports the donor’s preference list as R k ≻ R j . Since theCA-DTB method awards the best available option from this preference list, therefore,misreporting only gets the donor D i an option R k which might not be the best availableas per the donor’s truthful preference list. The only way a donor D i can gain is if R k extracted and updated preference list of D i . However, thatis a run-time phenomenon not affected by the preference list of the donor, and hence,not affected by manipulation. The above line of logic can be extended to other inputdetails of the donors like location and type of food. Also, since an ICT based platformis used for tracking donations, it eliminates misreporting of factual data from thedonors’ end. Note that misreporting the amount of food donated by D i does not affectthe the order in which receivers are chosen for matching, it only changes the count ofreceivers assigned to the donor D i . Secondly, donors cannot influence the choice of theirneighbourhood as it depends on the run-time availability of volunteers ( V ) and thedetails of the transport used. Thirdly, ties are broken primarily in favour of the earliestfood donation or requirement timings which can be misreported. Consider a donor D i who misreported food pickup time to a time ( t a ) before the food is available for pickup( t b ; t a < t b ). Since, food pickup is a volunteer mediated activity and volunteers onlyhave a window of time available, therefore, the availability of a volunteer V j at amisreported time ( t a ) does not guarantee the donor the availability of any volunteerat the donor’s truthful pickup time ( t b ). Worst case scenario, no volunteers may beavailable at the truthful pickup time ( t b ). This concludes the proof.It can be proved, along similar lines, that FDRM-CA is strategyproof for receiversas well. Lemma 7.1.3.
FDRM-CA is Pareto-optimal for donors.
Proof:
This we prove by contradiction and mathematical induction. Let us assumethat FDRM-CA is not Pareto-optimal. Also, let there be some other algorithm, sayOTH, that assigns Pareto-optimally.The basis condition for induction is trivial for zero iterations. For the inductionstep, say until an iteration i , both algorithms generate a similar matching M i . In the( i + 1) th iteration, the CA-DTB sub-process of the FDRM-CA mechanism assigns thebest available option for donors as per their respective preference lists and updatesthe matching to M i +1 . If OTH assigns anything other than the above, then it doesnot generate a Pareto-optimal matching ( M i +1 ) at this iteration. Therefore, by thePrinciple of Mathematical Induction, the final matching generated by OTH will alsonot be optimal. This is a direct contradiction to our initial assumption. Thus, we cansay that our initial assumption was not correct and that FDRM-CA is Pareto-optimalfor donors. This concludes the proof. Lemma 7.1.4.
FDRM-CA produces results in real (polynomial) time.
Proof:
We only analyze the time complexity of a single iteration of the FDRM-CAmechanism since after each iteration agents get their assignments. Since food is onlyrecoverable inside a time window, we will focus our analysis from the donors’ point ofview. For this, we analyze the time complexity of each sub-process of the mechanism.Note that receivers with large requirements may get their complete matching (that isequal to their total requirement) after several iterations of the mechanism. • The NUIR sub-process is parallel to the main process and thus does not haveany impact on the time complexity as it does not need to finish for the mainprocess to execute, • The CTFU sub-process takes O( d + r + v ) < O( r ), • The CA-DTB sub-process can be viewed as having two sub-parts: ◦ The sub-part to get the neighbourhood of each donor and volunteer assign-ment to the donor takes O( dv ) < O( r ),25 The update of preference and match generation sub-part has a time com-plexity of O( d r ) < O( r ),since r > d for most practical situations, especially in developing countries likeIndia, at the time of writing this paper,where d , r , and v are the numbers of donors, receivers, and volunteers respectively,per iteration of the FDRM-CA mechanism. Therefore, the effective time complexityof each iteration of the FDRM-CA mechanism is capped at O( r ) which is polynomial(real) time. This concludes the proof. Lemma 7.1.5.
Using an off routing threshold T l % , the maximum total off-routingpercentage (Γ) for any volunteer for each meal transportation will always be less thanequal to four times this threshold percent of the route distance of the correspondingvolunteer, i.e., Γ ≤ × T l . Proof:
Analyzing a worst case scenario, let the donor D i ’s location be opposite to thevolunteer V j ’s route, and at a maximum possible distance of T l % of the volunteer’stravel distance. Therefore, the donation pickup will contribute to an extra travel dis-tance of 2 × T l % for the volunteer. At the drop-off end, let us again assume a worstcase scenario by allowing the receiver R k to be at a 180 ° off-route location yieldinganother 2 × T l % travel overhead for the volunteer V j . Thus, even in the worst casescenario, the volunteer V j has to do a maximum total off-routing percentage given bythe inequality Γ ≤ × T l . This concludes the proof. In this section we produce the simulation results of the algorithm and analyze them.
We generate random, logically coherent data for 5000 agent requests for the simulation.We have chosen to model our operational city to be 50 ×
50 kilometers across, ourworking hours to be from 06:00 hours to 23:59 hours, any volunteer’s maximum payloadcapacity to be 100 kilograms. We have taken our threshold values as: T o = 0 .
25 hour, T d = 2 hours, T r = 3 hours, T w = 0 .
25 hour, T l = 5%, T a = 20%, T m = 1 kilogram, T mP = 20 kilometers, T nmP = 5 kilometers, and T NP = 100 kilometers. The simulation results have been presented in
Figure 8. Simulation Results .In all the graphs, volunteer numbers have been expressedin terms of multiples of donation numbers ( × Donors ). From
Figure 8(a). Agent Allocation vs Volunteer Availability , it is evi-dent that the allocation percentage of agents initially increases rapidlywith increase of volunteer availability and then plateaus as the availabil-ity grows further.
Figure 8(b). Start vs End Sorting for Receivers sup-ports our initial claim that volunteers going for the receiver having theearliest requirement end time first will be able to address more requests.Similarly,
Figure 8(c). Original vs Eligible Preferences for Agents de-picts the importance of updating the submitted agent preferences toreflect run-time temporal and spatial availability of agents. At last,26 a) Allocation vs Volunteer Availability (b) Start vs End Sorting for Receivers(c) Original vs Eligible Preferences for Agents (d) Agent Preference Manipulation Results
Figure 8.
Simulation Results
Figure 8(d). Results of Manipulation of Agent Preferences establishesthat manipulation of preferences will not help agents to gain a better allo-cation other than when a small percentage of them do not have their falsehigher preferred donors unavailable while calculating their eligibility lists. In thefirst graph of
Figure 8(a). Agent Allocation vs Volunteer Availability ,actual spacing between volunteer values have been maintainedfor volunteer availability to reveal the true nature of the allo-cation curve.
Figure 8(b). Start vs End Sorting for Receivers uses agent preferences updated with their eligibility list, and
Figure 8(c). Original vs Eligible Preferences for Agents uses end sortingfor receivers.
Figure 8(d). Results of Manipulation of Agent Preferences hasboth end sorting and updated preferences running in the background.
8. Conclusion and Future Work
Food redistribution is visibly not a long term solution for food wastage, and it has tobe tackled at the roots by putting a check on the inclination of the society towardsa permanent over-supply of food, and a fear of ever running-out of food. However,until this society structure is fixed, ICT will continue to bridge the gap between theover-supplied and the under-provided. Although, 100% of the food waste cannot betargeted by this approach, the 60% avoidable waste will be well diverted from landfillsto the under-provided people. The FDRM-CA mechanism, delivered over handheld27evice apps, provides a great platform for doing this specifically. It prevents donorsfrom misreporting, addresses donor and receiver preferences properly, prioritizes fooddonation/requirement events chronologically, matches donors optimally with receiversand volunteers, and above all, does all these to provide agents with their respective as-signments in real time, making it an attractive choice for the task. As receivers broadenthe spectrum of their requirements from the more common freshly cooked or packagedsolid food types towards the statistically rarer fresh produce or frozen uncooked foodtypes, and as donors get diversified from households to farmers and businesspersonsgradually, this redistribution approach will be able to target the different stages of foodproduction wherein food gets wasted. With the use of the proposed mechanism, thepreferences of all the parties can be addressed better, leading to a higher satisfaction ofall the agents involved. This is guaranteed to attract more participation into the foodredistribution network, eventually lowering the food wastage and hunger challenges ofthe world for a sustainable and scalable food future. In the future, if some volunteers find incentives as their primary motivation to partici-pate in the system, the same can be integrated with the model for a hybrid functionalityso as to attract a broader volunteer participation leading to an overall better surplusmovement.
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