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Sequencing and scheduling: algorithms and complexity

Lot sizing is one of the most important and also one of the most difficult problems in production planning. This subject has been studied extensively in the literature. In this article, we consider single-level lot sizing problems, their variants and solution approaches. After introducing factors affecting formulation and the complexity of production planning problems, and introducing different variants of lot sizing and scheduling problems, we discuss single-level lot sizing problems, together with exact and heuristic approaches for their solution. We conclude with some suggestions for future research.

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The capacitated lot sizing problem: a review of models and algorithms

In this paper we present a reference framework and a classification of warehouse design and control problems Based on this framework, we review the existing literature on warehousing systems and indicate important gaps In particular, we emphasize the need for design oriented studies, as opposed to the strong analysis oriented research on isolated subproblems that seems to be dominant in the current literature

Warehouse design and control: framework and literature review

Research on warehouse design and performance evaluation: A comprehensive review

Publisher Summary This chapter discusses different types of sequencing and scheduling problems, and describes different types of algorithms and the concepts of complexity theory. A class of deterministic machine scheduling problems has been introduced in the chapter. The chapter also deals with the single machine, parallel machine and multi-operation problems in this class, respectively. The two generalizations of the deterministic machine-scheduling model have been presented in the chapter. A deterministic scheduling model may give rise to various stochastic counterparts, as there is a choice in the parameters that are randomized, in their distributions, and in the classes of policies that can be applied. A characteristic feature of these models is that the stochastic parameters are regarded as independent random variables with a given distribution and that their realization occurs only after the scheduling decision has been made. In the deterministic model, one has perfect information, and capitalizing on it in minimizing the realization of a performance measure may require exponential time.

Chapter 9 Sequencing and scheduling: Algorithms and complexity

A decomposition algorithm for the single machine total tardiness problem

The multi-item capacitated lot-sizing problem consists of determining the magnitude and the timing of some operations of durable results for several items in a finite number of processing periods so as to satisfy a known demand in each period. The subgradient algorithm implemented to minimize the processing costs is based on a Lagrangean relaxation of the capacity constraints imposed on the resources. The method incorporates a primal partitioning scheme—with a network flow subproblem—to obtain good feasible solutions.

Lagrangean Relaxation for the Multi-Item Capacitated Lot-Sizing Problem: A Heuristic Implementation

This paper considers the problem of scheduling n jobs, each having a processing time, a due date and a weight, on a single machine to minimize the weighted number of late jobs. An O(n log n) algorithm is given for solving the linear programming problem obtained by relaxing the integrality constraints in a zero-one programming formulation of the problem. This linear programming lower bound is used in a reduction algorithm that eliminates jobs from the problem. Also, a branch and bound algorithm that uses the linear programming lower bound is proposed. Computational results with branch and bound algorithms that use this and other lower bounds and with a dynamic programming algorithm for problems with up to 1000 jobs are given.

L Van Wassenhove

Papers

A decomposition algorithm for the single machine total tardiness problem

Lagrangean Relaxation for the Multi-Item Capacitated Lot-Sizing Problem: A Heuristic Implementation

Algorithms for scheduling a single machine to minimize the weighted number of late jobs

Dynamic programming and decomposition approaches for the single machine total tardiness problem

A review of FMS planning models