Piecewise linear approximations for the static-dynamic uncertainty strategy in stochastic lot-sizing

In this paper, we develop mixed integer linear programming models to compute near-optimal policy parameters for the non-stationary stochastic lot sizing problem under Bookbinder and Tan's static-dynamic uncertainty strategy. Our models build on piecewise linear upper and lower bounds of the first order loss function. We discuss different formulations of the stochastic lot sizing problem, in which the quality of service is captured by means of backorder penalty costs, non-stockout probability, or fill rate constraints. These models can be easily adapted to operate in settings in which unmet demand is backordered or lost. The proposed approach has a number of advantages with respect to existing methods in the literature: it enables seamless modelling of different variants of the above problem, which have been previously tackled via ad-hoc solution methods; and it produces an accurate estimation of the expected total cost, expressed in terms of upper and lower bounds. Our computational study demonstrates the effectiveness and flexibility of our models.Comment: 38 pages, working draf

Solution methods for an integrated lot sizing and scheduling problem

In this talk we present results of an ongoing study, based on a problem of a textile factory. The core problem is an integrated lotsizing and scheduling one, characterized by sets of parallel machines, arbitrary demands and due dates for products, a compatibility matrix between machines and components and release dates of machines. In a solution, the quantities to produce by product/component/size are split among smaller lots, the machines in which those lots will be produced are determined, as well as the order in which they will be done. We present a MIP model and results of a VNS heuristic

A review of discrete-time optimization models for tactical production planning

This is an Accepted Manuscript of an article published in International Journal of Production Research on 27 Mar 2014, available online: http://doi.org/10.1080/00207543.2014.899721[EN] This study presents a review of optimization models for tactical production planning. The objective of this research is to identify streams and future research directions in this field based on the different classification criteria proposed. The major findings indicate that: (1) the most popular production-planning area is master production scheduling with a big-bucket time-type period; (2) most of the considered limited resources correspond to productive resources and, to a lesser extent, to inventory capacities; (3) the consideration of backlogs, set-up times, parallel machines, overtime capacities and network-type multisite configuration stand out in terms of extensions; (4) the most widely used modelling approach is linear/integer/mixed integer linear programming solved with exact algorithms, such as branch-and-bound, in commercial MIP solvers; (5) CPLEX, C and its variants and Lindo/Lingo are the most popular development tools among solvers, programming languages and modelling languages, respectively; (6) most works perform numerical experiments with random created instances, while a small number of works were validated by real-world data from industrial firms, of which the most popular are sawmills, wood and furniture, automobile and semiconductors and electronic devices.This study has been funded by the Universitat Politècnica de València projects: ‘Material Requirement Planning Fourth Generation (MRPIV)’ (Ref. PAID-05-12) and ‘Quantitative Models for the Design of Socially Responsible Supply Chains under Uncertainty Conditions. Application of Solution Strategies based on Hybrid Metaheuristics’ (PAID-06-12).Díaz-Madroñero Boluda, FM.; Mula, J.; Peidro Payá, D. (2014). A review of discrete-time optimization models for tactical production planning. International Journal of Production Research. 52(17):5171-5205. doi:10.1080/00207543.2014.899721S51715205521

A Metaheuristic-Based Simulation Optimization Framework For Supply Chain Inventory Management Under Uncertainty

The need for inventory control models for practical real-world applications is growing with the global expansion of supply chains. The widely used traditional optimization procedures usually require an explicit mathematical model formulated based on some assumptions. The validity of such models and approaches for real world applications depend greatly upon whether the assumptions made match closely with the reality. The use of meta-heuristics, as opposed to a traditional method, does not require such assumptions and has allowed more realistic modeling of the inventory control system and its solution. In this dissertation, a metaheuristic-based simulation optimization framework is developed for supply chain inventory management under uncertainty. In the proposed framework, any effective metaheuristic can be employed to serve as the optimizer to intelligently search the solution space, using an appropriate simulation inventory model as the evaluation module. To be realistic and practical, the proposed framework supports inventory decision-making under supply-side and demand-side uncertainty in a supply chain. The supply-side uncertainty specifically considered includes quality imperfection. As far as demand-side uncertainty is concerned, the new framework does not make any assumption on demand distribution and can process any demand time series. This salient feature enables users to have the flexibility to evaluate data of practical relevance. In addition, other realistic factors, such as capacity constraints, limited shelf life of products and type-compatible substitutions are also considered and studied by the new framework. The proposed framework has been applied to single-vendor multi-buyer supply chains with the single vendor facing the direct impact of quality deviation and capacity constraint from its supplier and the buyers facing demand uncertainty. In addition, it has been extended to the supply chain inventory management of highly perishable products. Blood products with limited shelf life and ABO compatibility have been examined in detail. It is expected that the proposed framework can be easily adapted to different supply chain systems, including healthcare organizations. Computational results have shown that the proposed framework can effectively assess the impacts of different realistic factors on the performance of a supply chain from different angles, and to determine the optimal inventory policies accordingly

Comparison of different approaches to multistage lot sizing with uncertain demand

We study a new variant of the classical lot sizing problem with uncertain demand where neither the planning horizon nor demands are known exactly. This situation arises in practice when customer demands arriving over time are confirmed rather lately during the transportation process. In terms of planning, this setting necessitates a rolling horizon procedure where the overall multistage problem is dissolved into a series of coupled snapshot problems under uncertainty. Depending on the available data and risk disposition, different approaches from online optimization, stochastic programming, and robust optimization are viable to model and solve the snapshot problems. We evaluate the impact of the selected methodology on the overall solution quality using a methodology-agnostic framework for multistage decision-making under uncertainty. We provide computational results on lot sizing within a rolling horizon regarding different types of uncertainty, solution approaches, and the value of available information about upcoming demands

The integrated control of production-inventory systems

In this thesis, we investigate a multi-product, multi-machine production-inventory (PI) system that is characterized by: ?? relatively high and stable demand; ?? uncertainty in the precise timing of demand; ?? variability in the production process; ?? job shop routings; ?? considerable setup times and costs. This type of PI system can be found in the supply chain of capital goods. Typically, it represents a manufacturer of parts that are assembled in later stages of the supply chain. Our exploratory research aims at identifying promising control approaches for this type of PI systems and the conditions in which they are applicable. The control approaches developed in this thesis are based on an integrated view of the PI system. The objective of the control approaches is to minimize the sum of setup costs, work-in-process holding costs and ¿nal inventory holding costs, while target customer service levels are satis¿ed. The research reveals that the exact analysis and optimization of this type of PI systems is impossible. Therefore, we are restricted to the development of heuristic control approaches. We propose two control strategies that are based on distinct control principles. For each of the control strategies, we develop and test decision-support systems that can be used to determine cost-e¢ cient (but not necessarily optimal) control decisions. Part I of this thesis deals with the ¿rst approach, called Coordinated Batch Control (CBC). This strategy uses a periodic review, order-up-to inventory pol- icy to control the stock points. The replenishment orders generated by this inventory policy are manufactured by the production system. The CBC strat- egy integrates production and inventory control decisions by determining cost- e¢ cient review periods. There is no further integration of control decisions. At the shop ¿oor, a myopic rule is used to sequence the orders, which ensures a certain degree of ¿exibility for responding to unexpected circumstances. We develop three decision-support systems for the CBC approach. The ¿rst decision-support system is based on an approximate analytical model of the PI system. In the approximate analytical model, we apply standard results from inventory theory, queueing theory and renewal theory. The second and third decision-support system use simulation optimization techniques to determine the near-optimal review periods. The three heuristic decision-support systems for CBC are tested in an exten- sive simulation study. The test bed consists of ¿ve basic problem con¿gurations, which de¿ne a routing structure, processing times, etc. We vary four factors over several levels: setup costs, setup times, net utilization and target ¿ll rates. In this way, we obtain 48 instances based on the same basic problem con¿guration, leading to 5 x 48 = 240 problem instances. The simulation study shows that the use of simulation optimization resulted in relatively small improvements over the solution obtained from the approximate analytical model. Since simulation optimization requires large amounts of computation e¤ort, we decide that the use of the decision-support system based on the approximate analytical model is justi¿ed. Part II is concerned with the Cyclical Production Planning (CPP) strategy. This strategy approaches the control of the PI system from a totally di¤erent angle. In this strategy, a detailed production schedule is used to control the production system. The schedule prescribes the sequence in which the orders are produced on the work centers and this schedule is repeated at regular time intervals. The time that elapses between the start of two schedules is called the ¿cycle time¿. The schedule is determined such that the total costs are minimized. The stock points are controlled with periodic review, order-up-to policies. The main advantage of the use of a production schedule is that ¿ow of the orders through the production system is controlled better, which results in more re- liable throughput times. A drawback of this approach is that the production frequencies of the di¤erent products need to be matched in order to make a cyclic production schedule. Hence, there is less ¿exibility in setting the lot sizes, which may result in higher costs. Another drawback of the CPP approach is that production capacity may be wasted by strictly following the prespeci¿ed processing sequences. We propose a decision-support system for the CPP strategy which is based on a deterministic model of the PI system. The decision-support system is used to determine cost-e¢ cient production plans. We present a heuristic method to approximately minimize the total costs of the deterministic model. When the solution of the deterministic model is used in a stochastic environment, the solution may be instable or nearly instable. Therefore, we use a simulation procedure to check whether the proposed solution is stable. If not, slack-time is added to the schedule and deterministic model is solved again. We test the decision-support system for CPP in an extensive simulation study. The test bed is identical to the one used in Part I. We test wether the Summary 273 decision-support system responds soundly to changes in the factors. Further- more, we investigate the estimation quality of the deterministic model that is embedded in the decision-support system. Finally, we test the optimization quality of the decision-support system. Based on the results of these tests, we decide that it is acceptable to use the proposed decision-support system to determine the control variables of the CPP strategy. Part III compares the performance of the CBC and the CPP strategy. Both strategies are compared in a simulation study consisting of the same instances as in Part I and II. We compare the strategies in terms of realized total costs. In about 62% of the instances, the CPP strategy outperforms the CBC strategy. In the remaining 38% of the instances, the CBC strategy realizes lower costs than the CPP strategy. An analysis of variance reveals that the following factors have a signi¿cant impact on the performance di¤erence between CPP and CBC: ?? net utilization; ?? setup costs; ?? interaction between setup costs and net utilization; ?? basic problem con¿guration. Based on our investigations, we can provide an explanation for these obser- vations. The simulation results show that the performance di¤erence is pro- portional to the di¤erence between the average review periods (CBC) and the common cycle length (CPP), denoted as dR. The factors mentioned above have an in¿uence on dR through their impact on capacity utilization. At low lev- els of capacity utilization, we observe that dR is low, which indicates that the CPP and CBC strategy operate with comparable review periods and common cycle lengths. In situations where the CBC strategy operates at higher levels of capacity utilization (because net utilization increases and/or setup costs de- crease), it becomes more di¢ cult for the CPP strategy to ¿nd a feasible cyclical production schedule, mainly because production capacity is wasted by strictly following a prespeci¿ed processing sequence. In these cases, the CPP strategy needs to increase the common cycle length to free up production capacity that is used to compensate for the loss of capacity. This leads to increases in dR and to higher costs. The speci¿c characteristics of a problem instance have a strong in¿uence on the magnitude of this e¤ect. Based on the insights obtained from our research, we formulate some guidelines for the application of CPP and CBC

MRP IV: Planificación de requerimientos de materiales cuarta generación. Integración de la planificación de la producción y del transporte de aprovisionamiento

Tesis por compendioEl sistema de planificación de requerimientos de materiales o MRP (Material Requirement Planning), desarrollado por Orlicky en 1975, sigue siendo en nuestros días y, a pesar de sus deficiencias identificadas, el sistema de planificación de la producción más utilizado por las empresas industriales. Las evoluciones del MRP se vieron reflejadas en el sistema MRPII (Manufacturing Resource Planning), que considera restricciones de capacidad productiva, MRPIII (Money Resource Planning), que introduce la función de finanzas; y la evolución comercial del mismo en el ERP (Enterprise Resource Planning), que incorpora modularmente todas las funciones de la empresa en un único sistema de decisión, cuyo núcleo central es el MRP. Los desarrollos posteriores de los sistemas ERP han incorporado las nuevas tecnologías de la información y comunicaciones. Asimismo, éstos se han adaptado al contexto económico actual caracterizado por la globalización de los negocios y la deslocalización de los proveedores desarrollando otras funciones como la gestión de la cadena de suministro o del transporte, entre otros. Por otro lado, existen muchos trabajos en la literatura académica que han intentado resolver algunas de las debilidades del MRP tales como la optimización de los resultados, la consideración de la incertidumbre en determinados parámetros, el inflado de los tiempos de entrega, etc. Sin embargo, tanto en el ámbito comercial como en el científico, el MRP y sus variantes se centran en el requerimiento de los materiales y en la planificación de las capacidades de producción, lo que es su desventaja principal en aquellas cadenas de suministro donde existe una gran deslocalización de los proveedores de materias primas y componentes. En estos entornos, la planificación del transporte adquiere un protagonismo fundamental, puesto que los elevados costes y las restricciones logísticas suelen hacer subóptimos e incluso infactibles los planes de producción propuestos, siendo la re-planificación manual una práctica habitual en las empresas. Esta tesis doctoral propone un modelo denominado MRPIV, que considera de forma integrada las decisiones de la planificación de materiales, capacidades de recursos de producción y el transporte, con las restricciones propias de este último, tales como diferentes modos de recogida (milk-run, camión completo, rutas) en la cadena de suministro con el objetivo de evitar la suboptimización de estos planes que en la actualidad se generan usualmente de forma secuencial e independiente. El modelo propuesto se ha validado en una cadena de suministro del sector del automóvil confirmando la reducción de costes totales y una planificación más eficiente del transporte de los camiones necesarios para efectuar el aprovisionamiento.Díaz-Madroñero Boluda, FM. (2015). MRP IV: Planificación de requerimientos de materiales cuarta generación. Integración de la planificación de la producción y del transporte de aprovisionamiento [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/48524TESISCompendi