Strategies for a centralized single product multiclass M/G/1 make-to-stock queue

Make-to-stock queues are typically investigated in the M/M/1 settings. For centralized single-item systems with backlogs, the multilevel rationing (MR) policy is established as optimal and the strict priority (SP) policy is a practical compromise, balancing cost and ease of implementation. However, the optimal policy is unknown when service time is general, i.e., for M/G/1 queues. Dynamic programming, the tool commonly used to investigate the MR policy in make-to-stock queues, is less practical when service time is general. In this paper we focus on customer composition: the proportion of customers of each class to the total number of customers in the queue. We do so because the number of customers in M/G/1 queues is invariant for any nonidling and nonanticipating policy. To characterize customer composition, we consider a series of two-priority M/G/1 queues where the first service time in each busy period is different from standard service times, i.e., this first service time is exceptional. We characterize the required exceptional first service times and the exact solution of such queues. From our results, we derive the optimal cost and control for the MR and SP policies for M/G/1 make-to-stock queues

Optimal inventory reallocation to customer orders in ceramic tile companies characterized by the lack of homogeneity in the product (LHP)

[ES] La Falta de Homogeneidad en el Producto (FHP), se define como la carencia de la homogeneidad requerida por el cliente en los productos. La FHP aparece en empresas en las que los productos finales obtenidos no son homogéneos, dando lugar a la existencia de diferentes referencias (subtipos) de un mismo producto final. Esta falta de homogeneidad supone un problema cuando el cliente requiere ser servido a través de unidades homogéneas de un mismo producto y sus pedidos se comprometen en base cantidades planificadas, cuyas características de homogeneidad finales se desconocen en el momento de adquirir los compromisos con el cliente. Las constantes discrepancias provocadas por la FHP entre las cantidades planificadas y las realmente obtenidas y disponibles, pueden impedir servir pedidos comprometidos previamente. Para resolver este problema, se propone un modelo de programación matemática que permite reasignar el inventario en empresas caracterizadas por la FHP que fabrican contra almacén (Make to Stock: MTS) que combina varios objetivos. El modelo matemático propuesto se ha validado mediante su aplicación a un caso real de una empresa cerámica. El análisis de los resultados indica la obtención de mejoras considerables en la cantidad de pedidos completados a tiempo y en los ingresos por ventas.[EN] The lack of homogeneity in the product (LHP) is defined as the lack of uniformity required by the customer in the products. The LHP appears in companies where the final products obtained are not homogeneous, leading to the existence of different references (subtypes) of the same product. This lack of homogeneity is a problem when the client needs to be served through homogeneous units of a product and commit orders are based on planned quantities, whose final homogeneity characteristics are unknown at the time of acquiring the customer commitments. The frequent discrepancies caused by the LHP between planned homogeneous amounts and those actually obtained and available, can prevent the delivery of committed orders. To solve this problem, we propose a mathematical programming model for the reallocation of inventory in Make to Stock (MTS) ceramic tile companies characterized by the LHP that combines multiple objectives. The proposed mathematical model has been validated by its application to a real case of a ceramic company. The analysis of the obtained results indicates significant improvements in the number of orders completed on time and in sales revenue achieved.El presente trabajo se ha desarrollado parcialmente, tanto en el marco del proyecto de investigación titulado “Personalización en Masa y Cadenas de Suministro Inteligentes, con Productos y Procesos Complejos” (DPI 2008-06788-C02-01), financiado por el Ministerio de Ciencia e Innovación español, como en el proyecto de investigación titulado “Métodos y modelos para la planificación y gestión de pedidos en cadenas de suministro caracterizadas por la incertidumbre en la producción debido a la Falta de Homogeneidad en el Producto” (DPI2011-23597), financiado por el Ministerio de Economía y Competitividad español y por el Vicerrectorado de Investigación de la Universidad Politécnica de Valencia (PAID-06-11/1840), dentro de los cuales se ha tenido oportunidad de validar el funcionamiento del modelo propuesto aplicándolo a una empresa líder en el sector cerámico.Alemany Díaz, MDM.; Alarcón Valero, F.; Oltra Badenes, RF.; Lario Esteban, FC. (2013). Reasignación óptima del inventario a pedidos en empresas cerámicas caracterizadas por la falta de homogeneidad en el producto (FHP). Boletín de la Sociedad Española de Cerámica y Vidrio. 52(1):31-41. doi:10.3989/cyv.42013S314152

Two-Class M/M/1 Make-to-Stock Queueing Systems with Both Backlogs and Lost Sales

We introduce a new simple allocation policy which is a very good approximation of the optimal allocation policy in an inventory system with a single product and two priority classes of customers. A production facility produces new items with exponentially distributed production times as long as the inventory level is below a base-stock level of inventory. We assume that customers arrive to the system according to a Poisson process. They may be satisfied, backlogged, or rejected depending on their priority, the inventory level upon their arrivals, availability of products in stock, and availability of a finite waiting area. We define a categorized cost function to investigate the efficiency of the new allocation policy and several known allocation policies in the literature. The system is modeled as a combination of one- and two-dimensional Birth-and-Death processes under four different allocation policies: Sharing with Minimum Allocation (SMA) policy, Complete Partitioning (CP) policy, Multilevel Rationing (MR) policy, and Lost Sales (LS) policy. By solving the model and deriving the relevant probabilities, we calculate the relative gap between each policy and the optimal policy. Based on the numerical results, we find that the SMA policy provides a very good approximation of the optimal policy, and is applicable in practical problems with high dimensions and static levels of inventory and waiting areas. We show that the MR and LS policies are special cases of the SMA policy. Therefore, their performances can be evaluated using the results obtained under the SMA allocation policy.1 yea

Dynamic inventory pooling policies to deliver differentiated service

Resource pooling strategies have been widely used in industry to match supply with demand. However, effective implementation of these strategies can be challenging. Firms need to integrate the heterogeneous service level requirements of different customers into the pooling model and allocate the resources (inventory or capacity) appropriately in the most effective manner. The traditional analysis of inventory pooling, for instance, considers the performance metric in a centralized system and does not address the associated issue of inventory allocation. Using Blackwell’s Approachability Theorem, we derive a set of necessary and sufficient conditions to relate the fill rate requirement of each customer to the resources needed in the system. This provides a new approach to studying the value of resource pooling in a system with differentiated service requirements. Furthermore, we show that with “allocation flexibility,” the amount of safety stock needed in a system with independent and identically distributed demands does not grow with the number of customers but instead diminishes to zero and eventually becomes negative as the number of customers grows sufficiently large. This surprising result holds for all demand distributions with bounded first and second moments. This paper was accepted by Martin Lariviere, operations management. </jats:p

Assessing the Benefits of Different Stock-Allocation Policies for a Make-to-Stock Production System

We consider a manufacturing facility that produces a single item that is demanded by several different classes of customers. The inventory-related cost performance of such a system can be improved by effective allocation of production and inventories. We obtain the optimal parameters for three easily implementable allocation policies. Our results cover the case of linear backorder costs as well as fill-rate constraints. We compare the optimal performance of these control policies to gain insights into the benefits of different production and stock-allocation rules.Inventory/Production, Optimal Policies, Stock Allocation, Queues, Make-to-Stock System

STOCHASTIC MODELS FOR SERVICE AND TAXI SYSTEMS

This dissertation consists of two topics: inventory systems and service systems. The first topic involves a single-item inventory system with two demand classes with backorders. We introduce a four-parameter (A; B; C1; C2) policy to manage such a system. Under this policy, we place an order of size A if the on-hand inventory level is less than or equal to B, and reject demands of class k if the inventory level is below or at Ck (k = 1; 2). We develop methods of computing the long-run average cost that can be used to numerically obtain the four parameters that minimize this average cost. When the demands arrive according to Poisson processes and the production lead times are exponential and the order size A is fixed, we formulate the problem as a Markov Decision Process. We prove structural properties when A = 1, and numerically show that the four-parameter policies are optimal when A > 1. We also study the cases where demand interarrival times or production lead times are generally distributed. The numerical optimality is done using the Genetic Algorithm. The second topic considers a system of customers and taxis with Poisson arrivals and exponential patience times and delayed matching. We formulate the system as a Continuous Time Markov Chain and study the fluid and diffusion approximations. We consider Kurtz's Approximation and Gaussian Approximation and compare their performance numerically with simulation. We next formulate an optimal control problem to maximize the total net revenue over a fixed time horizon by controlling the arrival rate of taxis. We solve the optimal control problem numerically and compare its performance to simulation. We propose a heuristic control policy. We show that the expected regret of the heuristic policy is a bounded function of the horizon.Doctor of Philosoph

Identificación de tendencias de los Sistemas Integrados de Gestión Empresarial. Análisis funcional y diseño de herramientas para el desarrollo de un ERP vertical adaptado al sector cerámico

Durante la última década, los avances en las Tecnologías de la Información han tenido un enorme efecto sobre el entorno empresarial. La aparición de rápidas redes de comunicación, hardware extremadamente potente y software de gran versatilidad, todo ello conectado entre sí a escala mundial, ha permitido a las organizaciones desarrollar de forma más eficaz sus productos y servicios y comercializarlos en menos tiempo. Estos cambios han marcado la transición entre la era industrial y la era de la información, en la que todo está conectado y funciona de un modo más rápido y dinámico. En este contexto, la información y el conocimiento son elementos fundamentales para generar valor y riqueza. Se considera que la información es un recurso que se encuentra al mismo nivel que los recursos financieros, materiales y humanos, que hasta el momento habían constituido los ejes sobre los que había girado la gestión empresarial. Si la teoría económica tradicional mantenía el capital, la tierra y el trabajo como elementos primarios de estudio, la información se ha convertido, ahora, en el cuarto elemento a gestionar. De esta forma, los sistemas de información para la gestión de empresas se han convertido en un factor clave en el desarrollo empresarial, imprescindibles para lograr objetivos estratégicos de negocio. Estos sistemas se han visto obligados a evolucionar drásticamente en los últimos tiempos, y están en continuo proceso de mejora, debido a los incesantes cambios del entorno, cada vez más complejo y cambiante. Por ese motivo los principales fabricantes de sistemas de información para la gestión de empresas dedican gran parte de sus recursos a la investigación, desarrollo e innovación de dichos sistemas. En consecuencia, se considera importante estudiar cómo pueden evolucionar estos sistemas en un futuro cercano y cómo van a integrar los cambios tecnológicos que se están dando y se prevé que se van a dar en cuanto a las TIC�s. Esto puede afectar en gran medida, tanto a los fOltra Badenes, RF. (2012). Identificación de tendencias de los Sistemas Integrados de Gestión Empresarial. Análisis funcional y diseño de herramientas para el desarrollo de un ERP vertical adaptado al sector cerámico [Tesis doctoral]. Editorial Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/16003Palanci

Pooling and polling : creation of pooling in inventory and queueing models

The subject of the present monograph is the ‘Creation of Pooling in Inventory and Queueing Models’. This research consists of the study of sharing a scarce resource (such as inventory, server capacity, or production capacity) between multiple customer classes. This is called pooling, where the goal is to achieve cost or waiting time reductions. For the queueing and inventory models studied, both theoretical, scientific insights, are generated, as well as strategies which are applicable in practice. This monograph consists of two parts: pooling and polling. In both research streams, a scarce resource (inventory or server capacity, respectively production capacity) has to be shared between multiple users. In the first part of the thesis, pooling is applied to multi-location inventory models. It is studied how cost reduction can be achieved by the use of stock transfers between local warehouses, so-called lateral transshipments. In this way, stock is pooled between the warehouses. The setting is motivated by a spare parts inventory network, where critical components of technically advanced machines are kept on stock, to reduce down time durations. We create insights into the question when lateral transshipments lead to cost reductions, by studying several models. Firstly, a system with two stock points is studied, for which we completely characterize the structure of the optimal policy, using dynamic programming. For this, we formulate the model as a Markov decision process. We also derived conditions under which simple, easy to implement, policies are always optimal, such as a hold back policy and a complete pooling policy. Furthermore, we identified the parameter settings under which cost savings can be achieved. Secondly, we characterize the optimal policy structure for a multi-location model where only one stock point issues lateral transshipments, a so-called quick response warehouse. Thirdly, we apply the insights generated to the general multi-location model with lateral transshipments. We propose the use of a hold back policy, and construct a new approximation algorithm for deriving the performance characteristics. It is based on the use of interrupted Poisson processes. The algorithm is shown to be very accurate, and can be used for the optimization of the hold back levels, the parameters of this class of policies. Also, we study related inventory models, where a single stock point servers multiple customers classes. Furthermore, the pooling of server capacity is studied. For a two queue model where the head-of-line processor sharing discipline is applied, we derive the optimal control policy for dividing the servers attention, as well as for accepting customers. Also, a server farm with an infinite number of servers is studied, where servers can be turned off after a service completion in order to save costs. We characterize the optimal policy for this model. In the second part of the thesis polling models are studied, which are queueing systems where multiple queues are served by a single server. An application is the production of multiple types of products on a single machine. In this way, the production capacity is pooled between the product types. For the classical polling model, we derive a closedform approximation for the mean waiting time at each of the queues. The approximation is based on the interpolation of light and heavy traffic results. Also, we study a system with so-called smart customers, where the arrival rate at a queue depends on the position of the server. Finally, we invent two new service disciplines (the gated/exhaustive and the ??-gated discipline) for polling models, designed to yield ’fairness and efficiency’ in the mean waiting times. That is, they result in almost equal mean waiting times at each of the queues, without increasing the weighted sum of the mean waiting times too much