Abstract
The classical assignment problem has been widely applied in span manufacturing, personnel scheduling and transportation, to name just a few areas. Generally, the problem seeks to minimize the cost of assigning a given set of jobs (tasks) to a group of machines (worker). Computationally, the assignment problem is considered “easy” because it can be solved in polynomial time using several efficient algorithms. In this paper, we use a limited-cycle model with multiple periods where the risk itself is also affected greatly by the risks which existed in the earlier periods, and we focus on the property of the optimal assignment with minimized total expected risk (cost) in the limited-cycle model. First, the reset model, a simple model of the limited-cycle model, is presented. Then, the optimal assignment problem under the reset model is defined. After that, the property of the optimal assignment with two special workers is proposed. Finally, the property is proved using a mathematical approach and investigated via numerical experiments with a program in which an algorithm based on the branch and bound method is used.
