Optimal order and distribution strategies in production networks

Production networks are usually defined as a set of processes utilized to efficiently integrate suppliers, manufacturers, and customers so that goods are produced and distributed in the right quantities, to the right locations, and at the right time and in order to reduce costs while satisfying delivery conditions. We focus on a network of suppliers or producers which order goods from each other, process a product according to orders, and receive payments according to a pricing strategy. Modeling manufacturing systems is characterized by many different scales and several different mathematical approaches. We follow a dynamic approach: we are interested in the time behavior of the entire system. Therefore we introduce a coupled system of ordinary differential delay equations, where time-dependent distribution and order strategies of individual manufacturers influence the flow of goods and the total revenue. We also allow manufacturers to face bankruptcy. All order and distribution strategies are degrees of freedom which can vary in time. We determine them as solution to an optimization problem where additionally economic factors such as production and inventory costs and credit limits influence the maximization of profit. Instead of using a simulation-based optimization procedure, we derive an efficient way to transform the original model into a mixed-integer programing problem.