Capacitated production planning with outsourcing in an OKP company

This paper addresses a dynamic capacitated production planning (CPP) problem in small to medium-sized enterprises (SMEs). These companies practise their businesses based on a manufacturing paradigm called one-of-a-kind production (OKP). Typically, they employ outsourcing in their CPP practice. Therefore, the CPP problem in this paper includes outsourcing, which is called the outsourcing CPP problem. The outsourcing strategy considered in this paper has the following features: (1) outsourcing takes place when the demand exceeds the capacity; (2) all excessive demands are outsourced without backlogging; and (3) production, inventory, and outsourcing levels all have a limit. One important difference of the problem considered in this paper from other problems is that the cost functions are considered arbitrarily time-varying. The outsourcing CPP problem is formulated into an optimization problem which captures the mentioned features. The objective of the problem is to minimize the total cost. It is very likely that there is no solution in our model so we propose a necessary and sufficient condition for feasible solutions. Dynamic programming techniques are employed in searching for a global optimal solution with a pseudo-polynomial time. This paper also presents a case study for a real-life problem in an OKP company to illustrate our approach and to show its effectiveness. The case study has shown that our approach is very effective.