A dynamic lot-sizing model with demand time windows

One of the basic assumptions of the classical dynamic lot-sizing model is that the aggregate demand of a given period must be satisfied in that period. Under this assumption, if backlogging is not allowed then the demand of a given period cannot be delivered earlier or later than the period. If backlogging is allowed, the demand of a given period cannot be delivered earlier than the period, but can be delivered later at the expense of a backordering cost. Like most mathematical models, the classical dynamic lot-sizing model is a simplified paraphrase of what might actually happen in real life. In most real life applications, the customer offers a grace period - we call it a demand time window - during which a particular demand can be satisfied with no penalty. That is, in association with each demand, the customer specifies an earliest and a latest delivery time. The time interval characterized by the earliest and latest delivery dates of a demand represents the corresponding time window. This paper studies the dynamic lot-sizing problem with demand time windows and provides polynomial time algorithms for computing its solution. If shortages are not allowed, the complexity of the proposed algorithm is of the order T square. When backlogging is allowed, the complexity of the proposed algorithm is of the order T cube.dynamic programming;lot-sizing;time windows

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

Single Item Supplier Selection and Order Allocation Problem with a Quantity Discount and Transportation Costs

In this paper, we address a single item supplier selection, economic lot-sizing, and order assignment problem under quantity discount environment and transportation costs. A mixed-integer nonlinear program (MINP) model is developed with minimization of cost as its objective, while lead-time, the capacity of the supplier and demand of the product are incorporated as constraints. The total cost considered includes annual inventory holding cost, ordering cost, transportation cost and purchase cost. An efficient and effective genetic algorithm (GA) with problem-specific operators is developed and used to solve the proposed MINP model.  The  model is illustrated through a numerical example and the results show that the GA can solve the model in less than a minute. Moreover, the results of the numerical illustration show that the item cost and transportation cost are the deciding factors in selecting suppliers and allocating orders. Keywords: Supplier selection, Economic Order Quantity, Order allocation, Mixed-integer nonlinear programming

An Integrated Model for Lot Sizing with Supplier Selection Considering Quantity Discounts, Expiry Dates, and Budget Availability

In this paper, a dynamic multi-product multi-period lot sizing with supplier selection problem (DLSSP) with quantity discount, expiry dates, and budget availability is presented. Demand of products for each period are independent and known. The cost consists of ordering, purchasing, transportation, expiry, holding, and interest charge. The objective is to find the optimal order quantity of all items in each period to minimize inventory cost. A mixed integer nonlinear model programming (MINLP) is first developed to model the problem. Since model is hard to solve using exact method, Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) is applied, in which design parameters are set using Taguchi method. Computational results demonstrate the applicability of the proposed model and comparing the results show efficiency of both algorithms as well. The results show that, while both algorithms have statistically similar performances, GA is the better algorithm in all problems

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

From Cost Sharing Mechanisms to Online Selection Problems

We consider a general class of online optimization problems, called online selection problems, where customers arrive sequentially, and one has to decide upon arrival whether to accept or reject each customer. If a customer is rejected, then a rejection cost is incurred. The accepted customers are served with minimum possible cost, either online or after all customers have arrived. The goal is to minimize the total production costs for the accepted customers plus the rejection costs for the rejected customers. These selection problems are related to online variants of offline prize collecting combinatorial optimization problems that have been widely studied in the computer science literature. In this paper, we provide a general framework to develop online algorithms for this class of selection problems. In essence, the algorithmic framework leverages any cost sharing mechanism with certain properties into a poly-logarithmic competitive online algorithm for the respective problem; the competitive ratios are shown to be near-optimal. We believe that the general and transparent connection we establish between cost sharing mechanisms and online algorithms could lead to additional online algorithms for problems beyond the ones studied in this paper.National Science Foundation (U.S.) (CAREER Award CMMI-0846554)United States. Air Force Office of Scientific Research (FA9550-11-1-0150)United States. Air Force Office of Scientific Research (FA9550-08-1-0369)Solomon Buchsbaum AT&T Research Fun

Optimization Models for Cost Efficient and Environmentally Friendly Supply Chain Management

This dissertation aims to provide models which will help companies make sustainable logistics management and transportation decisions. These models are extensions of the economic lot sizing model with the availability of multiple replenishment modes. The objective of the models is to minimize total replenishment costs and emissions. The study provides applications of these models on contemporary supply chain problems. Initially, the impact of carbon regulatory mechanisms on the replenishment decisions are analyzed for a biomass supply chain under fixed charge replenishment costs. Then, models are extended to consider multiple-setups replenishment costs for age dependent perishable products. For a cost minimization objective, solution algorithms are proposed to solve cases where one, two or multiple replenishment modes are available. Finally, using a bi-objective model, tradeoffs in costs and emissions are analyzed in a perishable product supply chain

Models and Algorithms for the Optimisation of Replenishment, Production and Distribution Plans in Industrial Enterprises

Tesis por compendio[ES] La optimización en las empresas manufactureras es especialmente importante, debido a las grandes inversiones que realizan, ya que a veces estas inversiones no obtienen el rendimiento esperado porque los márgenes de beneficio de los productos son muy ajustados. Por ello, las empresas tratan de maximizar el uso de los recursos productivos y financieros minimizando el tiempo perdido y, al mismo tiempo, mejorando los flujos de los procesos y satisfaciendo las necesidades del mercado. El proceso de planificación es una actividad crítica para las empresas. Esta tarea implica grandes retos debido a los cambios del mercado, las alteraciones en los procesos de producción dentro de la empresa y en la cadena de suministro, y los cambios en la legislación, entre otros. La planificación del aprovisionamiento, la producción y la distribución desempeña un papel fundamental en el rendimiento de las empresas manufactureras, ya que una planificación ineficaz de los proveedores, los procesos de producción y los sistemas de distribución contribuye a aumentar los costes de los productos, a alargar los plazos de entrega y a reducir los beneficios. La planificación eficaz es un proceso complejo que abarca una amplia gama de actividades para garantizar que los equipos, los materiales y los recursos humanos estén disponibles en el momento y el lugar adecuados. Motivados por la complejidad de la planificación en las empresas manufactureras, esta tesis estudia y desarrolla herramientas cuantitativas para ayudar a los planificadores en los procesos de la planificación del aprovisionamiento, producción y distribución. Desde esta perspectiva, se proponen modelos realistas y métodos eficientes para apoyar la toma de decisiones en las empresas industriales, principalmente en las pequeñas y medianas empresas (PYMES). Las aportaciones de esta tesis suponen un avance científico basado en una exhaustiva revisión bibliográfica sobre la planificación del aprovisionamiento, la producción y la distribución que ayuda a comprender los principales modelos y algoritmos utilizados para resolver estos planes, y pone en relieve las tendencias y las futuras direcciones de investigación. También proporciona un marco holístico para caracterizar los modelos y algoritmos centrándose en la planificación de la producción, la programación y la secuenciación. Esta tesis también propone una herramienta de apoyo a la decisión para seleccionar un algoritmo o método de solución para resolver problemas concretos de la planificación del aprovisionamiento, producción y distribución en función de su complejidad, lo que permite a los planificadores no duplicar esfuerzos de modelización o programación de técnicas de solución. Por último, se desarrollan nuevos modelos matemáticos y enfoques de solución de última generación, como los algoritmos matheurísticos, que combinan la programación matemática y las técnicas metaheurísticas. Los nuevos modelos y algoritmos comprenden mejoras en términos de rendimiento computacional, e incluyen características realistas de los problemas del mundo real a los que se enfrentan las empresas de fabricación. Los modelos matemáticos han sido validados con un caso de una importante empresa del sector de la automoción en España, lo que ha permitido evaluar la relevancia práctica de estos novedosos modelos utilizando instancias de gran tamaño, similares a las existentes en la empresa objeto de estudio. Además, los algoritmos matheurísticos han sido probados utilizando herramientas libres y de código abierto. Esto también contribuye a la práctica de la investigación operativa, y proporciona una visión de cómo desplegar estos métodos de solución y el tiempo de cálculo y rendimiento de la brecha que se puede obtener mediante el uso de software libre o de código abierto.[CA] L'optimització a les empreses manufactureres és especialment important, a causa de les grans inversions que realitzen, ja que de vegades aquestes inversions no obtenen el rendiment esperat perquè els marges de benefici dels productes són molt ajustats. Per això, les empreses intenten maximitzar l'ús dels recursos productius i financers minimitzant el temps perdut i, alhora, millorant els fluxos dels processos i satisfent les necessitats del mercat. El procés de planificació és una activitat crítica per a les empreses. Aquesta tasca implica grans reptes a causa dels canvis del mercat, les alteracions en els processos de producció dins de l'empresa i la cadena de subministrament, i els canvis en la legislació, entre altres. La planificació de l'aprovisionament, la producció i la distribució té un paper fonamental en el rendiment de les empreses manufactureres, ja que una planificació ineficaç dels proveïdors, els processos de producció i els sistemes de distribució contribueix a augmentar els costos dels productes, allargar els terminis de lliurament i reduir els beneficis. La planificació eficaç és un procés complex que abasta una àmplia gamma d'activitats per garantir que els equips, els materials i els recursos humans estiguen disponibles al moment i al lloc adequats. Motivats per la complexitat de la planificació a les empreses manufactureres, aquesta tesi estudia i desenvolupa eines quantitatives per ajudar als planificadors en els processos de la planificació de l'aprovisionament, producció i distribució. Des d'aquesta perspectiva, es proposen models realistes i mètodes eficients per donar suport a la presa de decisions a les empreses industrials, principalment a les petites i mitjanes empreses (PIMES). Les aportacions d'aquesta tesi suposen un avenç científic basat en una exhaustiva revisió bibliogràfica sobre la planificació de l'aprovisionament, la producció i la distribució que ajuda a comprendre els principals models i algorismes utilitzats per resoldre aquests plans, i posa de relleu les tendències i les futures direccions de recerca. També proporciona un marc holístic per caracteritzar els models i algorismes centrant-se en la planificació de la producció, la programació i la seqüenciació. Aquesta tesi també proposa una eina de suport a la decisió per seleccionar un algorisme o mètode de solució per resoldre problemes concrets de la planificació de l'aprovisionament, producció i distribució en funció de la seua complexitat, cosa que permet als planificadors no duplicar esforços de modelització o programació de tècniques de solució. Finalment, es desenvolupen nous models matemàtics i enfocaments de solució d'última generació, com ara els algoritmes matheurístics, que combinen la programació matemàtica i les tècniques metaheurístiques. Els nous models i algoritmes comprenen millores en termes de rendiment computacional, i inclouen característiques realistes dels problemes del món real a què s'enfronten les empreses de fabricació. Els models matemàtics han estat validats amb un cas d'una important empresa del sector de l'automoció a Espanya, cosa que ha permés avaluar la rellevància pràctica d'aquests nous models utilitzant instàncies grans, similars a les existents a l'empresa objecte d'estudi. A més, els algorismes matheurístics han estat provats utilitzant eines lliures i de codi obert. Això també contribueix a la pràctica de la investigació operativa, i proporciona una visió de com desplegar aquests mètodes de solució i el temps de càlcul i rendiment de la bretxa que es pot obtindre mitjançant l'ús de programari lliure o de codi obert.[EN] Optimisation in manufacturing companies is especially important, due to the large investments they make, as sometimes these investments do not obtain the expected return because the profit margins of products are very tight. Therefore, companies seek to maximise the use of productive and financial resources by minimising lost time and, at the same time, improving process flows while meeting market needs. The planning process is a critical activity for companies. This task involves great challenges due to market changes, alterations in production processes within the company and in the supply chain, and changes in legislation, among others. Planning of replenishment, production and distribution plays a critical role in the performance of manufacturing companies because ineffective planning of suppliers, production processes and distribution systems contributes to higher product costs, longer lead times and less profits. Effective planning is a complex process that encompasses a wide range of activities to ensure that equipment, materials and human resources are available in the right time and the right place. Motivated by the complexity of planning in manufacturing companies, this thesis studies and develops quantitative tools to help planners in the replenishment, production and delivery planning processes. From this perspective, realistic models and efficient methods are proposed to support decision making in industrial companies, mainly in small- and medium-sized enterprises (SMEs). The contributions of this thesis represent a scientific breakthrough based on a comprehensive literature review about replenishment, production and distribution planning that helps to understand the main models and algorithms used to solve these plans, and highlights trends and future research directions. It also provides a holistic framework to characterise models and algorithms by focusing on production planning, scheduling and sequencing. This thesis also proposes a decision support tool for selecting an algorithm or solution method to solve concrete replenishment, production and distribution planning problems according to their complexity, which allows planners to not duplicate efforts modelling or programming solution techniques. Finally, new state-of-the-art mathematical models and solution approaches are developed, such as matheuristic algorithms, which combine mathematical programming and metaheuristic techniques. The new models and algorithms comprise improvements in computational performance terms, and include realistic features of real-world problems faced by manufacturing companies. The mathematical models have been validated with a case of an important company in the automotive sector in Spain, which allowed to evaluate the practical relevance of these novel models using large instances, similarly to those existing in the company under study. In addition, the matheuristic algorithms have been tested using free and open-source tools. This also helps to contribute to the practice of operations research, and provides insight into how to deploy these solution methods and the computational time and gap performance that can be obtained by using free or open-source software.This work would not have been possible without the following funding sources: Conselleria de Educación, Investigación, Cultura y Deporte, Generalitat Valenciana for hiring predoctoral research staff with Grant (ACIF/2018/170) and the European Social Fund with the Grant Operational Programme of FSE 2014-2020. Conselleria de Educación, Investigación, Cultura y Deporte, Generalitat Valenciana for predoctoral contract students to stay in research centers outside the research centers outside the Valencian Community (BEFPI/2021/040) and the European Social Fund.Guzmán Ortiz, BE. (2022). Models and Algorithms for the Optimisation of Replenishment, Production and Distribution Plans in Industrial Enterprises [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/187461Compendi

Lot Sizing Heuristics Performance

Each productive system manager knows that finding the optimal trade‐off between reducing inventory and decreasing the frequency of production/ replenishment orders allows a great cut‐back in operations costs. Several authors have focused their contributions, trying to demonstrate that among the various dynamic lot sizing rules there are big differences in terms of performance, and that these differences are not negligible. In this work, eight of the best known lot sizing algorithms have been described with a unique modelling approach and have then been exhaustively tested on several different scenarios, benchmarking versus Wagner and Whitin’s optimal solution. As distinct from the contributions in the literature, the operational behaviour has been evaluated in order to determine which one is more suitable to the characteristics of each scenario