Joint Requirement of Two Multi-skill Resource Types in Multi-period Multi-site Assignment Problem

Abstract

A classic assignment problem determines how to assign resources to tasks in the best possible way. Over the past years, the classic assignment problem has been extended and more complicated assignment models have been proposed. A multi-period multi-site assignment problem is one extension of the classic assignment problem. The number of site and period are increased to more than one and the decision is extended to consider assigning resources to site while concerning tasks in each site and period. Most multi-period multi-site assignment models do not concern joint of resources for operation; however, in some real-life problems, there is a case in which joint of resources for doing tasks is required. In this study, we consider joint requirement of two multi-skill resource types in the multi-period multi-site assignment problem and propose the mathematical model and heuristic. The developed heuristic is separated into two parts. The first part is to create an initial solution by CPLEX In the second part, to improve solution, algorithms for allocating resources to sites and assigning resources to tasks are developed. The computational experiment is done for studying the characteristic of the proposed problem when joint requirement is added and also evaluating the efficiency of the developed algorithm. The result shows that the complexity of the problem highly depends on the ratio of task requiring one and two resource types and while other parameters are fixed except the number of resource, there is only one range of the number of resource that makes the problem complex. For the efficiency of the algorithm, the developed heuristic can find good solutions in a short time in all ranges of the number of resource in all test problems (average optimal gap of all test problems is 7.25%).