Adjustment of credit period and stock-dependent demands in a supply chain model with variable imperfectness

Abstract

In this model, a supply chain model has been developed where a manufacturer continuously transports perfect quality items at no cost to a distribution center to maintain the market demand. At the beginning of the process, the production process is in an "in-control" state, but after a random time, it goes to an "out-of-control" state. Thus the production process produces perfect as well as imperfect items in this state. The rate of imperfect production depends on production rate and production-run length in the "out-of-control" state. The unit production cost of the manufacturer depends on the production rate which indicates that the higher production rate is the cause of higher production cost if it exceeds the normal production rate set by the manufacturer. The manufacturer provides a credit period to the distributor to increase his sales growth. In the competitive business world, credit period affects the demand rate of a retailer/buyer due to its late payment facility. So, here, credit period dependent demand function is introduced for the distributor. During the festive season, demand factor of products is usually affected by stock level. Also, for some types of products (such as clothing), the demand factor depends on its stock level. Thus we have considered stock-dependent demand function for the customers. Now, in an infinite time horizon, the problem is how they adjust their demands to sustain the whole system's financial  flow. The novelty of this model is to analyze the compatibility of this two-type of demand in their businesses so that both can maintain their profits. Also, there is another credit length which is offered by the distributor. The proposed model has been discussed in type-2 fuzzy environment due to the uncertainty of the credit period. The purpose of this model is to optimize the integrated profit of the system by optimizing production rate and production-run time. Finally, numerical examples have been provided to illustrate the feasibility of both crisp and fuzzy model and some conclusions are derived conducting a sensitivity analysis of different parameters.