The symmetric longest queue system

Houtum, Geert‐Jan van; Adan, I.J.B.F.; Wal, J. van der

doi:10.1080/15326349708807416

Cited by 18 publications

(5 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, such an approach is practically feasible only for small systems (e.g., with two locations) and for relatively low utilization levels at the production facility. Nevertheless, evidence shows that the difference in cost between the FCFS and an optimal policy diminishes as utilization increases, with this difference becoming negligible when utilization is high (see Zheng and Zipkin 1990, Zipkin 1995, van Houtum et al 1997. Assigning static priorities among the different locations could provide an alternative to the FCFS policy.…”

Section: Model Formulationmentioning

confidence: 99%

Demand Allocation in Systems with Multiple Inventory Locations and Multiple Demand Sources

Benjaafar

et al. 2008

M&SOM

View full text Add to dashboard Cite

We consider the problem of allocating demand that originates from multiple sources among multiple inventory locations. Demand from each source arrives dynamically according to an independent Poisson process. The cost of fulfilling each order depends on both the source of the order and its fulfillment location. Inventory at all locations is replenished from a shared production facility with a finite production capacity and stochastic production times. Consequently, supply lead times are load dependent and affected by congestion at the production facility. Our objective is to determine an optimal demand allocation and optimal inventory levels at each location so that the sum of transportation, inventory, and backorder costs is minimized. We formulate the problem as a nonlinear optimization problem and characterize the structure of the optimal allocation policy. We show that the optimal demand allocations are always discrete, with demand from each source always fulfilled entirely from a single inventory location. We use this discreteness property to reformulate the problems as a mixed-integer linear program and provide an exact solution procedure. We show that this discreteness property extends to systems with other forms of supply processes. However, we also show that supply systems exist for which the property does not hold. Using numerical results, we examine the impact of different parameters and provide some managerial insights.production-inventory systems, optimal demand allocation, make-to-stock queues, facility location

show abstract

Section: Model Formulationmentioning

confidence: 99%

Demand Allocation in Systems with Multiple Inventory Locations and Multiple Demand Sources

Benjaafar

et al. 2008

M&SOM

View full text Add to dashboard Cite

show abstract

“…However, because of the well-known curse of dimensionality for multidimensional MDPs, an optimal policy cannot be identified in any reasonable amount of time, except for the smallest systems (e.g., a single facility with two products) and for relatively low utilization levels. Nevertheless, there is evidence that the difference in cost between the FCFS and an optimal policy diminishes in utilization, with this difference becoming negligible when utilization is high (see Wein 1992, Zheng and Zipkin 1990, Zipkin 1995, or Van Houtum et al 1997. Static priorities among the different products can also provide an alternative to the FCFS policy.…”

Section: Model Descriptionmentioning

confidence: 94%

Demand Allocation in Multiple-Product, Multiple-Facility, Make-to-Stock Systems

2004

View full text Add to dashboard Cite

We consider the problem of allocating demand arising from multiple products to multiple production facilities with finite capacity and load-dependent lead times. Production facilities can choose to manufacture items either to stock or to order. Products vary in their demand rates, holding and backordering costs, and service-level requirements. We develop models and solution procedures to determine the optimal allocation of demand to facilities and the optimal inventory level for products at each facility. We consider two types of demand allocation, one in which we allow the demand for a product to be split among multiple facilities and the other in which demand from each product must be entirely satisfied by a single facility. We also consider two forms of inventory warehousing, one in which inventory locations are factory based and one in which they are centralized. For each case, we offer a solution procedure to obtain optimal demand allocations and optimal inventory base-stock levels. For systems with multiple customer classes, we also determine optimal inventory rationing levels for each class for each product. We use the models to characterize analytically several properties of the optimal solution. In particular, we highlight eight principles that relate the effects of cost, congestion, inventory pooling, multiple sourcing, customer segmentation, inventory rationing, and process and demand variability.production/inventory systems, queueing systems, generalized assignment problem, multi-item/multifacility systems

show abstract

“…Zipkin (1995) examines the performance of LQ on systems with more than two products. Van Houtum et al (1997) derive lower and upper bounds for the mean waiting time for the symmetric longest queue system in order to minimize the base stock levels required to achieve a target fill rate. Wein (1992) allows for asymmetric products and derives an approximating Brownian control problem for the multi-item make-to-stock queuing problem.…”

Section: Literature Reviewmentioning

confidence: 99%

Dynamic control in multi-item production/inventory systems

2016

View full text Add to dashboard Cite

We consider a production/inventory system consisting of one production line and multiple products. Finished goods are kept in stock to serve stochastic demand. Demand is fulfilled immediately if there is an item of the requested product in stock and otherwise it is backordered and fulfilled later. The production line is modeled as a non-preemptive single server and the objective is to minimize the sum of the average inventory holding costs and backordering costs. We investigate the structure of the optimal production policy, propose a new scheduling policy, and develop a method for calculating base stock levels under an arbitrary but given scheduling policy. The performance of the various production policies is evaluated in extensive numerical experiments.

show abstract

The symmetric longest queue system

Cited by 18 publications

References 11 publications

Demand Allocation in Systems with Multiple Inventory Locations and Multiple Demand Sources

Demand Allocation in Systems with Multiple Inventory Locations and Multiple Demand Sources

Demand Allocation in Multiple-Product, Multiple-Facility, Make-to-Stock Systems

Dynamic control in multi-item production/inventory systems

Contact Info

Product

Resources

About