Results 1  10
of
29
Heuristic Scheduling of Parallel Heterogeneous Queues with SetUps
 MANAGEMENT SCIENCE
, 1996
"... We consider the problem of allocating a single server to a system of queues with Poisson arrivals. Each queue represents a class of jobs and possesses a holding cost rate, general service distribution, and general setup time distribution. The objective is to minimize the expected holding cost due t ..."
Abstract

Cited by 20 (7 self)
 Add to MetaCart
We consider the problem of allocating a single server to a system of queues with Poisson arrivals. Each queue represents a class of jobs and possesses a holding cost rate, general service distribution, and general setup time distribution. The objective is to minimize the expected holding cost due to the waiting of jobs. A setup time is required to switch from one queue to another. We provide a limited characterization of the optimal policy and a simple heuristic scheduling policy for this problem. Simulation results demonstrate the effectiveness of our heuristic over a wide range of problem instances.
Analysis of a decentralized productionInventory system
 Sloan School of Management, MIT
, 1999
"... We model an isolated portion of a competitive supply chain as a M/M/1 maketostock queue. The retailer carries finished goods inventory to service a Poisson demand process, and specifies a policy for replenishing his inventory from an upstream supplier. The supplier chooses the service rate, i.e., c ..."
Abstract

Cited by 20 (0 self)
 Add to MetaCart
(Show Context)
We model an isolated portion of a competitive supply chain as a M/M/1 maketostock queue. The retailer carries finished goods inventory to service a Poisson demand process, and specifies a policy for replenishing his inventory from an upstream supplier. The supplier chooses the service rate, i.e., capacity, of his manufacturing facility, which behaves as a singleserver queue with exponential service times. Demand is backlogged and both agents share the backorder cost. In addition, a linear inventory holding cost is charged to the retailer, and a linear cost for building production capacity is incurred by the supplier. The inventory level, demand rate and cost parameters are common knowledge to both agents. Under the continuousstate approximation that the M/M/1 queue has an exponential rather than geometric steadystate distribution, we characterize the optimal centralized and Nash solutions, and show that a contract with linear transfer payments replicates a cost sharing agreement and coordinates the system. We also compare the total system costs, the agents ’ decision variables and the customer service levels of the centralized versus Nash versus Stackelberg solutions. 1
Managing Stochastic Multiproduct Systems: Model, Measures, and Analysis
 Operations Research
, 1995
"... We consider a model for managing a single stage that produces multiple items. The production rates are finite and there are switchover times. The interarrival times and quantities of demands for the items are random, and demand may occur for a set of items. We consider order focussed measures: co ..."
Abstract

Cited by 13 (4 self)
 Add to MetaCart
We consider a model for managing a single stage that produces multiple items. The production rates are finite and there are switchover times. The interarrival times and quantities of demands for the items are random, and demand may occur for a set of items. We consider order focussed measures: cost based on response times, service levels based on quoted lead times and Type1 service. We operate the stage in the following manner: (1) There is a cyclic schedule that determines the sequence of items and the number of times a particular item is produced in a cycle; (2) Given a cyclic schedule, production of each item follows a modified basestock policy or a (s,S) policy. We present a simulation based procedure to obtain good values for the base stock levels or S (for any fixed Ss) for each of the above performance measures. Numerical results indicate that good solutions can be obtained with modest computational effort. We also report on a real world implementation of this mode...
Iterative approximation of klimited polling systems
, 2006
"... The present paper deals with the problem of calculating queue length distributions in a polling model with (exhaustive) klimited service under the assumption of general arrival, service and setup distributions. The interest for this model is fueled by an application in the field of logistics. Knowl ..."
Abstract

Cited by 9 (0 self)
 Add to MetaCart
(Show Context)
The present paper deals with the problem of calculating queue length distributions in a polling model with (exhaustive) klimited service under the assumption of general arrival, service and setup distributions. The interest for this model is fueled by an application in the field of logistics. Knowledge of the queue length distributions is needed to operate the system properly. The multiqueue polling system is decomposed into singlequeue vacation systems with klimited service and statedependent vacations, for which the vacation distributions are computed in an iterative approximate manner. These vacation models are analyzed via matrixanalytic techniques. The accuracy of the approximation scheme is verified by means of an extensive simulation study. The developed approximation turns out be accurate, robust and computationally efficient.
Tactical Planning Models for Supply Chain Management
 Elvesier Publishers, 2003. OR/MS Handbook on Supply Chain Management: Design, Coordination and Operation
, 2004
"... ..."
(Show Context)
Dynamic Scheduling to Minimize Lost Sales Subject to Setup Costs
, 1998
"... We consider scheduling a shared server in a twoclass, maketostock, closed queueing network. We include server switching costs and lost sales costs (equivalently, server starvation penalties) for lost jobs. If the switching costs are zero, the optimal policy has a monotonic threshold type of sw ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
We consider scheduling a shared server in a twoclass, maketostock, closed queueing network. We include server switching costs and lost sales costs (equivalently, server starvation penalties) for lost jobs. If the switching costs are zero, the optimal policy has a monotonic threshold type of switching curve provided that the service times are identical. For completely symmetric systems without setups, it is optimal to serve the longer queue. Using simple analytical models as approximations, we derive a heuristic scheduling policy. Numerical results demonstrate the effectiveness of our heuristic, which is typically within 10% of optimal. We also develop and test a heuristic policy for a model in which the shared resource is part of a series network under a CONWIP release policy.
Heavy Traffic Analysis of the Dynamic Stochastic InventoryRouting Problem
"... We analyze three queueing control problems that model a dynamic stochastic distribution system, where a single capacitated vehicle serves a finite number of retailers in a maketostock fashion. The objective in each of these vehicle routing and inventory problems is to minimize the long run average ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
We analyze three queueing control problems that model a dynamic stochastic distribution system, where a single capacitated vehicle serves a finite number of retailers in a maketostock fashion. The objective in each of these vehicle routing and inventory problems is to minimize the long run average inventory (holding and backordering) and transportation cost. In all three problems, the controller dynamically specifies whether a vehicle at the warehouse should idle or embark with a full load. In the first problem, the vehicle must travel along a prespecified (TSP) tour of all retailers, and the controller dynamically decides how many units to deliver to each retailer. In the second problem, the vehicle delivers an entire load to one retailer (direct shipping) and the controller decides which retailer to visit next. The third problem allows the additional dynamic choice between the TSP and direct shipping options. Motivated by existing heavy traffic limit theorems, we make a time scale decomposition assumption that allows us to approximate these queueing control problems by diffusion control problems, which are explicitly solved in the fixed route problems, and numerically solved in the dynamic routing case. Simulation experiments confirm that the heavy traffic approximations are quite accurate over a broad range of problem parameters. Our results lead to some new observations about the behavior of this complex system. A prototypical example of the inventoryrouting problem (IRP) is the challenge faced by a large oil company as it distributes gasoline to its various gas stations: several warehouses hold inventory of a particular item (gasoline) and serve a set of retailers (stations) in a maketostock fashion; arriving customers (automobiles) consume the product at these retail sites, and a fleet of finite capacity vehicles (tanker trucks) is used to transport the product from the warehouse to the various retailers. The management decisions involved in the design and operation of such a system are manyfold and complex. Traditionally, a hierarchical decomposition of the problem is used to allow for a solvable model
General Dynamic Programming Algorithms Applied To Polling Systems
 COMMUNICATIONS IN STATISTICS: STOCHASTIC MODELS
, 1998
"... We formulate the problem of scheduling a single server in a multiclass queueing system as a Markov decision process under the discounted cost and the average cost criteria. We develop a new implementation of the modified policy iteration (MPI) dynamic programming algorithm to efficiently solve prob ..."
Abstract

Cited by 4 (3 self)
 Add to MetaCart
We formulate the problem of scheduling a single server in a multiclass queueing system as a Markov decision process under the discounted cost and the average cost criteria. We develop a new implementation of the modified policy iteration (MPI) dynamic programming algorithm to efficiently solve problems with large state spaces and small action spaces. This implementation has an enhanced policy evaluation (PE) step and an adaptive termination test. To numerically evaluate various solution approaches, we implemented value iteration and forms of modified policy iteration, and we further developed and implemented aggregationdisaggregation based (replacement process decomposition and groupscaling) algorithms appropriate to controlled queueing system models. Tests provide evidence that MPI outperforms the other algorithms for both the discounted cost and the average cost optimal polling problems. In light of the complexity of implementation for the aggregationdisaggregation based algorithm...
Mean value analysis for polling systems in heavy traffic
 In Proceedings of ValueTools, Pisa Article
, 2006
"... In this paper we present a new approach to derive heavytraffic asymptotics for polling models. We consider the classical cyclic polling model with exhaustive service at each queue, and with general servicetime and switchover time distributions, and study its behavior when the load tends to one. F ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
(Show Context)
In this paper we present a new approach to derive heavytraffic asymptotics for polling models. We consider the classical cyclic polling model with exhaustive service at each queue, and with general servicetime and switchover time distributions, and study its behavior when the load tends to one. For this model, we explore the recently proposed mean value analysis (MVA), which takes a new view on the dynamics of the system, and use this view to provide an alternative way to derive closedfrom expressions for the expected asymptotic delay; the expressions were derived earlier in [32], but in a different way. Moreover, the MVAbased approach enables us to derive closedform expressions for the heavytraffic limits of the covariances between the successive visit periods, which are key performance metrics in many application areas. These results, which have not been obtained before, reveal a number of insensitivity properties of the covariances with respect to the system parameters under heavytraffic assumptions, and moreover, lead to simple approximations for the covariances between the successive visit times for stable systems. Numerical examples demonstrate that the approximations are accurate when the load is close enough to one.
Setting basestock levels in multiproduct systems with setups and random yield (Working paper, Olin School of Business
, 2004
"... This paper shows how to set basestock levels in a multiproduct system with setups and random yield. The system is represented by a polling model and the inventory level of each product is controlled using a basestock policy. When the queue is empty, the inventory level is equal to the basestock leve ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
(Show Context)
This paper shows how to set basestock levels in a multiproduct system with setups and random yield. The system is represented by a polling model and the inventory level of each product is controlled using a basestock policy. When the queue is empty, the inventory level is equal to the basestock level, thus the server will continue to serve the queue until it is empty. If the capacity of the queue is equal to the inventory allocated to the item, then when the queue is full, inventory is fully depleted and new demand is either backlogged, lost or expedited. Defects are routed to temporary storage queues associated with each item, and then routed back to the original queue for service during the next cycle. For a system with backlogging, we provide a cost function that is minimized by solving N single item newsvendor problems. For a system with lost sales or expediting, we introduce a cost function and provide a heuristic for finding the basestock levels. The effectiveness of the heuristic and accuracy of the cost approximation are validated through numerical tests.