Dobrila Petrovic

Supply chain modelling using fuzzy sets

Abstract This paper considers a production supply chain (SC) with all facilities in a serial connection. The SC includes inventories and production facilities between them. It is assumed that the SC operates in an uncertain environment. Uncertainty is associated with: (1) customer demand, (2) supply deliveries along the SC and (3) external or market supply. Uncertainties are described by vague and imprecise phrases that are interpreted and represented by fuzzy sets. The SC fuzzy model described in this paper is developed to determine the order quantities for each inventory in the SC in the presence of uncertainties, that give an acceptable service level of the SC at reasonable total cost. Two control concepts of the SC are treated: (1) decentralised control of each inventory and (2) partial coordination in the inventories control. A special purpose simulator has been developed for examining the dynamics and performance of all the parts of the SC and the SC as a whole. Various simulation tests have been carried out to assess particularly the effects of uncertain external supply on the SC service level. Different approaches to improve SC performance in an uncertain environment have been simulated and analysed.

Modelling and simulation of a supply chain in an uncertain environment

This paper describes fuzzy modelling and simulation of a supply chain (SC) in an uncertain environment, as the first step in developing a decision support system. An SC is viewed as a series of facilities that performs the procurement of raw material, its transformation to intermediate and end-products, and distribution and selling of the end-products to customers. All the facilities in the SC are coupled and interrelated in a way that decisions made at one facility affect the performance of others. SC fuzzy models and a simulator cover operational SC control. The objective is to determine the stock levels and order quantities for each inventory in an SC during a finite time horizon to obtain an acceptable delivery performance at a reasonable total cost for the whole SC. Two sources of uncertainty inherent in the external environment in which the SC operates were identified and modelled: customer demand and external supply of raw material. They were interpreted and represented by fuzzy sets. In addition to the fuzzy SC models, a special SC simulator was developed. The SC simulator provides a dynamic view of the SC and assesses the impact of decisions recommended by the SC fuzzy models on SC performance.

Simulation of supply chain behaviour and performance in an uncertain environment

Abstract This paper describes a special purpose simulation tool, SCSIM, developed for analysing supply chain (SC) behaviour and performance in the presence of uncertainty. SCSIM treats a SC which includes a raw material inventory, a number of in-process inventories, an end-product inventory and production facilities between them, linked in a series. Main sources of uncertainty inherent in the serial SC and its environment are identified, including customer demand, external supply of raw material and lead times to the facilities. Uncertainties perceived in these SC data are described by imprecise natural language expressions and they are modelled in SCSIM by fuzzy sets. Two types of models are combined in SCSIM: (1) SC fuzzy analytical models to determine the optimal order-up-to levels for all inventories in a fuzzy environment and (2) a SC simulation model to evaluate SC performance achieved over time by applying the order-up-to levels recommended by the fuzzy models. SCSIM can be used for various SCs analyses to gain a better understanding of SC behaviour and performance in the presence of uncertainty and to enhance decision making on operational SC control parameters. The application of SCSIM in analysing and quantifying the effects of changing uncertainty in customer demand is discussed and illustrated by a numerical example.

EOQ formula when inventory cost is fuzzy

Abstract Various types of uncertainties and imprecision are inherent in real inventory problems. They are classically modeled using the approaches from the probability theory. However, there are uncertainties that cannot be appropriately treated by usual probabilistic models. The questions how to define inventory optimization tasks in such environment and how to interpret optimal solutions arise. This paper considers the modification of EOQ formula in the presence of imprecisely estimated parameters. For example, holding and ordering costs are often not precisely known and are usually expressed by linguistic terms such as: ”Holding cost is approximately of value c h ″, or: “Ordering cost is about value c o or more”. These imprecise parameters are presented by fuzzy numbers, defined on a bounded interval on the axis of real numbers. Alternative approaches to determining the optimal order quantity in a fuzzy environment are developed, illustrated by a selection of examples, and discussed.

Fuzzy models for the newsboy problem

Abstract This paper presents two fuzzy models for the newboy problem in an uncertain environment. It is assumed that uncertainties may appear in demand and in inventory costs. Fuzzy demand is used to describe a subjective estimate, linguistically expressed by the phrase “demand is about d ”. Also, fuzzy demand could be derived from evidences about demand recorded in the past. Imprecise inventory costs, such as overage and shortage costs, are represented by fuzzy sets, too. The quantity that should be ordered for a fixed time period minimizes the possible total cost. The computational aspects of the fuzzy models and their interpretations are illustrated by examples.

A fuzzy logic based-method for prognostic decision making in breast and prostate cancers

Accurate and reliable decision making in oncological prognosis can help in the planning of suitable surgery and therapy, and generally, improve patient management through the different stages of the disease. In recent years, several prognostic markers have been used as indicators of disease progression in oncology. However, the rapid increase in the discovery of novel prognostic markers resulting from the development in medical technology, has dictated the need for developing reliable methods for extracting clinically significant markers where complex and nonlinear interactions between these markers naturally exist. The aim of this paper is to investigate the fuzzy k-nearest neighbor (FK-NN) classifier as a fuzzy logic method that provides a certainty degree for prognostic decision and assessment of the markers, and to compare it with: 1) logistic regression as a statistical method and 2) multilayer feedforward backpropagation neural networks an artificial neural-network tool, the latter two techniques having been widely used for oncological prognosis. In order to achieve this aim, breast and prostate cancer data sets are considered as benchmarks for this analysis. The overall results obtained indicate that the FK-NN-based method yields the highest predictive accuracy, and that it has produced a more reliable prognostic marker model than both the statistical and artificial neural-network-based methods.

A FUZZY LOGIC BASED PRODUCTION SCHEDULING/RESCHEDULING IN THE PRESENCE OF UNCERTAIN DISRUPTIONS

Abstract In this paper, a new fuzzy logic based decision support system for parallel machine scheduling/rescheduling in the presence of uncertain disruptions is presented. It is applied to a real-life problem identified in a pottery company. The uncertain disruption considered is glaze shortage, defined by two parameters: number of glaze shortage occurrences and glaze shortage duration. Both parameters are specified imprecisely. They are modelled and combined using standard fuzzy sets and level 2 fuzzy sets, respectively. In order to deal with the glaze shortage disruption, a predictive–reactive scheduling approach is proposed and implemented. It is defined as a two-step procedure. In the first step, a predictive schedule is generated in such a way as to being capable of absorbing the impact of the glaze shortage disruption. In the second step, rescheduling is applied when the impact of the glaze shortage disruption is too high. Two sets of Sugeno type rules are proposed to support rescheduling decision making. One set of the fuzzy rules determines when to reschedule, whilst the other one determines which rescheduling method to use. Various tests are carried out that show that (1) the predictive schedules have good performance in the presence of uncertain disruptions and (2) the fuzzy inference generates appropriate rescheduling decisions.

A fuzzy goal programming method with imprecise goal hierarchy

Two most widely used approaches to treating goals of different importance in goal programming (GP) are: (1) weighted GP, where importance of goals is modelled using weights, and (2) preemptive priority GP, where a goal hierarchy is specified implying infinite trade-offs among goals placed in different levels of importance. These approaches may be too restrictive in modelling of real life decision making problems. In this paper, a novel fuzzy goal programming method is proposed, where the hierarchical levels of the goals are imprecisely defined. The imprecise importance relations among the goals are modelled using fuzzy relations. An additive achievement function is defined, which takes into consideration both achievement degrees of the goals and degrees of satisfaction of the fuzzy importance relations. Examples are given to illustrate the proposed method.

Optimisation of integrated reverse logistics networks with different product recovery routes

The awareness of importance of product recovery has grown swiftly in the past few decades. This paper focuses on a problem of inventory control and production planning optimisation of a generic type of an integrated Reverse Logistics (RL) network which consists of a traditional forward production route, two alternative recovery routes, including repair and remanufacturing and a disposal route. It is assumed that demand and return quantities are uncertain. A quality level is assigned to each of the returned products. Due to uncertainty in the return quantity, quantity of returned products of a certain quality level is uncertain too. The uncertainties are modelled using fuzzy trapezoidal numbers. Quality thresholds are used to segregate the returned products into repair, remanufacturing or disposal routes. A two phase fuzzy mixed integer optimisation algorithm is developed to provide a solution to the inventory control and production planning problem. In Phase 1, uncertainties in quantity of product returns and quality of returns are considered to calculate the quantities to be sent to different recovery routes. These outputs are inputs into Phase 2 which generates decisions on component procurement, production, repair and disassembly. Finally, numerical experiments and sensitivity analysis are carried out to better understand the effects of quality of returns and RL network parameters on the network performance. These parameters include quantity of returned products, unit repair costs, unit production cost, setup costs and unit disposal cost.

Coordinated control of distribution supply chains in the presence of fuzzy customer demand

This paper considers a single product inventory control in a Distribution Supply Chain (DSC). The DSC operates in the presence of uncertainty in customer demands. The demands are described by imprecise linguistic expressions that are modelled by discrete fuzzy sets. Inventories at each facility within the DSC are replenished by applying periodic review policies with optimal order up-to-quantities. Fuzzy customer demands imply fuzziness in inventory positions at the end of review intervals and in incurred relevant costs per unit time interval. The determination of the minimum of defuzzified total cost of the DSC is a complex problem which is solved by applying decomposition; the original problem is decomposed into a number of simpler independent optimisation subproblems, where each retailer and the warehouse determine their optimum periodic reviews and order up-to-quantities. An iterative coordination mechanism is proposed for changing the review periods and order up-to-quantities for each retailer and the warehouse in such a way that all parties within the DSC are satisfied with respect to total incurred costs per unit time interval. Coordination is performed by introducing fuzzy constraints on review periods and fuzzy tolerances on retailers and warehouse costs in local optimisation subproblems.