Developing a New Algorithm for a Utility-based Network Design Problem with Elastic Demand


Department of Industrial Engineering, Yazd University, Yazd, Iran


Developing the infrastructures for preventing non-communicable diseases is one of the most important goals of healthcare context in recent years. In this regard, the number and capacity of preventive healthcare facilities as well as assignment of customers to facilities should be determined for each region. Besides the accessibility, the utility of customers is a determinative factor in participation of people in the offered programs. In this paper, a service network design problem is studied such that the utility function is incorporated in the objective function, and the constraints set. The travel distance is deterministic and demand elasticity results in congestion delays. After simplifying the nonlinear model, a bi-level optimization algorithm is proposed to obtain the optimal solution. Computational results assure the efficiency of the developed algorithm. Finally, the capability of the model is represented by discussing a case study of locating preventive healthcare facilities in Yazd, Iran.


1.     Schilling, D. A., Jayaraman, V. and Barkhi, R., "A review of covering problems in facility location", Computers & Operations Research,  Vol., 1 No., 1 (1993), 25-55.

2.     Farahani, R. Z., Asgari, N., Heidari, N., Hosseininia, M. and Goh, M., "Covering problems in facility location: A review", Computers & Industrial Engineering,  Vol. 62, No. 1, (2012), 368-407.

3.     Berman, O. and Krass, D., "facility location problems with stochastic demands and congestion", In Z. Drezner, & H. W. Hamacher (Eds.), Location Analysis: Applications and Theory, New York: Springer, (2002), 329-371.

4.     Marianov, V. and Serra, D., "Location problems in the public sector", Facility Location: Applications and Theory,  Vol. 1, (2002), 119-150.

5.     Daskin, M. S. and Dean, L. K., "Location of health care facilities", Operations Research and Health Care, (2005), 43-76.

6.     Shishebori, D., "Study of facility location-network design problem in presence of facility disruptions: A case study (research note)", International Journal of Engineering-Transactions A: Basics,  Vol. 28, No. 1, (2014), 97-108.

7.     Verter, V. and Lapierre, S. D., "Location of preventive health care facilities", Annals of Operations Research,  Vol. 110, (2002), 123-132.

8.     Zhang, Y., Berman, O. and Verter, V., "Incorporating congestion in preventive healthcare facility network design", European Journal of Operational Research,  Vol. 198, No. 3, (2009), 922-935.

9.     Zhang, Y., Berman, O., Marcotte, P. and Verter, V., "A bilevel model for preventive healthcare facility network design with congestion", IIE Transactions,  Vol. 42, No. 12, (2010), 865-880.

10.   Aboolian, R., Berman, O. and Krass, D., "Profit maximizing distributed service system design with congestion and elastic demand", Transportation Science,  Vol. 46, No. 2, (2012), 247-261.

11.   Aboolian, R., Berman, O. and Verter, V., "Maximal accessibility network design in the public sector", Transportation Science,  Vol. 50, No. 1, (2015), 336-347.

12.   Parker, B. R. and Srinivasan, V., "A consumer preference approach to the planning of rural primary health-care facilities", Operations Research,  Vol. 24, No. 5, (1976), 991-1025.

13.   Berman, O. and Parkan, C., "A facility location problem with distance‚Äźdependent demand", Decision Sciences,  Vol. 12, No. 4, (1981), 623-632.

14.   Berman, O. and Kaplan, E., "Facility location and capacity planning with delay-dependent demand", International Journal of Production Research,  Vol. 25, No. 12, (1987), 1773-1780.

15.   Berman, O. and Drezner, Z., "Location of congested capacitated facilities with distance-sensitive demand", IIE Transactions,  Vol. 38, No. 3, (2006), 213-221.

16.   Berman, O. and Krass, D., "The generalized maximal covering location problem", Computers & Operations Research,  Vol. 29, No. 6, (2002), 563-581.

17.   Berman, O., Krass, D. and Wang, J., "Locating service facilities to reduce lost demand", IIE Transactions,  Vol. 38, No. 11, (2006), 933-946.

18.   Marianov, V. and Serra, D., "Probabilistic, maximal covering location—allocation models forcongested systems", Journal of Regional Science,  Vol. 38, No. 3, (1998), 401-424.

19.   Marianov, V. and Rios, M., "A probabilistic quality of service constraint for a location model of switches in ATM communications networks", Annals of Operations Research,  Vol. 96, No. 1, (2000), 237-243.

20.   Wang, Q., Batta, R. and Rump, C. M., "Algorithms for a facility location problem with stochastic customer demand and immobile servers", Annals of Operations Research,  Vol. 111, No. 1, (2002), 17-34.

21.   Berman, O. and Drezner, Z., "The multiple server location problem", Journal of the Operational Research Society,  Vol. 58, No. 1, (2007), 91-99.

22.   Arkat, J. and Jafari, R., "Network location problem with stochastic and uniformly distributed demands", International Journal of Engineering-Transactions B: Applications,  Vol. 29, No. 5, (2016), 654-662.

23.   Zabihi, F. and Sahraeian, R., "Trucks scheduling in a multi-product cross docking system with multiple temporary storages and multiple dock doors", International Journal of Engineering Transaction B: Applications, Vol. 29, No. 11, (2016), 1595-1603.

24.   Hotelling, H., "Stability in Competition", The Economic Journal, Vol. 39, No. 153, (1929), 41-57.