NII Technical Reports
National Institute of Informatics
| Title | On Long-Term Optimal Production-Inventory Plan for a Closed Loop Supply Chain |
| Authors | Oscar Salviano(1), Frederic Andres(2) |
| Abstract | Middle and long-term inventory-production plans have deserved huge interest of managers of supply chains since the 80’s. However, from 90’s to now, providing plans to the reverse channel of supply chains become also an important business practice. In this report, we are interested in developing long-term plans for closed-loop supply chains that allow managers building future production scenarios with minimum costs. In this way, we consider a stochastic quadratic problem subject to linear discrete-time inventory-production systems with probabilistic constraints. The objective of this problem is to determine long-term optimal production plan that allows managers attending demand for a single product. Products can be produced by manufacturing from a forward channel and/or by remanufacturing from a backward (i.e. reverse) channel. The demand fluctuation is a random variable, with monthly mean and standard deviation previously known. In its turn, the rate of return is deterministic, but with the average monthly rate determined from a percentage of the average levels of demand taken with a delay of some period. The random fluctuation of demand makes the serviceable inventory system in the forward channel a stochastic process. As a consequence, the variance of serviceable inventory grows over the periods of the planning horizon. It is shown that such a growing can make the stochastic problem infeasible. In order to mitigate such variability, a feedback gain that relates remanufacture rate to serviceable inventory level is provided from a minimum variance problem. As a result, an optimal long-term plan is developed from an equivalent Mean Value problem whose constraints are regulated by this gain. A simple example shows that optimal plans with gain have better performance than optimal plans that do not use a gain. Based on this example, we also evaluate the concept of the green company. In this case, we assume the premise that how less we discard more we are contributing to preserving the environment. Thus, we compare our optimal long-term solution with another one where the cost of discarding is three times more expensive; in the sequence, we make our conclusions about the benefits of being a green company and how much that can cost. At the end of the document, appendixes with additional information about the modeling process and other issues related to this study are provided. |
| Language | English |
| Published | February 22, 2017 |
| Pages | 25p |
| PDF File | 17-001E.pdf |