In this study, we consider an imperfect production system in which the manager not only faces the Economic Lot Scheduling Problem, but also needs to conduct multiple inspections during a production lot of any product. Inspection plays an important role in an imperfect production system since it saves the cost from producing and restoring defective items though it also incurs extra inspection cost at the same time. In this study, we employ the common cycle approach in which all the products share the same replenishment cycle, and adopt a consensus inspection policy. The focus of this study is to determine the optimal cycle time and an optimal production and inspection schedule that minimize the total cost per unit time. We formulate a mathematical model in which we take into accounts both the production capacity and inspection capacity constraints. Also, we conduct full theoretical analysis and propose an effective search algorithm for solving an optimal solution. Our numerical experiments demonstrate the effectiveness of the proposed search algorithm.
- Search algorithm