# An Inventory-Location Model: Formulation, Solution Algorithm and Computational Results

*Mark Daskin*,
*Collette Coullard* and
*Zuo-Jun Shen*

*Annals of Operations Research*, 2002, vol. 110, issue 1, 83-106

**Abstract:**
We introduce a distribution center (DC) location model that incorporates working inventory and safety stock inventory costs at the distribution centers. In addition, the model incorporates transport costs from the suppliers to the DCs that explicitly reflect economies of scale through the use of a fixed cost term. The model is formulated as a non-linear integer-programming problem. Model properties are outlined. A Lagrangian relaxation solution algorithm is proposed. By exploiting the structure of the problem we can find a low-order polynomial algorithm for the non-linear integer programming problem that must be solved in solving the Lagrangian relaxation subproblems. A number of heuristics are outlined for finding good feasible solutions. In addition, we describe two variable forcing rules that prove to be very effective at forcing candidate sites into and out of the solution. The algorithms are tested on problems with 88 and 150 retailers. Computation times are consistently below one minute and compare favorably with those of an earlier proposed set partitioning approach for this model (Shen, 2000; Shen, Coullard and Daskin, 2000). Finally, we discuss the sensitivity of the results to changes in key parameters including the fixed cost of placing orders. Significant reductions in these costs might be expected from e-commerce technologies. The model suggests that as these costs decrease it is optimal to locate additional facilities. Copyright Kluwer Academic Publishers 2002

**Date:** 2002

**References:** Add references at CitEc

**Citations:** View citations in EconPapers (76) Track citations by RSS feed

**Downloads:** (external link)

http://hdl.handle.net/10.1023/A:1020763400324 (text/html)

Access to full text is restricted to subscribers.

**Related works:**

This item may be available elsewhere in EconPapers: Search for items with the same title.

**Export reference:** BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text

**Persistent link:** https://EconPapers.repec.org/RePEc:spr:annopr:v:110:y:2002:i:1:p:83-106:10.1023/a:1020763400324

**Ordering information:** This journal article can be ordered from

http://www.springer.com/journal/10479

**DOI:** 10.1023/A:1020763400324

Access Statistics for this article

Annals of Operations Research is currently edited by *Endre Boros*

More articles in Annals of Operations Research from Springer

Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().