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...

Coordinated replenishment problems are common in manufacturing and distribution when a family of items shares a common production line, supplier, or a mode of transportation. In these situations the coordination of shared, and often limited, resources across items is economically attractive. This paper describes a mixed-integer programming formulation and Lagrangian relaxation solution procedur...

Despite its great applicability in several industries, the combined cutting stock and lot-sizing problem has not been sufficiently studied because of its great complexity. This paper analyses the trade-off that arises when we solve the cutting stock problem by taking into account the production planning for various periods. An optimal solution for the combined problem probably contains non-opti...

This paper addresses a mixed integer programming (MIP) formulation for the multi-item uncapacitated lot-sizing problem that is inspired from the trailer manufacturer. The proposed MIP model has been utilized to find out the optimum order quantity, optimum order time, and the minimum total cost of purchasing, ordering, and holding over the predefined planning horizon. This problem is known as NP...

This paper deals with a problem of determining lot-sizes of jobs in a real-world job shop-scheduling in the presence of uncertainty. The main issue discussed in this paper is lot-sizing of jobs. A fuzzy rule-based system is developed which determines the size of lots using the following premise variables: size of the job, the static slack of the job, workload on the shop floor, and the priority...

0377-2217/$ see front matter 2012 Elsevier B.V. A http://dx.doi.org/10.1016/j.ejor.2012.11.044 ⇑ Corresponding author. Tel.: +33 (0)3 87 31 56 25 E-mail addresses: [email protected] (N. Absi), dauzere Pérès), [email protected] (S. Kedad-Sidhou inp.fr (B. Penz), [email protected] (C This paper introduces new environmental constraints, namely carbon emission constraints, in ...

In this research we develop mathematical models of Joint Economic Lot-sizing Problem (JELP) in a situation when a supplier offers time-based temporary price discounts to a buyer during a sale period. To respond this, the buyer places a special order with higher quantity. In literature, it has been assumed that the buyer tends to place the special order at the end of the sale period. We relax th...

To establish production plans or replenishment plans, firms use forecasting systems. Such a system is composed of a forecasting method and a lot-sizing method. We propose a scheme to evaluate the reliability of such a system. This evaluation is based on the impact of demand randomness on the long run total cost. The scheme is illustrated with a system including an exponential smoothing techniqu...

While many review articles exist on (deterministic) lot sizing models used in the context of price and quantity discounts, buyer–vendor coordination, supply chain management, and joint economic lot sizing problems, they do not convey the impact of important findings which date back to at least 2002, or, in hindsight, to 1984. As a result, many recent articles still model the financial implicati...