Control policy and algorithm analysis for production planning and inventory control

Abstract

In this thesis, research literature is reviewed in the field of production planning and inventory control. The scope of the work focuses on the optimal policies and algorithm analysis for stochastic and deterministic models from production planning and inventory control. Specifically, three fundamental mathematical models are investigated in detail. For the single product periodic review problem with setup costs and equal capacity constraint, this study considers the model where inventory cost function is convex, which has not been investigated deeply in the literature earlier. The optimal policy with property of X-Y band is characterized. The average computation time of newly designed algorithm grows more or less doubly with the periodic numbers, which is more efficient than the others for solving such a model so far. This study also considers a particular model in stochastic multiple product flexible manufacturing system, where the respective model parameter is the same for each product. The obtained results particularly characterize the optimal hedging point policy, and also give a chance to observe the order policy of the general model which has been an open problem for about four decades. Further, parameter analysis is conducted for the uncapacitated economic lot-sizing problem where backlogging is allowed, and some new results are achieved. For instance, it is proved that there are critical values for periodic setup and unit production costs respectively. If the setup cost or unit production cost is higher than their respective critical value, the period will be a production period; if it is equal to or lower than the value, the period will be a non-production period. Recommendations for future research in this field are also proposed. Specifically, a hypothesis is suggested to extend the special stochastic multiple-product model into a general one.

Multi-period inventory sharing between independent retailers : models for different degrees of information sharing

“…Chen (2004) shows the optimal hedging point policy for stochastic two-item, periodic review, single facility, flexible manufacturing systems. Later Feng (2005) extends the control policy in Chen (2004) to multiple products system and the results in Van Hoesel and Wagelmans (1993) to allow for backlogging.…”