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

Coping with production time variability via dynamic lead-time quotation

In this paper, we propose two dynamic lead-time quotation policies in an M/GI/1 type make-to-stock queueing system serving lead-time sensitive customers with a single type of product. Incorporating non-exponential service times in an exact method for make-to-stock queues is usually deemed difficult. Our analysis of the proposed policies is exact and requires the numerical inversion of the Laplace transform of the sojourn time of an order to be placed. The first policy assures that the long-run probability of delivering the product within the quoted lead-time is the same for all backlogged customers. The second policy is a refinement of the first which improves the profitability if customers are oversensitive to even short delays in delivery. Numerical results show that both policies perform close to the optimal policy that was characterized only for exponential service times. The new insight gained is that the worsening impact of the production time variability, which is felt significantly in systems accepting all customers by quoting zero lead times, decreases when dynamic lead-time quotation policies are employed

Análisis del impacto del lead time en los costos totales y el nivel de servicio para una cadena de suministro con diferentes estructuras de productos y horizonte rodante de planificación

El principal objetivo de la investigación es analizar y evaluar el impacto o efectos que tienen el lead time por parte de los proveedores o eslabón primario sobre el sistema de costos y el desempeño del nivel de servicio, para una cadena de suministro de tipo multinivel. El sistema de producción, representado por el segundo eslabón de la cadena, se planifica y se programa mediante un horizonte rodante, el cual se optimiza para cada periodo, teniendo en cuenta los periodos de replanificación y los periodos de congelamiento. Se consideran también en esta etapa, los niveles de inventario, las recepciones programadas, y la limitación de los recursos. A través del modelo matemático GMOP (Generic Materials & Operations Planning), se optimiza el plan de requerimientos de materiales, basándose en el concepto de Stroke y Skus, y otro factor, entre ellos; los tiempos de entrega y las variantes en las estructuras de ensamble de los productos. El tercer eslabón de la cadena está condicionada por la heterogeneidad de la demanda, basada en el índice de Gini y un coeficiente de variación que simula un entorno con incertidumbre. Con los resultados de la simulación, se efectúa un análisis de varianza, con el propósito de evaluar el comportamiento, e interacción de los factores de entrada sobre el comportamiento de los costos totales y el efecto bullwhip, medido a través del nivel de servicio del sistemaThe main objective of the research is to analyze and evaluate the impact or effects of the waiting time on the part of suppliers or the primary language on the cost system and the performance of the service level, for a supply chain of type multilevel. The production system, the second link in the chain, the program is based on a rolling horizon, which is optimized for each period, taking into account the replanning periods and the freezing periods. Inventory levels, scheduled receptions, and limitation of resources are also considered in this stage. Through the mathematical model GMOP (Generic Materials and Operations Planning), the material requirements plan is optimized, the results in the concept of Stroke and Skus, and another factor, among them; Delivery times and variants in the structures of all the products. The third link in the chain is conditioned by the heterogeneity of the demand, based on the Gini index and the coefficient of variation that simulates an environment with uncertainty. With the results of the simulation, an analysis of the variance is carried out, with the purpose of evaluating the behavior, and the interaction of the factors of the entrance on the behavior of the total costs and the effect of the dome, the measured through of the service level of the syste

The impact of production time variability on make-to-stock queue performance

In this paper, we exploit the distributional Little's law to obtain the steady-state distribution of the number of customers in a GI/G/1 make-to-stock queueing system. Non-exponential service times in make-to-stock queue modeling are usually avoided or at best, considered in approximations due to difficulties in developing an exact method. By providing a numerical solution of the GI/G/1 make-to-stock queue, we observed the impact of production time variability on optimal inventory control policies. The numerical results prove the degree of errors in the results if an exponential service time distribution were assumed instead of the actual distribution.Make-to-stock GI/G/1 queue Little's distributional law

Análisis del impacto del Lead Time en una cadena de suministro en un horizonte rodante de planificación con flexibilidad en las operaciones e incertidumbre en la demanda /

Son varios los aspectos y factores que inciden en el desempeño y gestión de la cadena de suministro, esto ha motivado a los investigadores en la búsqueda y solución de problemas de diversa índole, realizando aportes en la formulación y solución con modelos y herramientas algorítmicas muy variadas, y aportes significativos que han contribuido al mejoramiento, u optimización, de una parte o de la totalidad de los problema que afectan el desempeño o eficiencia de un sistema de abastecimiento. Un primer aspecto está relacionado con la dinámica misma e incertidumbre de los mercados, un segundo aspecto tiene que ver con la complejidad para articular todos y cada uno de los eslabones o procesos que conforman toda la red de abastecimiento –producción y distribución, de bienes o productos terminados, y un tercer aspecto, hace referencia con la globalización de la economía. Por otro lado, esta globalización ha provocado la disminución de barreras y en muchos casos la pérdida de fronteras comerciales, obligando a las organizaciones a aunar esfuerzos y a repensar lo negocios de forma colaborativa, ya sea para mantener los mercados que se han ganado y enfrentar la competencia, o también con el fin de ganar otros espacios, y aumentar su participación comercial.Incluye referencias bibliográfica