Capacitated lot sizing problems with inventory bounds

Akbalιk, Ayşe; Penz, Bernard; Rapine, Christophe

doi:10.1007/s10479-015-1816-6

Cited by 19 publications

(3 citation statements)

References 27 publications

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“…The natural extension of the single-item ELSPBI also considering the bounds on the production and replenishment quantity at each period has been addressed recently by Akbalik et al [25]. Concretely, for the single-item CLSP-IB with a constant production capacity, time-dependent inventory bounds and concave costs, the authors showed that the problem could be solved in time O T 4 .…”

Section: Referencementioning

confidence: 99%

Effective Algorithms for the Economic Lot-Sizing Problem with Bounded Inventory and Linear Fixed-Charge Cost Structure

et al. 2021

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Efficient algorithms for the economic lot-sizing problem with storage capacity are proposed. On the one hand, for the cost structure consisting of general linear holding and ordering costs and fixed setup costs, an dynamic programming algorithm is introduced, where is the number of time periods. The new approach induces an accurate partition of the planning horizon, discarding most of the infeasible solutions. Moreover, although there are several algorithms based on dynamic programming in the literature also running in quadratic time, even considering more general cost structures and assumptions, the new solution uses a geometric technique to speed up the algorithm for a class of subproblems generated by dynamic programming, which can now be solved in linearithmic time. To be precise, the computational results show that the average occurrence percentage of this class of subproblems ranges between 13% and 45%, depending on both the total number of periods and the percentage of storage capacity availability. Furthermore, this percentage significantly increases from 13% to 35% as the capacity availability decreases. This reveals that the usage of the geometric technique is predominant under restrictive storage capacities. Specifically, when the percentage of capacity availability is below 50%, the average running times are on average 100 times faster than those when this percentage is above 50%. On the other hand, an on-line array searching method in Monge arrays can be used when the costs are non-speculative costs.

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Section: Referencementioning

confidence: 99%

Effective Algorithms for the Economic Lot-Sizing Problem with Bounded Inventory and Linear Fixed-Charge Cost Structure

et al. 2021

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“…Constraints (5) and (13) are respectively the classical inventory balance equations and capacity constraints. Constraints (14) relate production variables and batch variables while Constraints (15) and (16)…”

Section: Minimizementioning

confidence: 99%

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

Brahimi

Absi

Dauzère‐Pérès

et al. 2017

European Journal of Operational Research

153

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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...

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“…It is noticeable, however, that most of the works related to storage capacities are very recent when compared to those considering production capacities (Bitran & Yanasse, 1982;Trigeiro, Thomas, & McClain, 1989;Buschkühl, Sahling, Helber, & Tempelmeier, 2010;Vincent, Duhamel, Ren, & Tchernev, 2020;Tavaghof-Gigloo & Min-ner, 2020). Akbalik, Penz, and Rapine (2015a) study capacitated lot-sizing problems with storage capacities. The authors propose polynomial-time algorithms for the single-item variant of the problem and show NPhardness results for the multi-item variation.…”

Section: Introductionmentioning

confidence: 99%

A hybrid heuristic for capacitated three-level lot-sizing and replenishment problems with a distribution structure

Cunha¹,

Mateus²,

Melo³

2021

Preprint

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In this paper, we consider the capacitated three-level lot-sizing and replenishment problem with a distribution structure (3LSPD-C), recently proposed in the literature. In 3LSPD-C, a single production plant delivers items to the warehouses from where they are distributed to their corresponding retailers. There is a capacity on the total amount the plant can produce in each period, whereas there are no capacities on transportation. The goal of this optimization problem consists in determining an integrated three-echelon production and distribution plan minimizing the total cost, which is composed of fixed costs for production and transportation setups as well as variable inventory holding costs. Additionally, we consider a generalization of the problem which also establishes storage capacities (or inventory bounds) on the warehouses and/or retailers, given the importance of such characteristics in practical industrial and commercial environments. Such extension is denoted generalized capacitated three-level lot-sizing and replenishment problem with a distribution structure (G3LSPD-C). We propose a hybrid mixed integer programming (MIP) heuristic consisting of a relax-and-fix approach to generate initial feasible solutions and a fix-and-optimize improvement procedure grounded on varying-size neighborhoods to obtain high-quality solutions. Computational experiments are performed to analyze the potential cost reductions achieved using the new hybrid heuristic when compared with a state-of-the-art MIP formulation. The results show that the proposed hybrid heuristic can match or improve the solution quality obtained by the MIP formulation for the majority of the 3LSPD-C instances within a specified time limit. Additionally, such superior behavior remains valid when the approaches are applied to the more general G3LSPD-C. Furthermore, we investigate the economic impacts of the storage capacities and how they affect the performance of our newly proposed hybrid heuristic.

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Capacitated lot sizing problems with inventory bounds

Cited by 19 publications

References 27 publications

Effective Algorithms for the Economic Lot-Sizing Problem with Bounded Inventory and Linear Fixed-Charge Cost Structure

Effective Algorithms for the Economic Lot-Sizing Problem with Bounded Inventory and Linear Fixed-Charge Cost Structure

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

A hybrid heuristic for capacitated three-level lot-sizing and replenishment problems with a distribution structure

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