Solving a Location, Allocation, and Capacity Planning Problem with Dynamic Demand and Response Time Service Level

Carrie Ka Yuk Lin

doi:10.1155/2014/492340

Abstract

Logistic systems with uncertain demand, travel time, and on-site processing time are studied here where sequential trip travel is allowed. The relationship between three levels of decisions: facility location, demand allocation, and resource capacity (number of service units), satisfying the response time requirement, is analysed. The problem is formulated as a stochastic mixed integer program. A simulation-based hybrid heuristic is developed to solve the dynamic problem under different response time service level. An initial solution is obtained from solving static location-allocation models, followed by iterative improvement of the three levels of decisions by ejection, reinsertion procedure with memory of feasible and infeasible service regions. Results indicate that a higher response time service level could be achieved by allocating a given resource under an appropriate decentralized policy. Given a response time requirement, the general trend is that the minimum total capacity initially decreases with more facilities. During this stage, variability in travel time has more impact on capacity than variability in demand arrivals. Thereafter, the total capacity remains stable and then gradually increases. When service level requirement is high, the dynamic dispatch based on first-come-first-serve rule requires smaller capacity than the one by nearest-neighbour rule.

Highlights

For many service systems in the public and private sector, the demand sites are often divided into one or more service regions to reduce the problem size for service delivery planning
This paper examines the combination of a facility location-allocation problem and a queuing problem on a network with response time service level requirement
When problem size increases beyond 100 nodes (Tables 2–4), it becomes increasingly difficult for the mixed integer program to obtain a feasible or improved solution

Summary

Introduction

For many service systems in the public and private sector, the demand sites are often divided into one or more service regions (or zones) to reduce the problem size for service delivery planning. The capacity refers to the number of service units available for dispatch to serve random requests occurring in a region represented in a network of nodes. Examples of such service systems include express delivery, mobile repair service, and emergency systems. This paper examines the combination of a facility location-allocation problem and a queuing problem on a network with response time service level requirement. The planning model includes three types of decisions: (1) number of facilities and locations, (2) allocation of demand sites to each facility, and (3) capacity required at each facility. The service level requirement is imposed on the average response time and/or percentage of served requests with response time within a predetermined limit

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Conclusion