This paper presents an integrated imperfect production inventory model under two layer supply chain management. To ensure the orders, manufacturer convinces the retailer to pay a percentage of the purchasing cost prior to replenish the products and offers the facilities such as (i) delay in payment on the remaining part of the purchasing cost and
(ii) free transportation on the basis of advance payment amount. Time dependent development cost is incurred to maintain the reliability of the production system and as a result it reduces the imperfectness of the product during production. Under such circumstances, an integrated profit function has been developed to find the optimum number of production cycle, optimum number of replenishment cycle and hence reliability parameter of the manufacturing
system, replenishment quantity for the retailer which maximize the integrated profit. Branch and Bound technique is used to obtain the integer solutions. Furthermore, we derived some useful lemmas and algorithms to obtain the optimum solution. Finally, the model has been illustrated with some numerical examples exploring the sensitivity analysis with respect to some parameters and obtains some managerial insights.
Three-layer supply chain in an imperfect production inventory model with two storage facilities under fuzzy rough environment
