Combined facility location and distribution network design problem: Progressive models and a case study

Abstract

This paper addresses to the facility location problem of ammunition stores considering the design of distribution network from stores to geographically dispersed army forces. The problem is to determine the construction sites of the ammunition stores among candidate sites and to give the decision on how many stores will be built from which kind. The problem also contains designing of a distribution network to concurrently determine the amounts of several military equipment transported from stores to army forces. A mathematical model is proposed to minimize the cost of the whole system, caused by the construction of the ammunition stores and the transportation of different equipment in diverse quantities from stores to dispersed army forces. The model is then improved progressively and several variants are presented to reflect the real-world conditions through a case study. Numerical results obtained from solving the case study using the proposed models coded in General Algebraic Modelling System (GAMS) are exhibited. The effect of the size of problem specific parameters on the model execution time is also investigated via experimental tests. The results demonstrate the promising problem-solving capacity of the proposed models, which can be applied practically.

Keywords

• Facility location,Distribution network design,Operations research,MILP

Birleşik depo yeri seçimi ve dağıtım ağı tasarımı problemi: Aşamalı modeller ve bir uygulama

Abstract

Bu çalışma, depolardan coğrafi olarak dağınık askeri birliklere dağıtım ağı tasarımını dikkate alarak mühimmat depolarının yer seçimi problemi konusunu ele almaktadır. Burada problem, aday bölgelerden hangilerine mühimmat depoları kurulacağını belirlemek ve hangi tip depolardan kaç adet inşa edileceğine karar vermektir. Ele alınan problem aynı zamanda mühimmat depolarından askeri birliklere sevk edilen pek çok askeri malzemenin miktarını belirlemek için bir dağıtım ağı tasarımı problemini içermektedir. Depo kurulumundan ve farklı askeri malzemelerin depolardan askeri birliklere farklı miktarlarda dağıtımından kaynaklanan toplam maliyeti minimize etmek için bir matematiksel model önerilmektedir. Bu model akabinde aşamalı olarak iyileştirilmekte ve gerçek hayat koşullarını bir uygulama vasıtasıyla daha iyi yansıtmak amacıyla modelin farklı versiyonları sunulmaktadır. Uygulamaya konu problem, önerilen modellerin GAMS (Genel Cebirsel Modelleme Sistemi)’te kodlanmasıyla çözülerek sayısal örnekler ortaya koyulmuştur. Probleme özgü parametrelerin büyüklüğünün model uygulama süresi üzerindeki etkisi de deneysel testlerle incelenmiştir. Sonuçlar, önerilen modellerin pratikte uygulanabilecek umut verici problem çözme kapasitesini göstermektedir.

Keywords

• Yer belirleme,Dağıtım ağı tasarımı,Yöneylem araştırması,Karışık tamsayılı programlama

References

1. Klose A. “An LP-based heuristic for two-stage capacitated facility location problems”. Journal of the Operational Research Society, 50(2), 157-66, 1999.
2. Daskin MS, Snyder LV, Berger RT. Facility Location in Supply Chain Design. Editors: Langevin A., Riopel D. Logistics Systems: Design and Optimization, 39-65, Springer, Boston, MA, 2005.
3. Drezner T, Drezner Z. “Modelling lost demand in competitive facility location”. Journal of the Operational Research Society, 63(2), 201-206, 2012.
4. Tang X, Lehuédé F, Péton O. “Location of distribution centers in a multi-period collaborative distribution network”. Electronic Notes in Discrete Mathematics, 52, 293-300, 2016.
5. Kuehn AA, Hamburger MJ. “A heuristic program for locating warehouses”. Management Science, 9(4), 643-666, 1963.
6. Church R, Velle CR. “The maximal covering location problem”. Papers in Regional Science, 32(1), 101-118, 1974.
7. Elloumi S, Labbé M, Pochet Y. “A new formulation and resolution method for the p-center problem”. INFORMS Journal on Computing, 16(1), 84-94, 2004.
8. Rahmaniani R, Ghaderi A. “A combined facility location and network design problem with multi-type of capacitated links”. Applied Mathematical Modelling 37(9), 6400-6414, 2013.

9. Contreras I, Fernández E. “General network design: A unified view of combined location and network design problems”. European Journal of Operational Research, 219(3), 680-697, 2012.
10. Rahmaniani R, Ghaderi A. “An algorithm with different exploration mechanisms: Experimental results to capacitated facility location/network design problem”. Expert Systems with Applications, 42(7), 3790-3800, 2015.
11. Crainic TG, Kim KH. Chapter 8 Intermodal Transportation. Editors: Barnhart C, Laporte G. Handbooks in Operations Research and Management Science. 14, 467-537, Elsevier, 2007.
12. SteadieSeifi M, Dellaert NP, Nuijten W, Van Woensel T, Raoufi R. “Multimodal freight transportation planning: A literature review”. European Journal of Operational Research, 233(1), 1-15, 2014.
13. Melkote S, Daskin MS. “An integrated model of facility location and transportation network design”. Transportation Research Part A: Policy and Practice, 35(6), 515-538, 2001.
14. Daskin MS, Hurter AP, Van Buer MG. “Toward an integrated model of facility location and transportation network design”. The Transportation Center, Northwestern University, Working Paper Evanston, IL, USA, 1993.
15. Berman O, Ingco DI, Odoni AR. “Improving the location of minisum facilities through network modification”. Annals of Operations Research, 40(1), 1-16, 1992.
16. Peeters D, Thomas I. “Effect of spatial structure on p-median results”. Transportation Science, 29(4), 366-373, 1995.
17. Melkote S, Daskin MS. “Capacitated facility location/network design problems”. European Journal of Operational Research, 129(3), 481-495, 2001.
18. Drezner Z, Wesolowsky GO. “Network design: selection and design of links and facility location”. Transportation Research Part A: Policy and Practice, 37(3), 241-256, 2003.
19. Cocking C. Solutions to Facility Location–Network Design Problems. PhD Thesis, University of Heidelberg, Germany, 2008.
20. Ghaderi A, Jabalameli MS. “Modeling the budget-constrained dynamic uncapacitated facility location–network design problem and solving it via two efficient heuristics: A case study of health care”. Mathematical and Computer Modelling, 57(3), 382-400, 2013.
21. Murawski L, Church RL. “Improving accessibility to rural health services: The maximal covering network improvement problem”. Socio-Economic Planning Sciences, 43(2), 102-110, 2009.
22. Bigotte JF, Krass D, Antunes AP, Berman O. “Integrated modeling of urban hierarchy and transportation network planning”. Transportation Research Part A: Policy and Practice, 44(7), 506-522, 2010.
23. Contreras I, Fernández E, Reinelt G. “Minimizing the maximum travel time in a combined model of facility location and network design”. Omega, 40(6), 847-860, 2012.
24. Afshari H, Sharafi M, ElMekkawy T, Peng Q. “Optimizing multi-objective dynamic facility location decisions within green distribution network design”. Procedia CIRP, 17, 675-679, 2014.
25. Bilir C, Ekici SO, Ulengin F. “An integrated multi-objective supply chain network and competitive facility location model”. Computers & Industrial Engineering, 108, 136-148, 2017.
26. Farahani RZ, Miandoabchi E, Szeto WY, Rashidi H. “A review of urban transportation network design problems”. European Journal of Operational Research, 229(2), 281-302, 2013.
27. Ortiz-Astorquiza C, Contreras I, Laporte G. “Multi-level facility location problems”. European Journal of Operational Research, 267(3), 791-805, 2018.
28. Farahani RZ, Asgari N, Heidari N, Hosseininia M, Goh M. “Covering problems in facility location: A review”. Computers & Industrial Engineering, 62(1), 368-407, 2012.
29. Staniec CJ. Design and Solution of an Ammunition Distribution Model by a Resource-Directive Multi Commodity Network Flow Algorithm. Master’s Thesis, Naval Postgraduate School, Monterey, California, 1984.
30. Saunders-Newton D. Adaptive Battlefield Ammunition Distribution: The Role of Systematic Adaptation in Dynamic Environments. PhD Thesis, RAND Graduate School, Santa Monica, 1993.
31. Hancock SR, Lee PJ. The Ammunition Supply Chain and Intermodalism: From Depot to Foxhole, Master’s Thesis, Naval Postgraduate School, California, 1998.
32. Bell J. A Simulated Annealing Approach for the Composite Facility Location and Resource Allocation Problem: A Study of Strategic Positioning of US Air Force Munitions, Doctoral Thesis, Auburn University, Auburn, 2003.
33. Gue KR. “A dynamic distribution model for combat logistics”. Computers & Operations Research, 30(3), 367-381, 2003.
34. Powell DS. An Optimization Model for Sea-Based Logistics Supply System for the Navy and Marine Corps. Master’s Thesis, Naval Postgraduate School, California, 2004.
35. Clark SJ, Barnhart C, Kolitz SE. “Large-scale optimization planning methods for the distribution of United States army munitions”. Mathematical and Computer Modelling, 39(6), 697-714, 2004.
36. Lenhardt TA. “Evaluation of a USMC combat service support logistics concept”. Mathematical and Computer Modelling, 44(3), 368-376, 2006.
37. Toyoglu H, Karasan OE, Kara BY. “Distribution network design on the battlefield”. Naval Research Logistics, 58(3), 188-209, 2011.
38. Karatas M, Yakıcı E, Razi N. Military Facility Location Problems: A Brief Survey. Editors: Tozan H, Karatas M. Operations Research for Military Organizations, 1-27, IGI Global, USA, 2019.