In this paper we study sensitivity analysis of the uncapacitated single level economic lot-sizing problem, which was introduced by Wagner and Whitin about thirty years ago. In particular we are concerned with the computation of the maximal ranges in which the numerical problem parameters may vary individually, such that a solution already obtained remains optimal. Only recently it was discovere...

We present a fully polynomial time approximation scheme (FPTAS) for a capacitated economic lot-sizing problem with a monotone cost structure. An FPTAS delivers a solution with a given relative error ε in time polynomial in the problem size and in 1/ε. Such a scheme was developed by van Hoesel and Wagelmans [8] for a capacitated economic lot-sizing problem with monotone concave (convex) producti...

In this paper we discuss two basic geometric techniques that can be used to speed up certain types of dynamic programs. We first present the algorithms in a general form, and then we show how these techniques can be applied to the economic lot-sizing problem and extensions. Furthermore, it is illustrated that the geometric techniques can be used to give elegant and insightful proofs of structur...

This study deals with a two-level supply chain consisting of one manufacturer and one retailer. We consider an integrated production inventory system where the manufacturer processes raw materials in order to deliver finished product with imperfect quality to the retailer, where number of defective product has a uniform distribution. The retailer receives product and conducts a 100% inspection....

An important special case of the economic lot-sizing problem is the one in which there are no speculative motives to hold inventory, i. e., the marginal cost of ]n'oducing one unit m some period plus the cost of holding it until some future period is at least the marginal production cost in the latter period. It is already known that this special case can be solved in linear time. In this paper...

This paper considers the joint economic lot-sizing problem (JELP) for multi-layer supply chain with multi-retailers and single manufacturer and supplier. The paper extends the work of (Ben-Daya et al., 2013) and relaxes the assumption of deterministic demand and constant holding and ordering costs. The paper proposes modifying four computational intelligent algorithms to solve mixed integer pro...

In this paper we consider the uncapacitated economic lot-size model, where demand is a deterministic function of price. In the model a single price need to be set for all periods. The objective is to find an optimal price and ordering decisions simultaneously. In 1973 Kunreuther and Schrage proposed an heuristic algorithm to solve this problem. The contribution of our paper is twofold. First, w...

We study the classical multistage lot sizing problem that arises in distribution and inventory systems. A celebrated result in this area is the 94% and 98% approximation guarantee provided by power-of-two policies. In this paper, we propose a simple randomized rounding algorithm to establish these performance bounds. We use this new technique to extend several results for the capacitated lot si...

We propose a new algorithm to solve lot sizing, tool allocation and machining conditions optimization problems simultaneously to minimize total production cost in a CNC environment. Most of the existing lot sizing and tool management methods solve these problems independently using a two-level optimization approach. Thus, we not only improve the overall solution by exploiting the interactions a...