Closed-loop Lot-sizing Problem With Supply And Demand Uncertainties:A Robust Optimization Approach

During recent years,the market competition of electronic products is becoming more and more intense,cost reduction has become one of manufacturers' key focuses,and environmental regulations are tighter than before,many companies are required to take the responsibility to handle returned items.Hence,it is critical for manufacturers to carefully make production planning beforehand and reuse parts from returned items.However,minimizing total cost in the real manufacturing environment is often tough because of the uncertainties in product demands and number of returned items in different periods.In this paper,we focus on a closed-loop production planning and inventory control problem commonly encountered in the real manufacturing practice of electronic device manufacturers,where manufacturers product new items using raw materials and remanufactured items using both raw materials and returned items at the same time,and the new item demand can be satisfied by remanufactured ones,but not vice versa.There are several capability constraints regarding to manufacturing and disposal processes in each period.Manufacturers have to determine numbers of new and remanufactured items to be produced,returned items to be disposed and new items to be used to satisfy remanufactured demand in each period in a finite planning horizon.The aim is to minimize the total cost including new,remanufactured and returned items' unit costs,setup costs,holding costs and substitution costs over multiple time intervals.We firstly present a deterministic linear model for this particular problem,then we take into consideration the uncertainty of the new item demand,the remanufactured item demand and the returned item flow independently and form 3 robust models respectively,afterwards,we form a new robust model which considers the 3 uncertainties simultaneously,which has rarely been studied in the existing literature,all these models allow us to determine the influences of different sources of uncertainty on production planning separately and altogether.During the process,a robust optimization approach based on uncertain budgets is adopted to leverage the robustness.Extensive numerical experiments are conducted on both the nominal model and its several robust counterparts to help schedulers understand the changes brought by different uncertainties and we also generate a lot of useful managerial insights within this closed-loop manufacturing system,and the results show that the proposed model is a flexible tool which enables us to better balance the optimal solutions and the robustness.Finally,we analyze the probability of constraint violation in each period with different budgets of uncertainty.To the best of our knowledge,this is the first time a cumulative probability of constraint violation is calculated,and based on this,we also provide a simple method for managers who hope to control the probability of constraint violation under a certain level by designing budgets of uncertainty.