Ronald G. McGarvey

Constrained location of competitive facilities in the plane

This paper examines a competitive facility location problem occurring in the plane. A new gravity-based utility model is developed, in which the capacity of a facility serves as its measure of attractiveness. A new problem formulation is given, having elastic gravity-based demand, along with capacity, forbidden region, and budget constraints. Two solution algorithms are presented, one based on the big square small square method, and the second based on a penalty function formulation using fixed-point iteration. Computational testing is presented, comparing these two algorithms along with a general-purpose nonlinear solver.

Total flowtime and makespan for a no-wait m-machine flowshop with set-up times separated

This paper addresses the m-machine no-wait flowshop problem where the set-up time of a job is separated from its processing time. The performance measures considered are the total flowtime and makespan. The scheduling problem for makespan reduces to the travelling salesman problem (TSP), and the scheduling problem for total flowtime reduces to the time-dependent travelling salesman problem (TDTSP). Non-polynomial time solution methods are presented, along with a polynomial heuristic.

Food waste in campus dining operations: Inventory of pre- and post-consumer mass by food category, and estimation of embodied greenhouse gas emissions

There are many economic, social and environmental reasons to reduce the occurrence of food that is wasted. As communities consider options for managing their food waste streams, an understanding of the volume, composition and variability of these streams is needed to inform the decision-making process and potentially justify the capital investments needed for separation and treatment operations. This more detailed inventory also allows for the estimation of embodied resources in food that is wasted, demonstrated herein for greenhouse gas emissions (GHGs). Pre- and post-consumer food waste was collected from four all-you-care-to-eat Campus Dining Services (CDS) facilities at the University of Missouri, Columbia over 3 months in 2014. During the study period approximately 246.3 metric tons (t) of food reached the retail level at the four facilities. 232.4 t of this food was served and 13.9 t of it (10.1 t of edible and 3.8 t of inedible), was lost as pre-consumer waste. Over the same time period, an estimated 26.4 t of post-consumer food waste was generated at these facilities, 21.2 t of the waste edible and 5.3 t of it inedible. Overall, 5.6% of food reaching the retail level was lost at the pre-consumer stage and 10.7% was lost at the post-consumer stage. Out of the food categories examined, ‘fruits and vegetables’ constituted the largest source of food waste by weight, with grains as the second largest source of food waste by weight. GHGs embodied in edible food waste were calculated. Over the study period an estimated 11.1 t CO2e (100-yr) were embodied in the pre-consumer food waste and 56.1 t were embodied in post-consumer food waste for a total of 67.2 t. The ‘meat and protein’ category represents the largest embodiment of GHG emissions in both the pre- and post-consumer categories despite ranking fourth in total weight. Beef represents the largest contribution to post-consumer GHG emissions embodied in food waste with an estimated 34.1 t CO2e. This distinction between the greatest sources of food waste by weight and the greatest sources of GHG emissions is relevant when considering alternative management options for food waste.

Efficient frontiers in a frontier state: Viability of mobile dentistry services in rural areas

Abstract This study investigates the implications of adding mobile dentistry services to a community health center (CHC) in a rural area. CHCs are not-for-profit healthcare organizations which provide comprehensive primary care services to patients in the US, primarily for under-served and uninsured populations. We estimate the demand for the service in a five-county region in southwestern Montana, USA and work with stakeholders to determine a set of potential service locations. A mixed-integer optimization model is formulated to determine the frequency of stops in each location over a finite (six month) planning horizon with the goal of improving accessibility and availability of dental services while maintaining financial sustainability of the CHC. The financial considerations and social impact of offering a mobile dentistry service in southwestern Montana are assessed. Computational results based on a case study demonstrate the challenges facing mobile dentistry operations to increase access to under-served populations in a financially viable manner. Hybrid solutions, in which care is offered at a mix of fixed locations and mobile locations, appear to best balance the objectives of financial sustainability and expanded access to care.

On the frequency and location of set point adjustments in sequential tolerance control

Sequential tolerance control (STC) is an approach that uses real-time measurement information at the completion of a stage to exploit the available space inside a dynamic feasible zone and reposition the set points for the remaining operations. STC has been shown to produce significantly higher yields than conventional tolerance control given constant equipment precision. STC was developed under the premise that a measurement and set point adjustment would follow each operation. However, measuring after each operation may not be practical under certain conditions. This study develops techniques for determining when measurements and set point adjustments should take place so that the benefits of STC are realized without interrupting the process after every operation.

Planning Solid Waste Collection with Robust Optimization: Location-Allocation, Receptacle Type, and Service Frequency

Consider the problem faced by a purchaser of solid waste management services, who needs to identify waste collection points, the assignment of waste generation points to waste collection points, and the type and number of receptacles utilized at each collection point. Receptacles whose collection schedule is specified in advance are charged a fixed fee according to the number of times the receptacle is serviced (emptied) per week. For other receptacles, the purchaser pays a fee comprised of a fixed service charge, plus a variable cost that is assessed on a per-ton-removed basis. We develop a mathematical programming model to minimize the costs that the purchaser pays to the waste management provider, subject to a level of service that is sufficient to collect all of the purchaser’s required waste. Examining historical data from the University of Missouri, we observed significant variability in the amount of waste serviced for nonscheduled receptacles. Because this variability has a significant impact on cost, we modified our model using robust optimization techniques to address the observed uncertainty. Our model’s highly robust solution, while slightly more expensive than the nonrobust solution in the most-optimistic scenario, significantly outperforms the nonrobust solution for all other potential scenarios.

A unified framework for probabilistic sequential tolerance control

Sequential tolerance control (STC) is a methodology that uses available measurement information at the completion of one manufacturing operation to position the set point for subsequent operations. It has been shown that STC can lead to inferior solutions when the manufacturing process distributions are skewed. This paper presents an adaptive sphere-fitting method (ASF-STC) that adjusts for such skewness. ASF-STC requires as inputs both the direction of skewness and the probability distribution parameters for each operation. Heuristic methods for estimating each of these inputs are presented. Through computational testing, ASF-STC is shown to offer significant improvements over STC when such skewness exists.

Node-securing connectivity-based model to reduce infection spread in contaminated networks

Abstract Given a network with a set of contaminated and susceptible nodes, this article presents models for identifying a subset of susceptible nodes to secure (e.g., guard against infection, or remove from the network) such that the total number of nodes at risk of infection is minimized, subject to a limited budget for securing nodes. These models utilize a connectivity-based metric, in which a susceptible node is assumed to be at risk of infection if there exists a transmission path between it and any infected node, where no transmission path exists between two nodes if every path between them includes at least one secured node. The initial model presented, which is to the authors’ knowledge the first node-securing connectivity-based model for mitigating the spread of infection in contaminated networks, is then reformulated by use of a novel search space reduction algorithm. Computational testing is presented demonstrating the significant reductions in solution time achieved by the reformulated model.

Determining Reliable Networks of Prepositioning Materiel Warehouses for Public-Sector Rapid Response Supplies

Events such as natural disasters or combat operations require a rapid response capability from humanitarian service providers and military organizations. Such organizations can decrease their response times through the prepositioning of materiel in forward warehouses, reducing the time needed to transport items to the site of need. A particular challenge to the development of networks of prepositioning warehouses is that the warehouses themselves may be impacted by the very disruptions that drive demands for prepositioned materials. The objective of this research is to identify a reliable network posture, which is a set of utilized facility locations and an allocation of materiel to those locations, that can satisfy time-sensitive delivery requirements to potential locations around the globe, ensuring that demands can be satisfied even in the event of loss of access to a subset of storage sites (along with said sites’ materiel), all at minimum total cost. We develop new optimization formulations to account for differing levels of network reliability, all reflecting the time-sensitive environment faced by rapid response operations. We demonstrate an application of this methodology using rapid response material prepositioned by the US Air Force.

Determining the location and capacity of competitive facilities

This paper examines a competitive facility location problem in which the objective is to increase market capture subject to an expansion budget. This is accomplished by determining both the locations for a set of new facilities and the capacities of new and existing facilities. A gravity-based elastic-demand utility model is presented, in which the capacity of a facility serves as its measure of attractiveness. An examination of problem characteristics suggests that the model be divided into two subproblems. The first subproblem identifies locations for new facilities, and is solved using a penalty function formulation with fixed-point iteration. The second subproblem determines facility capacities and it is solved using a Successive Linear Programming algorithm. The interfacing of the two subproblem procedures into an iterative algorithm for solution of the overall problem is discussed. Computational testing shows the iterative algorithm to be superior to a general-purpose non-linear solver.