در یک طرح سرمایه گذاری تولید مطلوب برای یک زنجیره عرضه حلقه بسته شده

Middle and long-term inventory-production plans have deserved interest of managers of supply chains since the 80’s. However, from 90’s to now, to plan a reverse channel has been also an important business practice. This paper deals with such an issue. In this way, a chance constraint, stochastic quadratic problem subject to linear discrete-time inventory-production systems is formulated. The objective of this problem is to meet the demand for a single product, which can be manufactured from a forward channel and/or remanufactured (refurbished) from a backward channel. The demand fluctuation is a random variable, with mean and standard-deviation known over time. On the other hand, the return rate is assumed deterministic, but with some periods of delay over the planning horizon. The random nature of demand fluctuation affects the variability of serviceable inventory variable in the sense of its variance increases over periods of planning horizon. In order to mitigate such variability, a feedback gain, which relates remanufactured/refurbished rate to serviceable inventory level, is considered. This gain is obtained from a minimum variance problem. As a result, an optimal plan is developed from an equivalent Mean Value problem that has constraints regulated by the gain. Through a simple example, it will be shown that the open-loop optimal plan obtained with problem’s constraints fixed by optimal gain has a better performance than the optimal plan provided without such a gain.