Pricing and production lot-size/scheduling with finite capacity for a deteriorating item over a finite horizon
Although the lately evolved manufacturing technologies such as enterprise resource planning (ERP) provide a unified platform for managing and integrating core business processes within a firm, the decision-making between marketing and production planning still remains rather disjoint. It is due in large parts to the inherent weaknesses of ERP such as the fixed and static parameter settings and uncapacitated assumption. To rectify these drawbacks, we propose a decision model that solves optimally the production lot-size/scheduling problem taking into account the dynamic aspects of customer's demand as well as the restriction of finite capacity in a plant. More specifically, we consider a single product that is subject to continuous decay, faces a price-dependent and time-varying demand, and time-varying deteriorating rate, production rate, and variable production cost, with the objective of maximizing the profit stream over multi-period planning horizon. We propose both coordinated and decentralized decision-making policies that drive the solution of the multivariate maximization problem. Both policies are formulated as dynamic programming models and solved by numerical search techniques. In our numerical experiments, the solution procedure is demonstrated, comparative study is conducted, and sensitivity analysis is carried out with respect to major parameters. The numerical result shows that the solution generated by the coordinated policy outperforms that by the decentralized policy in maximizing net profit and many other quantifiable measures such as minimizing inventory investment and storage capacity. We consider a manufacturing firm who produces and sells a single product that is subjected to continuous decay over a lifetime, faces a price-dependent and time-varying demand function, shortages are allowed and a completely backlogged, and has the objective of determining price and production lot-size/scheduling so as to maximize the total profit stream over multi-period planning horizon. We develop a tactical-level decision model that solves the production scheduling problem taking into account the dynamic nature of customer's demand which is partially controllable through pricing schemes. As analogous to the sales and operations planning, the proposed scheme can be used as a coordination center of the APS system within a generic enterprise resource planning framework which integrates and coordinates distinct functions within a firm. This paper differs from the existing works in several ways. First, we propose a dynamic version of the joint pricing and lot-size/scheduling problem taking into account the capacitated constraint. Second, several key factors being considered in the model, such as the demand rate, deteriorating rate, production rate, and variable production cost are assumed time-varying that reflect the dynamic nature of the market and the learning effect of the production system. A third difference between the past research and ours is that the price can be adjusted upward or downward in our model, making the proposed pricing policy more responsive to the structural change in demand or supply.
deterioration time-varying demand dynamic programming lot-size and scheduling periodic pricing