NP{hard cases of the single{item capacitated lot{sizing problem have been the topic of extensive research and continue to receive considerable attention. However, surprisingly few theoretical results have been published on approximation methods for these problems. To the best of our knowledge, until now no polynomial approximation method is known which produces solutions with a relative deviati...

The single-item stochastic lot-sizing problem is to find an inventory replenishment policy in the presence of discrete stochastic demands under periodic review and finite time horizon. A closely related problem is the single-period newsvendor model. It is well known that the newsvendor problem admits a closed formula for the optimal order quantity whenever the revenue and salvage values are lin...

We study a two-level uncapacitated lot-sizing problem with inventory bounds that occurs in a supply chain composed of a supplier and a retailer. The first level with the demands is the retailer level and the second one is the supplier level. The aim is to minimize the cost of the supply chain so as to satisfy the demands when the quantity of item that can be held in inventory at each period is ...

Abstract In a single item dynamic lot-sizing problem, we are given time horizon and demand for in every period. The problem seeks solution that determines how much to produce carry at each period, so will incur the least amount of production inventory cost. When remanufacturing option is included, input comprises number returned products period can be potentially remanufactured satisfy demands,...

batch sizing in different planning period is categorized as a classical problem in production planning, that so many exact & heuristic methods have been proposed to solve this problem, each of which considering various aspects of the original problem. the solution obtained from majority – e.g. mrp – is in this format that there may be some periods of idleness or each period should produ...