Single-item dynamic lot-sizing problems: An updated survey

Abstract

Following our previous paper (Brahimi, N., Dauzère-Pérès, S., Najid, N. M., and Nordli, A. Single item lot sizing problems. European Journal of Operational Research, 168(1):1-16, 2006), we present an updated and extended survey of Single-Item Lot-Sizing Problems with focus on publications from 2004 to 2016. Exact and heuristic solution procedures are surveyed. A concise and comprehensive summary of different extensions of the problem is given. The classification of the extensions is based on different characteristics such as resource limitations, assumptions on demand and cost structure. The large number of surveyed papers shows the increased interest of researchers in lot-sizing problems in general and in single-item problems in particular. The survey and the proposed classification should help researchers to identify new research topics, to propose relevant problems and/or novel solution approaches.Since the publication of the seminal work of Wagner and Whitin (1958) in 1958, a lot of research has been conducted on the Single-Item Lot-Sizing Problem (SILSP) and its extensions. The SILSP is interesting in itself to model some tactical production and distribution planning problems, e.g. when planning the replenishment of one raw material with fixed and variable ordering and transportation costs. It is also important to efficiently solve the SILSP because it appears as a subproblem in the solution procedures of many complex lot-sizing problems such as capacitated multi-item problems.Extensions of the SILSP include production capacity, remanufacturing, backlogging, lost sales, demand and production time windows, bounded inventory, perishability, etc. The large number of publications on the SILSP and the large variety of its applications and extensions call for a literature review to put together all the relevant references and classify them. This will allow researchers in the field to more easily identify research trends and gaps to be filled in lot sizing in particular and in production ACCEPTED MANUSCRIPT and distribution planning in general. This survey is an extension and an update of a previous survey published by three of the authors in European Journal of Operational Research in 2006(Brahimi et al. (2006). Since this survey was published, there has been a growing interest in the study of the SILSP.There were at least 100 publications on the SILSP and its extensions in the past 8 years. The objective of this paper is to update the previous literature review and enrich it with the new research in the area. To avoid repetition and for space reasons, most of the references and details in (Brahimi et al. (2006)) are omitted.The SILSP can be defined as a planning problem in which there is time-varying demand for a single product over a planning horizon of T periods. The objective is to determine periods where production will take place and the quantities that have to be produced in these periods. The total production should satisfy the demands while minimizing the total costs. The basic costs are the unit producti...

Tactical production planning for physical and financial flows of supply chain in a multi-site context

“…This fact could strongly affect the solution procedure to apply. For similar reason, other parameters considered in this problem may also be stochastic, as surveyed in Brahimi et al (2017).…”

Management of the subsystem of production logistics in an enterprise

“…The article suggests a SILSP (Single-item capacitated lot-sizing problem) mathematical model of production management. It's an LSP (Lot Sizing Problems) model for planning the size of a production batch which helps determine an optimal size of production realized for one product in a situation of demand intermittence and limited production resources [8]. The model was built for the enterprise described in the previous chapter.…”

Stabilized‐Cycle Strategy for Capacitated Lot Sizing with Multiple Products: Fill‐Rate Constraints in Rolling Schedules

“…Ultimately, they favor the static-dynamic uncertainty strategy to keep the setup-oriented system nervousness low. For a stateof-the-art survey on (general) single-item lot sizing, we refer to Brahimi et al (2017).…”