A discrete EOQ problem with maximum order size costs

Mikhail Y. Kovalyov; Edwin Tai Chiu Cheng; Vladimir Kotov; Chi To Ng

A discrete EOQ problem with maximum order size costs

Mikhail Y. Kovalyov
, Edwin Tai Chiu Cheng
, Vladimir Kotov
, Chi To Ng

Research output: Chapter in book / Conference proceeding › Conference article published in proceeding or book › Academic research › peer-review

Abstract

The Economic Order Quantity (EOQ) problem is a fundamental problem in supply and inventory management. An optimal solution to this problem in a closed form exists under the assumption that time and the product are continuously divisible. This paper studies problem D-EOQ, in which time and the product are discrete. Furthermore, in the objective function, there is a fixed cost for each order and a fixed cost for each product unit in an order of the maximum size. It is shown that the continuous relaxation of problem D-EOQ provides a solution that can be up to 50% worse than the optimal solution and this worst-case error bound is tight. Properties of an optimal solution of the problem D-EOQ are established. These properties allow to solve many special cases in polynomial time and can be used to derive a polynomial time algorithm for the general case of the problem D-EOQ.

Original language	English
Title of host publication	12th IFAC Symposium on Information Control Problems in Manufacturing, INCOM 2006, and Associated Industrial Meetings
Subtitle of host publication	EMM'2006, BPM'2006, JT'2006
Volume	12
Edition	PART 1
Publication status	Published - 1 Dec 2006
Event	12th IFAC Symposium on Information Control Problems in Manufacturing, INCOM 2006, and Associated Industrial Meetings: EMM'2006, BPM'2006, JT'2006 - Saint - Etienne, France Duration: 17 May 2006 → 19 May 2006

Conference

Conference	12th IFAC Symposium on Information Control Problems in Manufacturing, INCOM 2006, and Associated Industrial Meetings: EMM'2006, BPM'2006, JT'2006
Country/Territory	France
City	Saint - Etienne
Period	17/05/06 → 19/05/06

Keywords

Algorithms
Inventory control

ASJC Scopus subject areas

Control and Systems Engineering

Cite this

@inproceedings{cff8f8b5e8e7425f93f899506c006835,

title = "A discrete EOQ problem with maximum order size costs",

abstract = "The Economic Order Quantity (EOQ) problem is a fundamental problem in supply and inventory management. An optimal solution to this problem in a closed form exists under the assumption that time and the product are continuously divisible. This paper studies problem D-EOQ, in which time and the product are discrete. Furthermore, in the objective function, there is a fixed cost for each order and a fixed cost for each product unit in an order of the maximum size. It is shown that the continuous relaxation of problem D-EOQ provides a solution that can be up to 50\% worse than the optimal solution and this worst-case error bound is tight. Properties of an optimal solution of the problem D-EOQ are established. These properties allow to solve many special cases in polynomial time and can be used to derive a polynomial time algorithm for the general case of the problem D-EOQ.",

keywords = "Algorithms, Inventory control",

author = "Kovalyov, \{Mikhail Y.\} and Cheng, \{Edwin Tai Chiu\} and Vladimir Kotov and Ng, \{Chi To\}",

year = "2006",

month = dec,

day = "1",

language = "English",

isbn = "9783902661043",

volume = "12",

booktitle = "12th IFAC Symposium on Information Control Problems in Manufacturing, INCOM 2006, and Associated Industrial Meetings",

edition = "PART 1",

note = "12th IFAC Symposium on Information Control Problems in Manufacturing, INCOM 2006, and Associated Industrial Meetings: EMM'2006, BPM'2006, JT'2006 ; Conference date: 17-05-2006 Through 19-05-2006",

}

Kovalyov, MY, Cheng, ETC, Kotov, V & Ng, CT 2006, A discrete EOQ problem with maximum order size costs. in 12th IFAC Symposium on Information Control Problems in Manufacturing, INCOM 2006, and Associated Industrial Meetings: EMM'2006, BPM'2006, JT'2006. PART 1 edn, vol. 12, 12th IFAC Symposium on Information Control Problems in Manufacturing, INCOM 2006, and Associated Industrial Meetings: EMM'2006, BPM'2006, JT'2006, Saint - Etienne, France, 17/05/06.

A discrete EOQ problem with maximum order size costs. / Kovalyov, Mikhail Y.; Cheng, Edwin Tai Chiu; Kotov, Vladimir et al.
12th IFAC Symposium on Information Control Problems in Manufacturing, INCOM 2006, and Associated Industrial Meetings: EMM'2006, BPM'2006, JT'2006. Vol. 12 PART 1. ed. 2006.

Research output: Chapter in book / Conference proceeding › Conference article published in proceeding or book › Academic research › peer-review

TY - GEN

T1 - A discrete EOQ problem with maximum order size costs

AU - Kovalyov, Mikhail Y.

AU - Cheng, Edwin Tai Chiu

AU - Kotov, Vladimir

AU - Ng, Chi To

PY - 2006/12/1

Y1 - 2006/12/1

N2 - The Economic Order Quantity (EOQ) problem is a fundamental problem in supply and inventory management. An optimal solution to this problem in a closed form exists under the assumption that time and the product are continuously divisible. This paper studies problem D-EOQ, in which time and the product are discrete. Furthermore, in the objective function, there is a fixed cost for each order and a fixed cost for each product unit in an order of the maximum size. It is shown that the continuous relaxation of problem D-EOQ provides a solution that can be up to 50% worse than the optimal solution and this worst-case error bound is tight. Properties of an optimal solution of the problem D-EOQ are established. These properties allow to solve many special cases in polynomial time and can be used to derive a polynomial time algorithm for the general case of the problem D-EOQ.

AB - The Economic Order Quantity (EOQ) problem is a fundamental problem in supply and inventory management. An optimal solution to this problem in a closed form exists under the assumption that time and the product are continuously divisible. This paper studies problem D-EOQ, in which time and the product are discrete. Furthermore, in the objective function, there is a fixed cost for each order and a fixed cost for each product unit in an order of the maximum size. It is shown that the continuous relaxation of problem D-EOQ provides a solution that can be up to 50% worse than the optimal solution and this worst-case error bound is tight. Properties of an optimal solution of the problem D-EOQ are established. These properties allow to solve many special cases in polynomial time and can be used to derive a polynomial time algorithm for the general case of the problem D-EOQ.

KW - Algorithms

KW - Inventory control

UR - https://www.scopus.com/pages/publications/79961177293

M3 - Conference article published in proceeding or book

SN - 9783902661043

VL - 12

BT - 12th IFAC Symposium on Information Control Problems in Manufacturing, INCOM 2006, and Associated Industrial Meetings

T2 - 12th IFAC Symposium on Information Control Problems in Manufacturing, INCOM 2006, and Associated Industrial Meetings: EMM'2006, BPM'2006, JT'2006

Y2 - 17 May 2006 through 19 May 2006

ER -

A discrete EOQ problem with maximum order size costs

Abstract

Conference

Keywords

ASJC Scopus subject areas

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