A heuristic approach for big bucket multi-level production planning problems

Multi-level production planning problems in which multiple items compete for the same resources frequently occur in practice, yet remain daunting in their difficulty to solve. In this paper, we propose a heuristic framework that can generate high quality feasible solutions quickly for various kinds of lot-sizing problems. In addition, unlike many other heuristics, it generates high quality lower bounds using strong formulations, and its simple scheme allows it to be easily implemented in the Xpress-Mosel modeling language. Extensive computational results from widely used test sets that include a variety of problems demonstrate the efficiency of the heuristic, particularly for challenging problems

Lot-Sizing Problem for a Multi-Item Multi-level Capacitated Batch Production System with Setup Carryover, Emission Control and Backlogging using a Dynamic Program and Decomposition Heuristic

Wagner and Whitin (1958) develop an algorithm to solve the dynamic Economic Lot-Sizing Problem (ELSP), which is widely applied in inventory control, production planning, and capacity planning. The original algorithm runs in O(T^2) time, where T is the number of periods of the problem instance. Afterward few linear-time algorithms have been developed to solve the Wagner-Whitin (WW) lot-sizing problem; examples include the ELSP and equivalent Single Machine Batch-Sizing Problem (SMBSP). This dissertation revisits the algorithms for ELSPs and SMBSPs under WW cost structure, presents a new efficient linear-time algorithm, and compares the developed algorithm against comparable ones in the literature. The developed algorithm employs both lists and stacks data structure, which is completely a different approach than the rest of the algorithms for ELSPs and SMBSPs. Analysis of the developed algorithm shows that it executes fewer number of basic actions throughout the algorithm and hence it improves the CPU time by a maximum of 51.40% for ELSPs and 29.03% for SMBSPs. It can be concluded that the new algorithm is faster than existing algorithms for both ELSPs and SMBSPs. Lot-sizing decisions are crucial because these decisions help the manufacturer determine the quantity and time to produce an item with a minimum cost. The efficiency and productivity of a system is completely dependent upon the right choice of lot-sizes. Therefore, developing and improving solution procedures for lot-sizing problems is key. This dissertation addresses the classical Multi-Level Capacitated Lot-Sizing Problem (MLCLSP) and an extension of the MLCLSP with a Setup Carryover, Backlogging and Emission control. An item Dantzig Wolfe (DW) decomposition technique with an embedded Column Generation (CG) procedure is used to solve the problem. The original problem is decomposed into a master problem and a number of subproblems, which are solved using dynamic programming approach. Since the subproblems are solved independently, the solution of the subproblems often becomes infeasible for the master problem. A multi-step iterative Capacity Allocation (CA) heuristic is used to tackle this infeasibility. A Linear Programming (LP) based improvement procedure is used to refine the solutions obtained from the heuristic method. A comparative study of the proposed heuristic for the first problem (MLCLSP) is conducted and the results demonstrate that the proposed heuristic provide less optimality gap in comparison with that obtained in the literature. The Setup Carryover Assignment Problem (SCAP), which consists of determining the setup carryover plan of multiple items for a given lot-size over a finite planning horizon is modelled as a problem of finding Maximum Weighted Independent Set (MWIS) in a chain of cliques. The SCAP is formulated using a clique constraint and it is proved that the incidence matrix of the SCAP has totally unimodular structure and the LP relaxation of the proposed SCAP formulation always provides integer optimum solution. Moreover, an alternative proof that the relaxed ILP guarantees integer solution is presented in this dissertation. Thus, the SCAP and the special case of the MWIS in a chain of cliques are solvable in polynomial time

An economic lot and delivery scheduling problem with the fuzzy shelf life in a flexible job shop with unrelated parallel machines

This paper considers an economic lot and delivery scheduling problem (ELDSP) in a fuzzy environment with the fuzzy shelf life for each product. This problem is formulated in a flexible job shop with unrelated parallel machines, when the planning horizon is finite and it determines lot sizing, scheduling and sequencing, simultaneously. The proposed model of this paper is based on the basic period (BP) approach. In this paper, a mixed-integer nonlinear programming (MINLP) model is presented and then it is changed into two models in the fuzzy shelf life. The main model is dependent to the multiple basic periods and it is difficult to solve the resulted proposed model for large-scale problems in reasonable amount of time; thus, an efficient heuristic method is proposed to solve the problem. The performance of the proposed model is demonstrated using some numerical examples

Cooperation in Supply Chain Networks: Motives, Outcomes, and Barriers

This paper analyzes the phenomenon of cooperation in modern supply chains in the light of Game Theory. We first provide a discussion on the meaning of cooperation in supply chains, its motives, outcomes and barriers. We then highlighted the applicability of Cooperative Game Theory as methodology for analyzing cooperation in supply chains. Second, we review recent studies that analyze the cooperation in supply chains by means of cooperative game theory. A special emphasis will be given inventory centralizations games. Finally, gaps in the literature are identified to clarify and to suggest future research opportunities

On the equivalence of strong formulations for capacitated multi-level lot sizing problems with setup times

Several mixed integer programming formulations have been proposed for modeling capacitated multi-level lot sizing problems with setup times. These formulations include the so-called facility location formulation, the shortest route formulation, and the inventory and lot sizing formulation with (l,S) inequalities. In this paper, we demonstrate the equivalence of these formulations when the integrality requirement is relaxed for any subset of binary setup decision variables. This equivalence has significant implications for decomposition-based methods since same optimal solution values are obtained no matter which formulation is used. In particular, we discuss the relax-and-fix method, a decomposition-based heuristic used for the efficient solution of hard lot sizing problems. Computational tests allow us to compare the effectiveness of different formulations using benchmark problems. The choice of formulation directly affects the required computational effort, and our results therefore provide guidelines on choosing an effective formulation during the development of heuristic-based solution procedures

Responsible Inventory Models for Operation and Logistics Management

The industrialization and the subsequent economic development occurred in the last century have led industrialized societies to pursue increasingly higher economic and financial goals, laying temporarily aside the safeguard of the environment and the defense of human health. However, over the last decade, modern societies have begun to reconsider the importance of social and environmental issues nearby the economic and financial goals. In the real industrial environment as well as in today research activities, new concepts have been introduced, such as sustainable development (SD), green supply chain and ergonomics of the workplace. The notion of “triple bottom line” (3BL) accounting has become increasingly important in industrial management over the last few years (Norman and MacDonald, 2004). The main idea behind the 3BL paradigm is that companies’ ultimate success should not be measured only by the traditional financial results, but also by their ethical and environmental performances. Social and environmental responsibility is essential because a healthy society cannot be achieved and maintained if the population is in poor health. The increasing interest in sustainable development spurs companies and researchers to treat operations management and logistics decisions as a whole by integrating economic, environmental, and social goals (Bouchery et al., 2012). Because of the wideness of the field under consideration, this Ph.D. thesis focuses on a restricted selection of topics, that is Inventory Management and in particular the Lot Sizing problem. The lot sizing problem is undoubtedly one of the most traditional operations management interests, so much so that the first research about lot sizing has been faced more than one century ago (Harris, 1913). The main objectives of this thesis are listed below: 1) The study and the detailed analysis of the existing literature concerning Inventory Management and Lot Sizing, supporting the management of production and logistics activities. In particular, this thesis aims to highlight the different factors and decision-making approaches behind the existing models in the literature. Moreover, it develops a conceptual framework identifying the associated sub-problems, the decision variables and the sources of sustainable achievement in the logistics decisions. The last part of the literature analysis outlines the requirements for future researches. 2) The development of new computational models supporting the Inventory Management and Sustainable Lot Sizing. As a result, an integrated methodological procedure has been developed by making a complete mathematical modeling of the Sustainable Lot Sizing problem. Such a method has been properly validated with data derived from real cases. 3) Understanding and applying the multi-objective optimization techniques, in order to analyze the economic, environmental and social impacts derived from choices concerning the supply, transport and management of incoming materials to a production system. 4) The analysis of the feasibility and convenience of governmental systems of incentives to promote the reduction of emissions owing to the procurement and storage of purchasing materials. A new method based on the multi-objective theory is presented by applying the models developed and by conducting a sensitivity analysis. This method is able to quantify the effectiveness of carbon reduction incentives on varying the input parameters of the problem. 5) Extending the method developed in the first part of the research for the “Single-buyer” case in a "multi-buyer" optics, by introducing the possibility of Horizontal Cooperation. A kind of cooperation among companies in different stages of the purchasing and transportation of raw materials and components on a global scale is the Haulage Sharing approach which is here taken into consideration in depth. This research was supported by a fruitful collaboration with Prof. Robert W. Grubbström (University of Linkoping, Sweden) and its aim has been from the beginning to make a breakthrough both in the theoretical basis concerning sustainable Lot Sizing, and in the subsequent practical application in today industrial contexts

Production lot sizing with rework and fixed quantity deliveries

This paper is concerned with determination of the optimal lot size for an economic production quantity (EPQ) model with the reworking of random defective items and fixed quantity multiple deliveries. Classic EPQ model assumes continuous issuing policy for satisfying product demand and perfect quality production for all items produced. However, in real life vendor-buyer integrated production-inventory system, multi-delivery policy is used practically in lieu of the continuous issuing policy and generation of defective items during production run is inevitable. In this study, all nonconforming items produced are considered to be repairable and are reworked in each cycle when regular production ends. The finished items can only be delivered to customers if the whole lot is quality assured at the end of the rework. Fixed quantity multiple installments of the finished batch are delivered to customers at a fixed interval of time. The long-run average integrated cost function per unit time is derived. A closed-form optimal batch size solution to the problem is obtained. A numerical example demonstrates its practical usage