An integrated production-inventory model with defective item dependent stochastic credit period

•An integrated production inventory model for defective item with stochastic credit period has been studied.•Manufacturer's offered credit period depends on the defective ratio of the item.•Defective ratio of the item is assumed to be random which follows beta distribution of first kind.•The lead time demand is also assumed to be random follows normal distribution.•Solution procedures and numerical examples for three cases are performed. Sensitivity analysis has been carried out.

In this paper an integrated production-inventory model has been developed for a defective item in a business of a buyer and a manufacturer. After production the manufacturer sells the packed products of the item to the buyer in some lots and then the buyer sells these products to the customer after checking them. There have chances to get the defectiveness of the products. So in this paper, it has been considered that the defective ratio of the item is random to be assumed as follows a beta distribution of first type. To compensate the losses due to defectiveness, the manufacturer offers a defective ratio dependent stochastic credit period to the buyer. Here also the lead time demand has been considered as a normal distribution and the lead time is composed of the cycle period and fixed delay time due to machinery set-up, waiting, transportation, etc. The integrated profit functions have been formulated for three cases which are illustrated numerically and solved by some proposed solution procedures. Finally a sensitivity analysis has been carried out with respect to some parameters.