Optimal Decision Of Manufacturing And Remanufacturing Under Return Compensation Policy

In recent years, energy shortages and environmental pollution problems havebecome increasingly prominent, remanufacturing as an effective way that not onlysolve the problems, but also reduce production costs, has attained more and moreattention from the government and enterprises. However, it also brings manydifficulties to firms. In this paper, we consider a return compensation policy foracquiring used products from customers. Under this policy, the return quantity of usedproducts is a proportion of demand. We study an optimal problem of manufacturingand remanufacturing with dependent return and demand. Our main results andcontributions are as follows:1. The paper studies a two-period inventory system and formulate the probleminto a three-stage stochastic programming problem, where the firm needs to makedecisions on replenishment quantity of new raw material inventory in each period andthe production quantities of manufacturing and remanufacturing ways. We give theoptimal production policy of manufacturing and remanufacturing ways for therealized demand and prove the objective function for each stage to be concave in theinventory replenishment quantity. Moreover, we prove that the basic inventory policyis still optimal for each period and give the analytical conditions of the optimalinventory levels which are unrelated to acquisition price. Finally, we investigatenumerical studies to analyze managerial insights.2. The paper considers a production planning problem in a multi-period system.The firm needs to make decisions on return price, replenishment quantity of new rawmaterial inventory in each period and the production quantities of manufacturing andremanufacturing ways. We first propose a Nominal model. Then a robust optimizationapproach is applied to deal with the uncertainty of the problem through formulating arobust programming model. Finally, we provide a set of numerical examples to verifythe robustness of the solution.