Hybrid resolution approaches for dynamic assignment problem of reusable containers

In this study, we are interested in the reusing activities of reverse logistics. We focus on the dynamic assignment of reusable containers problem (e.g. gas bottles, beverages, pallets, maritime containers, etc.). The objective is to minimize the collect, reloading, storage and redistribution operations costs over a fixed planning horizon taking into account the greenhouse gas emissions. We present a new generic Mixed Integer Programming (MIP) model for the problem. The proposed model was solved using the IBM ILOG CPLEX optimization software; this method yield exact solutions, but it is very time consuming. So we adapted two hybrid approaches using a genetic algorithm to solve the problem at a reduced time (The second hybrid approach is enhanced with a local search procedure based on the Variable Neighborhood Search VNS). The numerical results show that both developed hybrid approaches generate high-quality solutions in a moderate computational time, especially the second hybrid method

Émissions de carbone dans un modèle de production-stocks multi-echelon avec prise en compte des contraintes de délai

Colloque avec actes et comité de lecture. internationale.International audienceNous développons un modèle mathématique d'optimisation qui intègre les émissions de carbone dans un modèle gestion production-stock multi-échelon sous des contraintes de délai. Le modèle proposé capte l’impact de certaines décisions logistiques sur les émissions carbone. Nous nous intéressons principalement aux décisions suivantes : production des produits finis et intermédiaire, approvisionnement chez des fournisseurs internes et externes, positionnement des stocks des différents produits (fini et intermédiaires) aux différents niveaux de la chaîne logistique. Nous considérons deux types de réglementation environnementale: (1) taxe sur les émissions et (2) seuil infranchissable d'émissions carbone. Nous utilisons le modèle pour réaliser un ensemble d’expérimentations et fournir une série d’implications managériales

Improvement to an existing multi-level capacitated lot sizing problem considering setup carryover, backlogging, and emission control

This paper presents a multi-level, multi-item, multi-period capacitated lot-sizing problem. The lot-sizing problem studies can obtain production quantities, setup decisions and inventory levels in each period fulfilling the demand requirements with limited capacity resources, considering the Bill of Material (BOM) structure while simultaneously minimizing the production, inventory, and machine setup costs. The paper proposes an exact solution to Chowdhury et al. (2018)\u27s[1] developed model, which considers the backlogging cost, setup carryover & greenhouse gas emission control to its model complexity. The problem contemplates the Dantzig-Wolfe (D.W.) decomposition to decompose the multi-level capacitated problem into a single-item uncapacitated lot-sizing sub-problem. To avoid the infeasibilities of the weighted problem (WP), an artificial variable is introduced, and the Big-M method is employed in the D.W. decomposition to produce an always feasible master problem. In addition, Wagner & Whitin\u27s[2] forward recursion algorithm is also incorporated in the solution approach for both end and component items to provide the minimum cost production plan. Introducing artificial variables in the D.W. decomposition method is a novel approach to solving the MLCLSP model. A better performance was achieved regarding reduced computational time (reduced by 50%) and optimality gap (reduced by 97.3%) in comparison to Chowdhury et al. (2018)\u27s[1] developed model

The trade-off between costs and carbon emissions from economic lot-sizing decisions

Logistics decisions can have a significant impact on carbon emissions, a driver of global warming. We consider emissions reductions from better utilization of a given fleet of vehicles. We study an Economic Lot-Sizing setting in which a decision-maker determines the amount to be shipped in each period, and in which demand can fluctuate. Our paper assesses the trade-off between costs and carbon emissions. The emission parameters are based on a survey of results from empirical studies and on real-life considerations. In order to model the trade-off, we introduce a bi-objective lot-sizing model to find the Pareto optimal solutions with respect to costs and emissions. Our experiments show that it is often costly to reduce carbon emissions from the cost optimal solution, compared to carbon prices in the market. The cases in which carbon emissions can be reduced most cost-efficiently are those in which carbon emissions are large relative to costs, typically because costs are the results of past investments and can be considered sunk.</p

The trade-off between costs and carbon emissions from lot-sizing decisions

Logistics decisions can have a significant impact on carbon emissions, a driver of global warming. One possible way to reduce emissions is by adapting a lower delivery frequency, which enables better vehicle utilization or the usage of relatively effcient large vehicles. We study the situation in which a decision maker decides on the amount to be shipped in each period, where he/she can order items in each period and keep items on inventory. If the shipped quantity is large, vehicle capacity is well utilized, but many products have to be stored. Existing studies in this field of research, called lot-sizing, have introduced models for incorporating carbon emissions in the decision making, but do not focus on realistic values of the emission parameters. Therefore, we conduct a survey of empirical studies in order to establish the possible marginal emissions from holding inventory and performing a shipment with a truck.

Mathematical Modelling and a Meta-heuristic for Cross Border Supply Chain Network of Re-configurable Facilities

In supply chain management (SCM), Facility location-allocation problem (FLAP) comes under strategic planning and has been a well-established research area within Operations Research (OR). Owing to the billion dollar trade between USA-Canada the supply chain costs and difficulties are growing. Binary Integer Linear Programming (BILP) mathematical model is formulated to incorporate several parameters which would optimize the overall supply chain cost. Capacitated, single commodity, multiple time period (dynamic) and multi-facility location allocation problem is considered. Canada being a part of “The Kyoto protocol”, a part of the United Nations Framework Convention on Climate Change, has declared to abide by global effort to reduce GHG emissions. Developed math model will include an important constraint to optimize production keeping the Carbon di-oxide gas [��2] emission levels within specified limits. Simulated annealing based Meta-heuristic is developed to solve the problem to near optimality

Programming problems on time scales: Theory and computation

In this dissertation, novel formulations for several classes of programming problems are derived and proved using the time scales technique. The new formulations unify the discrete and continuous programming models and extend them to other cases in between. Moreover, the new formulations yield the exact optimal solution for the programming problems on arbitrary isolated time scales, which solve an important open problem. Throughout this dissertation, six distinct classes of programming problems are presented as follows. First, the primal as well as the dual time scales linear programming models on arbitrary time scales are formulated. Second, separated linear programming primal and dual models have been established using the time scales approach. Third, state-constraints separated linear programming primal and dual models on time scales are considered. Fourth, linear fractional primal and dual models have been constructed on time scales. Fifth, quadratic programming problems are formulated using the time scales technique. Sixth, quadratic fractional programming problems have been constructed using a hybrid of the parametric approach and the time scales technique. In addition, for each class of these programming problems the weak duality theorem and the optimality conditions theorem are established for arbitrary time scales, while the strong duality theorem is given for isolated time scales to ensure that our formulation is indeed a perfect formulation. Furthermore, examples for the most well-known isolated time scales are given to illustrate the main results --Abstract, page iv

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

OR in Spare Parts Management:A Review

Abstract Spare parts are held to reduce the consequences of equipment downtime, playing an important role in achieving the desired equipment availability at a minimum economic cost. In this paper, a framework for OR in spare parts management is presented, based on the product lifecycle process and including the objectives, main tasks, and OR disciplines for supporting spare parts management. Based on the framework, a systematic literature review of OR in spare parts management is undertaken, and then a comprehensive investigation of each OR discipline's contribution is given. The gap between theory and practice of spare parts management is investigated from the perspective of software integration, maintenance management information systems and adoption of new OR methods in software. Finally, as the result of this review, an extended version of the framework is proposed and a set of future research directions is discussed

Essays on Shipment Consolidation Scheduling and Decision Making in the Context of Flexible Demand

This dissertation contains three essays related to shipment consolidation scheduling and decision making in the presence of flexible demand. The first essay is presented in Section 1. This essay introduces a new mathematical model for shipment consolidation scheduling for a two-echelon supply chain. The problem addresses shipment coordination and consolidation decisions that are made by a manufacturer who provides inventory replenishments to multiple downstream distribution centers. Unlike previous studies, the consolidation activities in this problem are not restricted to specific policies such as aggregation of shipments at regular times or consolidating when a predetermined quantity has accumulated. Rather, we consider the construction of a detailed shipment consolidation schedule over a planning horizon. We develop a mixed-integer quadratic optimization model to identify the shipment consolidation schedule that minimizes total cost. A genetic algorithm is developed to handle large problem instances. The other two essays explore the concept of flexible demand. In Section 2, we introduce a new variant of the vehicle routing problem (VRP): the vehicle routing problem with flexible repeat visits (VRP-FRV). This problem considers a set of customers at certain locations with certain maximum inter-visit time requirements. However, they are flexible in their visit times. The VRP-FRV has several real-world applications. One scenario is that of caretakers who provide service to elderly people at home. Each caretaker is assigned a number of elderly people to visit one or more times per day. Elderly people differ in their requirements and the minimum frequency at which they need to be visited every day. The VRP-FRV can also be imagined as a police patrol routing problem where the customers are various locations in the city that require frequent observations. Such locations could include known high-crime areas, high-profile residences, and/or safe houses. We develop a math model to minimize the total number of vehicles needed to cover the customer demands and determine the optimal customer visit schedules and vehicle routes. A heuristic method is developed to handle large problem instances. In the third study, presented in Section 3, we consider a single-item cyclic coordinated order fulfillment problem with batch supplies and flexible demands. The system in this study consists of multiple suppliers who each deliver a single item to a central node from which multiple demanders are then replenished. Importantly, demand is flexible and is a control action that the decision maker applies to optimize the system. The objective is to minimize total system cost subject to several operational constraints. The decisions include the timing and sizes of batches delivered by the suppliers to the central node and the timing and amounts by which demanders are replenished. We develop an integer programing model, provide several theoretical insights related to the model, and solve the math model for different problem sizes