An integrated production–inventory model with raw material, production and final product deteriorations

Typical models for the production planning problem assume a perfect production process. However, the production process may be affected by several factors, such as the deterioration of raw materials. In this case, the quality of the items produced could be decreased and the production could be reduced and/or stopped. Thus we consider in this paper an integrated production inventory model where raw materials, as well as items, are subject to deterioration. Most of the available models assume a single production rate independent of the deterioration of raw materials while one recent model assumes one possible shift in the production rate. This paper contributes to the existing literature by generalising this previous model to the case of unlimited shifts, to approach the real life problems in a more realistic way. In addition, we relax the assumption of constant deterioration, production and demand rates and consider them general functions of time. To derive an optimal production schedule, we develop an exact formula for the total inventory cost per unit of time. A potential application of our model is discussed and an illustrative example with sensitivity analysis is provided in order to investigate the effectiveness of the proposed model.