Modeling Industrial Lot Sizing Problems: A Review

In this paper we give an overview of recent developments in the field of modeling single-level dynamic lot sizing problems. The focus of this paper is on the modeling various industrial extensions and not on the solution approaches. The timeliness of such a review stems from the growing industry need to solve more realistic and comprehensive production planning problems. First, several different basic lot sizing problems are defined. Many extensions of these problems have been proposed and the research basically expands in two opposite directions. The first line of research focuses on modeling the operational aspects in more detail. The discussion is organized around five aspects: the set ups, the characteristics of the production process, the inventory, demand side and rolling horizon. The second direction is towards more tactical and strategic models in which the lot sizing problem is a core substructure, such as integrated production-distribution planning or supplier selection. Recent advances in both directions are discussed. Finally, we give some concluding remarks and point out interesting areas for future research

Valid inequalities for the single-item capacitated lot sizing problem with step-wise costs

This paper presents a new class of valid inequalities for the single-item capacitated lotsizing problem with step-wise production costs (LS-SW). We first provide a survey of different optimization methods proposed to solve LS-SW. Then, flow cover and flow cover inequalities derived from the single node flow set are described in order to generate the new class of valid inequalities. The single node flow set can be seen as a generalization of some valid relaxations of LS-SW. A new class of valid inequalities we call mixed flow cover, is derived from the integer flow cover inequalities by a lifting procedure. The lifting coefficients are sequence independent when the batch sizes (V) and the production capacities (P) are constant and if V divides P. When the restriction of the divisibility is removed, the lifting coefficients are shown to be sequence independent. We identify some cases where the mixed flow cover inequalities are facet defining. A cutting plane algorithmis proposed for these three classes of valid inequalities. The exact separation algorithmproposed for the constant capacitated case runs in polynomial time. Finally, some computational results are given to compare the performance of the different optimization methods including the new class of valid inequalities.single-item capacitated lot sizing problem, flow cover inequalities, cutting plane algorithm

The stochastic lot-sizing problem with quantity discounts

This paper addresses the stochastic lot-sizing problem with quantity discounts. In particular, we examine the uncapacitated finite-period economic lot-sizing problem in which the parameters in each period are random and discrete. When an order is placed, a fixed cost is incurred and an all-unit quantity discount is awarded based on the quantity ordered. The lead time is zero and the order is delivered immediately. First we study the case with overstocks by which the excess inventory incurs a holding cost. The objective in this case is to minimize the expected total cost including ordering and holding costs. The stochastic dynamics is modeled with a scenario tree. We characterize properties of the optimal policy and propose a polynomial time algorithm with complexity O ( n 3 ) for single discount level, where n is the number of nodes in the scenario tree. We extend the results to cases allowing stockout and multi-discount levels. Numerical experiments are conducted to evaluate the performance of the algorithm and to gain the man- agement insights

Optimality of (s, S) Inventory Policies under Renewal Demand and General Cost Structures

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/142450/1/poms12795_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/142450/2/poms12795.pd

A Heuristic Solution Technique to the Joint Replenishment Problem with Quantity Discounts and Full Truck Loads

In this project a stochastic multi-item inventory problem is considered. A wholesaler buys multiple products, with stochastic demand and similar holding and purchase costs, from a single supplier. The supplier offers an all-unit quantity discount whenever a full truckload is replenished. For the delivery of the products trucks with a finite capacity are available. The dispatched trucks arrive at the wholesaler after a constant leadtime and with each truck fixed shipping costs are charged independent on the number of units shipped. Since fixed transportation costs are high coordination of orders and full truckload shipments can benefit from economies of scale and quantity discounts. A new heuristic solution to this problem is proposed. The solution includes a direct grouping strategy and considers the optimal solution from both, the shipping trucks and products perspectives. In implementing the proposed solution an adjusted periodic review system is used. An excellent performance of the proposed solution can be observed when the fixed cost per order is high and the demand of the different products is similar. While the proposed solution presented in this project to the joint replenishment problem under consideration has been shown to be reliable, it nevertheless represents the first step towards the development of more efficient and versatile future solutions to the problem

A Conceptual Model for Integrating Transport Planning: MRP IV

In this article, a conceptual model, called MRP IV, is proposed in order to serve as a reference to develop a new production technology that integrates material planning decisions, production resource capacities and supply chain transport for the purpose of avoiding the suboptimization of these plans which, today, are usually generated sequentially and independently. This article aim is twofold: (1) it identifies the advances and deficiencies in the MRP calculations, mainly based on the dynamic multi-level capacitated lot-sizing problem (MLCLSP); and (2) it proposes a conceptual model, defining the inputs, outputs, modeling and solution approaches, to overcome the deficiencies identified in current MRP systems and act as a baseline to propose resolution models and algorithms required to develop MRP IV as a decision-making system. © 2012 IFIP International Federation for Information Processing. Mula, J.; Díaz-Madroñero Boluda, FM.; Peidro Payá, D. (2012). A conceptual model for integrating transport planning: MRP IV. En IFIP Advances in Information and Communication Technology. Springer. (384):54-65. doi:10.1007/978-3-642-33980-6_7 Senia 54 65 384 Document type: Part of book or chapter of boo

Evaluation of sales and operations planning in a process industry

Cette thèse porte sur la planification des ventes et des opérations (S±&OP) dans une chaîne d'approvisionnements axée sur la demande. L'objectif de la S±&OP, dans un tel contexte, est de tirer profit de l'alignement de la demande des clients avec la capacité de la chaîne d'approvisionnement par la coordination de la planification des ventes, de la production, de la distribution et de l'approvisionnement. Un tel processus de planification exige une collaboration multifonctionnelle profonde ainsi que l'intégration de la planification. Le but étant d'anticiper l'impact des décisions de vente sur les performances de la chaîne logistique , alors que l'influence de la dynamique des marchés est prise en compte pour les décisions concernant la production, la distribution et l'approvisionnement. La recherche a été menée dans un environnement logistique manufacturier multi-site et multi-produit, avec un approvisionnement et des ventes régis par des contrats ou le marché. Cette thèse examine deux approches de S±&OP et fournit un support à la décision pour l'implantation de ces méthodes dans une chaîne logistique multi-site de fabrication sur commande. Dans cette thèse, une planification traditionnelle des ventes et de la production basée sur la S±feOP et une planification S±fcOP plus avancée de la chaîne logistique sont tout d'abord caractérisées. Dans le système de chaîne logistique manufacturière multi-site, nous définissons la S±&OP traditionnelle comme un système dans lequel la planification des ventes et de la production est effectuée conjointement et centralement, tandis que la planification de la distribution et de l'approvisionnement est effectuée séparément et localement à chaque emplacement. D'autre part, la S±fcOP avancée de la chaîne logistique consiste en la planification des ventes, de la production, de la distribution et de l'approvisionnement d'une chaîne d'approvisionnement effectuée conjointement et centralement. Basés sur cette classification, des modèles de programmation en nombres entiers et des modèles de simulation sur un horizon roulant sont développés, représentant, respectivement, les approches de S±&OP traditionnelle et avancée, et également, une planification découplée traditionnelle, dans laquelle la planification des ventes est effectuée centralement et la planification de la production, la distribution et l'approvisionnement est effectuée séparément et localement par les unités d'affaires. La validation des modèles et l'évaluation pré-implantation sont effectuées à l'aide d'un cas industriel réel utilisant les données d'une compagnie de panneaux de lamelles orientées. Les résultats obtenus démontrent que les deux méthodes de S±feOP (traditionnelle et avancée) offrent une performance significativement supérieure à celle de la planification découplée, avec des bénéfices prévus supérieurs de 3,5% et 4,5%, respectivement. Les résultats sont très sensibles aux conditions de marché. Lorsque les prix du marché descendent ou que la demande augmente, de plus grands bénéfices peuvent être réalisés. Dans le cadre de cette recherche, les décisions de vente impliquent des ventes régies par des contrats et le marché. Les décisions de contrat non optimales affectent non seulement les revenus, mais également la performance manufacturière et logistique et les décisions de contrats d'approvisionnement en matière première. Le grand défi est de concevoir et d'offrir les bonnes politiques de contrat aux bons clients de sorte que la satisfaction des clients soit garantie et que l'attribution de la capacité de la compagnie soit optimisée. Également, il faut choisir les bons contrats des bons fournisseurs, de sorte que les approvisionnements en matière première soient garantis et que les objectifs financiers de la compagnie soient atteints. Dans cette thèse, un modèle coordonné d'aide à la décision pour les contrats e développé afin de fournir une aide à l'intégration de la conception de contrats, de l'attribution de capacité et des décisions de contrats d'approvisionnement pour une chaîne logistique multi-site à trois niveaux. En utilisant la programmation stochastique à deux étapes avec recours, les incertitudes liées à l'environnement et au système sont anticipées et des décisions robustes peuvent être obtenues. Les résultats informatiques montrent que l'approche de modélisation proposée fournit des solutions de contrats plus réalistes et plus robustes, avec une performance prévue supérieure d'environ 12% aux solutions fournies par un modèle déterministe

A Heuristic Solution Technique to the Joint Replenishment Problem with Quantity Discounts and Full Truck Loads

In this project a stochastic multi-item inventory problem is considered. A wholesaler buys multiple products, with stochastic demand and similar holding and purchase costs, from a single supplier. The supplier offers an all-unit quantity discount whenever a full truckload is replenished. For the delivery of the products trucks with a finite capacity are available. The dispatched trucks arrive at the wholesaler after a constant leadtime and with each truck fixed shipping costs are charged independent on the number of units shipped. Since fixed transportation costs are high coordination of orders and full truckload shipments can benefit from economies of scale and quantity discounts. A new heuristic solution to this problem is proposed. The solution includes a direct grouping strategy and considers the optimal solution from both, the shipping trucks and products perspectives. In implementing the proposed solution an adjusted periodic review system is used. An excellent performance of the proposed solution can be observed when the fixed cost per order is high and the demand of the different products is similar. While the proposed solution presented in this project to the joint replenishment problem under consideration has been shown to be reliable, it nevertheless represents the first step towards the development of more efficient and versatile future solutions to the problem

Carbon emissions Inventory Games

Carbon emissions reduction has been the center of attention in many organizations during the past few decades. Many international entities developed rules and regulations to monitor and control carbon emissions especially under supply chain context. Furthermore, researchers investigated techniques and methods on how reduce carbon emissions under operational adjustment which can be done by cooperation or coordination. The main contribution of this thesis is to measure to what extend cooperation can contribute to carbon emissions. Many research addresses the advantage of cooperation in reducing cost. However, there isn't a plenty of research addressing the effect of cooperation on carbon emissions when the incentive of the cooperation is to reduce cost only. The aim of this thesis is to show if joint replenishment leads to a reduction in carbon emissions and this to be considered as an advantage to be added to cooperation. Moreover, if a savings occur from cooperation, the aim will be to address the issue of allocating the savings among parties engaged in the coalition. The thesis methodology adapted and extended cooperative EOQ model and basic inventory model (EOQ) in order to formulate and build an adjusted model to measure carbon emissions. The adjusted model will be used to calculate carbon emission in centralized and decentralized systems with incentives to reduce cost and no incentives to reduce emission. The calculation shall yield the optimum ordering quantity which in turn yields the savings between the two systems. Finally core allocation principles will be leveraged to propose a fair allocation of savings. Furthermore, the model will be extended to consider some regulation and different environments to which it will cater for carbon-tax regulation and full Truckload system contexts. Findings indicate that applying inventory game theory leads to a reduction of carbon emissions along with cost. Additionally, the total carbon emissions in centralized system will always be less then decentralized system under all conditions. Moreover, the proposed proportional allocation which was proven to be a core allocation model will be based on the frequency of ordering and the amount of holding emissions