The effect of imperfect production processes on lot-sizing decisions has received a lot of attention in the literature. These efforts have mostly been confined to single-stage production systems. The issue of imperfect production processes has not been adequately addressed in the context of multistage production/inventory systems. In this paper, we propose a production inventory model that takes into account the effect of imperfect production processes, preventive maintenance and inspection errors. Numerical examples are presented for illustrative purposes.
In the real-world industrial settings, products are processed through multi-stage production systems, where raw material is transformed into the final product in a series of processing stages. Although several manufacturing stages are required in many industries (i.e., plastic industry, food processing, and machine industry), increasing automation in manufacturing processes has reduced the number of operations required for simple products and parts of complex products. Two-stage production systems can be found in many applications, for example processing and packaging food, extruding and milling plastics, shearing and punching or rolling and cutting metals Szendrovits (1983). In addition to representing many real-life applications, two-stage models can also be used to approximate more complex multi-stage systems.
Two-stage production systems gained considerable attention in the literature. Szendrovits (1983) proposed several two-stage production/inventory models in which smaller lots are produced at one stage and one larger lot is produced at the other stage. Kim (1999) carried out thorough analysis of the two-stage lot-sizing problem where the production rates are finite at both stages. He divided the problem into different cases. Moreover, he presented an optimal solution procedure for each case. Recently, Hill (2000) offered an alternative way to derive and present similar results. His presentation is more intuitive and concise. Moreover, he allowed the batch sizes at given stage to differ. In addition, his policies give minimum inventory of the finished product.
In the above models, it is assumed that the quality of the items produced is perfect. In general, the quality of product depends on the state of the process. Rosenblatt and Lee (1986), Lee and Rosenblatt (1989), Porteus (1986), Hariga and Ben-Daya (1998), among others, investigated the quality aspect for single-stage production systems. Ben-Daya et al. (2003) proposed imperfect production model with inspection errors. They extended Szendrovits (1983) model by considering the effect of imperfect production processes, inspection errors and preventive maintenance (PM) on lot-sizing decisions. The model calls for PM or restoration with each inspection. Moreover, the reduction in the age of the process after each PM is considered to be constant.
In this paper, we consider production/inventory model for imperfect production processes that incorporates inspection errors and PM. This model is different from the model developed by Ben-Daya et al. (2003) in several aspects. First, we follow Hill's presentation Hill (2000) which keeps the inventory of the finished items as low as possible while minimizing the expected total cost. Second, PM is not necessarily performed with each inspection. Although PM is performed at the time of the inspection, its frequency is a decision variable. Finally, each PM reduces the age of the process by factor which is proportional to the level of PM performed, in other words, more reduction in the age of the process requires higher PM cost.
This paper is organized as follows. The assumptions and necessary notation are described in the next section. In Section 3, the proposed model is presented. A hybrid Hooke and Jeeves–Tabu search solution procedure is presented in Section 4. In Section 5, a sensitivity analysis with respect to key model parameters is conducted. Finally, Section 6 concludes the paper.
This article studies two-stage production inventory system. The proposed model takes into consideration the effect of imperfect production processes inspection errors, and preventive maintenance. We extended Hill's model Hill (2000) which keeps the inventory of the finished items as low as possible while minimizing the expected total cost. In addition, PM is not tied with process inspection. The effect of PM on the behavior of the system is modeled by assuming that PM reduces the age of the process by factor which is proportional to the level of PM performed. In other words, more reduction in the age of the process requires higher PM cost. This model is a step forward in the modeling multistage production systems through the incorporation of real world considerations including quality and preventive maintenance. The effects of the model key parameters on the optimal solution have been investigated as well.