The Impact of Powers-of-Two Based Schedule on the Minimization of Inventory Costs in a Multi Product Manufacturing Environment

This paper discusses about the scheduling problem of a multi product manufacturing industry. Often there has been a problem of applying optimization algorithms to solve the makespan minimization criterion of a job shop due to its inherent NP-hard nature. It is therefore unrealistic to try obtaining a solution through a commercial solver in polynomial time. In this context, we propose a computationally effective heuristic, which is based on the powers-of-two policy in inventory, for solving the minimum makespan problem of job shop scheduling. The research discussed in the current paper is a real time scheduling problem faced by a large scale and complex turbine manufacturing job shop. It is worth noting that by integrating the material requirements planning (MRP) with the feasible schedule obtained, this policy also proves to be useful in minimizing the inventory costs

The Benefit of Information Sharing in a Logistics Outsourcing Context

The goal of this article is to examine the value of information sharing in outsourcing of logistics activities. Our examination is in the context of a fairly complex network in which location and capacity of carriers are considered. The current research also examines the moderating effect of network settings on the benefit of information sharing. A core component of our methodology is use of computational experiments to provide a variety of logistics network conditions under which we investigate information sharing value. The investigation involves comparing two strategies, namely full and no information sharing. Underlying the experiments are procedures to optimise the network under each strategy. The procedures are based on exact methods that combine integer linear programming with exhaustive enumeration. To gauge the robustness of the insights, we applied formal analysis of variance techniques to the data from the numerical experiments. The obtained insights are helpful to managers for selecting appropriate logistics service providers and level of information exchange

The submodular joint replenishment problem

The joint replenishment problem is a fundamental model in supply chain management theory that has applications in inventory management, logistics, and maintenance scheduling. In this problem, there are multiple item types, each having a given time-dependent sequence of demands that need to be satisfied. In order to satisfy demand, orders of the item types must be placed in advance of the due dates for each demand. Every time an order of item types is placed, there is an associated joint setup cost depending on the subset of item types ordered. This ordering cost can be due to machine, transportation, or labor costs, for example. In addition, there is a cost to holding inventory for demand that has yet to be served. The overall goal is to minimize the total ordering costs plus inventory holding costs. In this paper, the cost of an order, also known as a joint setup cost, is a monotonically increasing, submodular function over the item types. For this general problem, we show that a greedy approach provides an approximation guarantee that is logarithmic in the number of demands. Then we consider three special cases of submodular functions which we call the laminar, tree, and cardinality cases, each of which can model real world scenarios that previously have not been captured. For each of these cases, we provide a constant factor approximation algorithm. Specifically, we show that the laminar case can be solved optimally in polynomial time via a dynamic programming approach. For the tree and cardinality cases, we provide two different linear programming based approximation algorithms that provide guarantees of three and five, respectively.National Science Foundation (U.S.) (CAREER Grant CMMI-0846554)United States. Air Force Office of Scientific Research (Award FA9550-11-1-0150)SMA GrantSolomon Buchsbaum AT&T Research Fun

Supply Chain Management with Online Customer Selection

We consider new online variants of supply chain management models, where in addition to production decisions, one also has to actively decide on which customers to serve. Specifically, customers arrive sequentially during a selection phase, and one has to decide whether to accept or reject each customer upon arrival. If a customer is rejected, then a lost-sales cost is incurred. Once the selection decisions are all made, one has to satisfy all the accepted customers with minimum possible production cost. The goal is to minimize the total cost of lost sales and production. A key feature of the model is that customers arrive in an online manner, and the decision maker does not require any information about future arrivals. We provide two novel algorithms for online customer selection problems, which are based on repeatedly solving offline subproblems that ignore previously made decisions. For many important settings, our algorithms achieve small constant competitive ratio guarantees. That is, for any sequence of arriving customers, the cost incurred by the online algorithm is within a fixed constant factor of the cost incurred by the respective optimal solution that has full knowledge upfront on the sequence of arriving customers. Finally, we provide a computational study on the performance of these algorithms when applied to the economic lot sizing and joint replenishment problems with online customer selection.National Science Foundation (U.S.) (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

Resolución del problema del tamaño de lote multinivel capacitado aplicando optimización por enjambre de partículas con búsqueda local

Un problema que se presentan en los sistemas de manufactura de las empresas, especialmente pequeñas y medianas empresas, es que la programación de la producción está basada bajo modelos de arrastre de la demanda deterministas, es decir, el proceso de la planificación de los tamaños de lotes de insumos o componentes para la fabricación de productos finales que poseen jerarquías multiniveles y restricciones de capacidad como horas hombres, números de maquinas entre otras, son un problema que se pueden convertir en oportunidades de mejora debido a que se pueden equilibran los costos de ordenamiento de un lote y los costos de inventarios por productos que permita obtener una reducción en los costos totales y así mejorar la productividad de las empresas. Este trabajo presenta una metodología para la solución del problema del tamaño de lote multinivel capacitado, basado en una técnica metaheurísticas llamada optimización por enjambre de partículas o PSO por sus siglas en ingles (Particle Swarm Optimization), la cual se ha demostrado que tiene un buen desempeño dentro de las familia de metaheurísticas, así que se propone el desarrollo de este tema agregando el concepto una búsqueda local que permita generar óptimos locales y permita mejorar las soluciones encontradas por las partículas, denominando a está técnica como la utilización de una hiperheurística.Incluye bibliografía, anexo

Finite-horizon operations planning for a lean supply chain system

This dissertation studies an operational policy for a lean supply chain system consisting of a manufacturer, multiple suppliers and multiple buyers. The manufacturer procures raw materials from the suppliers and converts them into finished products, which are then shipped in batches to the buyers at certain intervals of times. Three distinct but inseparable problems are addressed: single supplier and single buyer with fixed delivery size (FD), multiple suppliers and multiple buyers with individual delivery schedule (MD), and time dependent delivery quantity with trend demand (TD). The mathematical formulations of these supply systems are categorized as mixed-integer, nonlinear programming problems (MINLAP) with discrete, non-convex objective functions and constraints. The operations policy determines the number of orders of raw material, beginning and ending times of cycles, production batch size, production start time, and beginning and ending inventories. The goal is to minimize the cost of the two-stage, just-in-time inventory system that integrates raw materials ordering and finished goods production system. The policy is designed for a finite planning horizon with various phases of life cycle demands such as inception (increasing), maturity (level) and phasing out (declining). Analytical results that characterize the exact, optimal policy for the problems described above are devised to develop efficient and optimal computational procedures. A closed-form heuristic that provides a near-optimal solution and tight lower bound is proposed for the problem FD. A network model to represent the problems is proposed and network-based algorithms are implemented to solve the problems FD, MD and TD optimally. The computational complexities of the algorithms are Θ(N2) or O(N3) where N is the total number of shipments in the planning horizon. Numerical tests to assess the robustness and quality of the methods show that the present research provides superior results. Production and supply chain management play an important role in ensuring that the necessary amounts of materials and parts arrive at the appropriate time and place. A manager, using the models obtained in this research, can quickly respond to consumers\u27 demand by effectively determining the right policies to order raw materials, to deliver finished goods, and to efficiently manage their production schedule

Applied Inventory Management: New Approaches to Age-Old Problems

Supply chain management is one of the fundamental topics in the field of operations research, and a vast literature exists on the subject. Many recent developments in the field are rapidly narrowing the gap between the systems handled in the literature and the real-life problems companies need to solve on a day-to-day basis. However, there are certain features often observed in real-world systems that elude even these most recent developments. In this thesis, we consider a number of these features, and propose some new heuristics together with methodologies to evaluate their performance. In Chapter 2, we consider a general two-echelon distribution system consisting of a depot and multiple sales outlets which face random demands for a given item. The replenishment process consists of two stages: the depot procures the item from an outside supplier, while the retailers' inventories are replenished by shipments from the depot. Both of the replenishment stages are associated with a given facility-specific leadtime. The depot as well as the retailers face a limited inventory capacity. We propose a heuristic for this class of dynamic programming models to obtain an upper bound on optimal costs, together with a new approach to generate lower bounds based on Lagrangian relaxation. We report on an extensive numerical study with close to 14,000 instances which evaluates the accuracy of the lower bound and the optimality gap of the various heuristic policies. Our study reveals that our policy performs exceedingly well almost across the entire parameter spectrum. In Chapter 3, we extend the model above to deal with distribution systems involving several items. In this setting, two interdependencies can arise between items that considerably complicate the problem. First, shared storage capacity at each of the retail outlets results in a trade-off between items; ordering more of one item means less space is available for another. Second, economies of scope can occur in the order costs if several items can be ordered from a single supplier, incurring only one fixed cost. To our knowledge, our approach is the first that has been proposed to handle such complex, multi-echelon, multi-item systems. We propose a heuristic for this class of dynamic programming models, to obtain an upper bound on optimal costs, together with an approach to generate lower bounds. We report on an extensive numerical study with close to 1,200 instances that reveals our heuristic performs excellently across the entire parameter spectrum. In Chapter 4, we consider a periodic-review stochastic inventory control system consisting of a single retailer which faces random demands for a given item, and in which demand forecasts are dynamically updated (for example, new information observed in one period may affect our beliefs about demand distributions in future periods). Replenishment orders are subject to fixed and variable costs. A number of heuristics exist to deal with such systems, but to our knowledge, no general approach exists to find lower bounds on optimal costs therein. We develop a general approach for finding lower bounds on the cost of such systems using an information relaxation. We test our approach in a model with advance demand information, and obtain good lower bounds over a range of problem parameters. Finally, in Appendix A, we begin to tackle the problem of using these methods in real supply chain systems. We were able to obtain data from a luxury goods manufacturer to inspire our study. Unfortunately, the methods we developed in earlier chapters were not directly applicable to these data. Instead, we developed some alternate heuristic methods, and we considered statistical techniques that might be used to obtain the parameters required for these heuristics from the data available