Analytics of an Imperfect Four-Layer Production Inventory Model Under Two-Level Credit Period Using Branch-and-Bound Technique

This paper explains an integrated production inventory supply chain model, which consists of a supplier, a manufacturer and a retailer under two-level credit period. One is manufacturer’s credit period offered by the supplier, and other is retailer’s credit period offered by the manufacturer. Here, the manufacturer replenishes raw materials from the supplier and produces non-deteriorating products in some cycles of equal length. It is noted that here four inventory structures have been considered to show the flow of the materials as either raw materials or finished products from supplier to retailer via manufacturer. Also in this model, manufacturer’s imperfect production has been considered. Here imperfect items are not repairable. The retailer receives good finished products from the manufacturer and sells these to his/her customers during some cycles of equal length in total time horizon. Our main objective is to find the optimal number of production and business cycles of the manufacturer such that the integrated system can get the maximum profit. The above discussed model is elaborated with the help of a numerical example, and a sensitivity analysis is done with respect to some parameters used in this model.