The present paper, discuss one of the most challenging subjects for the management namely production planning. It appears to be a hierarchical process ranging from long to medium to short term decisions. Production planning models are divided into two categories which are capacitated and uncapacitated. This paper reviews the literature on singlelevel single-resource lotsizing models and provide...

We consider a family of N items that are produced in, or obtained from, the same production facility. Demands are deterministic for each item and each period within a given horizon of T periods. If in a given period an order is placed, setup costs are incurred. The aggregate order size is constrained by a capacity limit. The objective is to find a lot-sizing strategy that satisfies the demands ...

Introduction. We study a class of capacitated stochastic lot-sizing inventory control problems with stochastic, non-stationary and correlated demands that evolve over time. Economies of scale and capacity constraints exist in many practical scenarios. However, models with fixed ordering costs and capacity constraints are typically computationally intractable, and even the structure of the optim...

The integration of sequencing decisions in lot-sizing and scheduling problems has received an increased attention from the research community due to its inherent applicability to the real-world problems. In this paper, we develop and solve a synchronized and integrated two-level lot-sizing and scheduling problem motivated by a real-world problem arisen in the soft drink production. The soft dri...

A parallel genetic algorithm is presented to solve the well-known ca-pacitated lot-sizing problem. The approach is implemented on a massively parallel single instruction multiple data architecture with 16384 4-bit processors. Based on a random keys representation a schedule is backward oriented obtained which enables us to apply a very simple capacity check. Genetic algorithms are a general pur...

This paper conducts a probabilistic analysis of an important class of heuristics for multiitem capacitated lot sizing problems. We characterize the asymptotic performance of so-called progressive interval heuristics as T , the length of the planning horizon, goes to infinity, assuming the data are realizations of a stochastic process of the following type: the vector of cost parameters follows ...

Lot-sizing and capacity planning are important supply chain decisions, and competition and cooperation affect the performance of these decisions. In this paper, we look into the dynamic lot sizing and resource competition problem of an industry consisting of multiple firms. A capacity competition model combining the complexity of time-varying demand with cost functions and economies os scale ar...

One of the most important tasks operations manager are confronted with is to determine production quantities over a medium-size planning horizon such that demand is met, scarce production facilities are not overloaded and that the sum of holding and setup costs is minimized. For the single machine case the well-known Capacitated Lot-Sizing Problem (CLSP) has been proposed to determine minimum c...

This is a summary of the author’s PhD thesis supervised by Philippe Chrétienne and Safia Kedad-Sidhoum and defended in December 2005 at the Université Pierre et Marie Curie (Paris VI). The thesis is written in French and is available from http://absi.nabil.free.fr/ABSI-Thesis.pdf. This work mainly deals with multi-item capacitated lot-sizing problems with setup times, shortages on demand and sa...

In this paper, we study a Capacitated Lot Sizing Problem with Stochastic Setup Times (CLSP-SST).We describe a mathematical model that considers both regular costs (including production, setup and inventory holding costs) and expected overtime costs (related to the excess usage of capacity). The CLSP-SST is formulated as a two-stage stochastic programming problem. A procedure is proposed to effe...