A Heuristic Approach to Solve Production Planning Problem with Machine Failure in a Series Parallel Multi-State System

We consider a production system containing a set of machines which are arranged according to a series-parallel configuration. The machines are unreliable and the failure rate of machine depends on the load assigned to the machine. The expected performance of the system is considered to be a non-monotonic function of its load. The issue of machine failure rate depending upon machine load brings the issue of load distribution problem to optimize total production output. This paper considers the integration of load distribution decisions with production planning decision for a given time horizon. The product demands during a specified time horizon are known in advance. The objective is to minimize the sum of capacity change costs, unused capacity costs, setup costs, holding costs, backorder costs, and production costs. The main constraints consist in satisfying the demand over the specified time horizon, and not exceeding available repair resources to repair the breakdown machine. The paper proposes a three phase heuristic approach to solve the integrated load distribution and production planning problem. The efficiency of the proposed heuristic is tested through several numerical examples.