Optimal control of production and distribution in a supply chain system operating under a JIT delivery policy

Abstract

This research deals with a supply chain system where the production or manufacturing facility operates under a just-in-time (JIT) environment, and the facility consists of raw material suppliers, manufacturers, and retailers where inventory of raw materials, work-in-process, and finished goods are involved, respectively. This work considers that the production of finished goods in one cycle starts just after the production or uptime in preceding cycle to minimize the idle time of the facility. Considering this scenario, inventory models are developed for different delivery situations: (a) perfect matching condition where no finished good remains after the shipments and (b) imperfect matching condition where some finished goods remain after the shipments. In this research, the problems are categorized as integer and mixed integer non-linear programming problems which are solved to find optimum number of orders and shipments, optimum production quantity, and minimum system cost. Moreover, multi-supplier and multi-buyer operations, where raw materials are ordered from different suppliers and finished goods are delivered to different customers, are considered. In addition to these problems, a single facility lot-sizing model is applied in perfect and imperfect matching cases, and, multi-supplier and multi-buyer case, to concentrate on more practical supply chain environments. All the problems described in this research are non-convex functions for which the closed form solutions are cumbersome. Therefore, the heuristic solutions are developed to find the optimal lot-sizing techniques. Additionally, the multi-supplier and multi-buyer problem is solved with the help of integer approximation and the divide and conquer rule. The solutions are tested through numerical examples. Furthermore, the sensitivity analyses are performed to observe the variations of the different cost functions. Also, this research proposes an alternate delivery schedule of finished product supply, for which both manufacturers and buyers will be benefited economically. The production and supply chain management play a significant role for the necessary amounts of materials and parts arrive at the proper time and place. With the models obtained in this research, managers can quickly respond to consumers' demand by determining the right policies to order raw materials, to manage their production schedule efficiently and to deliver finished goods just-in-time.