Optimizing the location-allocation problem of pharmacy warehouses: A case study in Gaziantep
, , , It is a known fact that basic health care services cannot reach the majority of the population due to poor geographical accessibility. Unless quantitative locationallocation models and geographic information systems (GIS) are used, the final decision may be made on pragmatic considerations which can result far from optimal. In this paper, current and possible (or potential) new locations of pharmacy warehouses in Gaziantep are investigated to provide optimal distribution of hospitals and pharmacies. To do so, first of all, geographic information of 10 current and 10 potential pharmacy warehouses, 231 pharmacies and 29 hospitals are gathered using GIS. Second, a set covering mathematical model is handled to determine coverage capability of current and potential pharmacy warehouses and minimize the number of warehouses to be opened. Finally, P-center and P-median mathematical models are applied to open potential warehouses and to assign pharmacies & hospitals to the opened warehouses so that the total distance and the demand’s longest distance to the source are minimized. Developed integer programming (IP) models and GIS software are compared with on a case study. Computational experiments prove that our approach can find new potential pharmacy warehouses which cover wider areas than current warehouses to service pharmacies and hospitals in the city.
[1] Tekiner, H., Pharmacy in Turkey : past, present, and future. Pharmazie, 69 (6):477-480 (2014).
[2] Tootelian, D.T., Wertheimer A.I., and Mikhailitchenko, A., Essentials of pharmacy management. Pharmaceutical Press (2012).
[3] Turkish Pharmacists Association, (2016) Available from:http://dergi.tebeczane.net/public_html/ARSIV -TEBHABERLER/index.html. Accessed 11 Jan 2017.
[4] Population statistics in 2015, (2016). Availablefrom:http://www.turkstat.gov.tr/PreHaberBultenleri .do?id=6178. Accessed 11 Jan 2017.
[5] Dokmeci, V., and Ozus, E., Spatial analysis of urban pharmacies in Istanbul. European Planning Studies, 12:585-594 (2004).
[6] Daskin, M.S., Network and discrete Locations: Models, algorithms and applications. Wiley and Sons, New York (1995).
[7] Owen, S.H., and Daskin, M.S., Strategic facility location: A review. European Journal of Operational Research, 111 (3):423-447 (1998).
[8] Narula, S.C., Minisum hierarchical locationallocation problems on a network: A survey. Annals of Operations Research, 6 (8):255-272 (1986).
[9] Arabani, A.B., and Farahani, R.Z., Facility location dynamics: An overview of classifications and applications. Computers & Industrial Engineering, 62 (1):408-420 (2012).
[10] ReVelle, C.S., and Eiselt, H.A., Location analysis: A synthesis and survey. European Journal of Operational Research, 165 (1):1-19 (2005).
[11] Rahman, S., and Smith, D.K., Use of locationallocation models in health service development planning in developing nations. European Journal of Operational Research, 123 (3):437-452 (2000).
[12] Daskin, S., and Dean, L., Location of health care facilities. Handbook of OR/MS in Health Care: A Handbook of Methods and Applications, 43–76 (2004)
[13] Rais, A., and Viana, A., Operations Research in Healthcare: a survey. International Transactions in Operational Research, 18 (1):1-31 (2011).
[14] Afshari,H., and Peng,Q., Challenges and Solutions for Location of Healthcare Facilities. Industrial Engineering & Management, 03 (02) (2014).
[15] Şahin, G., Süral, H., and Meral, S., Locational analysis for regionalization of Turkish Red Crescent blood services. Computers & Operations Research, 34 (3):692-704 (2007).
[16] Mestre, A., Oliveira, M.,D., and Barbosa-Póvoa, A., Organizing hospitals into networks: a hierarchical and multiservice model to define location, supply and referrals in planned hospital systems. OR spectrum, 34 (2):319-348 (2012).
[17] Farahani, R.Z., Hekmatfar, M., Fahimnia, B., and Kazemzadeh, N., Hierarchical facility location problem: Models, classifications, techniques, and applications. Computers & Industrial Engineering, 68:104-117 (2014).
[18] Teixeira, J.C., and Antunes, A.P., A hierarchical location model for public facility planning. European Journal of Operational Research, 185 (1):92-104 (2008).
[19] Berghmans, L., Schoovaerts, P., and Teghem, J.,Implementation of Health Facilities in a New City. The Journal of the Operational Research Society, 35 (12):1047-1054 (1984).
[20] Tavakoli, A., and Lightner, C., Implementing a mathematical model for locating EMS vehicles in fayetteville, NC. Computers & Operations Research, 31 (9):1549-1563 (2004).
[21] Jia, H., Ordóñez, F., and Dessouky, M., Solution approaches for facility location of medical supplies for large-scale emergencies. Computers & Industrial Engineering, 52 (2):257-276 (2007).
[22] Jia, H., Ordóñez, F., and Dessouky, M., A modeling framework for facility location of medical services for large-scale emergencies. IIE transactions, 39 (1):41-55 (2007).
[23] Shariff, R.S.S., Moin, N.H., Omar, M., Location allocation modeling for healthcare facility planning in Malaysia. Computers & Industrial Engineering, 62 (4):1000-1010 (2012).
[24] Valipour, M.T., Nedjati, A., and Kazemi, R., Solving Health Care Facility Location Problems with New Heuristic Algorithm Method. International Journal of Modeling and Optimization,12-14 (2013).
[25] Jia, T., Tao, H., Qin, K., Wang, Y., Liu, C., and Gao, Q., Selecting the optimal healthcare centers with a modified P-median model: a visual analytic perspective. International journal of health geographics, 13 (1):1 (2014).
[26] Kunkel, A.G., Van Itallie, E.S., and Wu, D., Optimal distribution of medical backpacks and health surveillance assistants in Malawi. Health care management science (2013).
[27] Guerriero, F., Miglionico, G., and Olivito, F., Location and reorganization problems: The Calabrian health care system case. European Journal of Operational Research, 250 (3):939-954 (2016).
[28] Harper, P., Planning health services with explicit geographical considerations: a stochastic locationallocation approach. Omega, 33 (2):141-152 (2005).
[29] Abdelaziz, F.B., and Masmoudi, M., A multiobjective stochastic program for hospital bed planning. Journal of the Operational Research Society, 63 (4):530-538 (2012).
[30] Mestre, A.M., Oliveira, M.D., and Barbosa-Póvoa, A.P., Location–allocation approaches for hospital network planning under uncertainty. European Journal of Operational Research, 240 (3):791-806 (2015).
[31] Lovejoy, W.S., and Li, Y., Hospital operating room capacity expansion. Management Science, 48 (11):1369-1387 (2002).
[32] Stummer, C., Doerner, K., Focke, A., and Heidenberger, K., Determining location and size ofmedical departments in a hospital network: A multiobjective decision support approach. Health care management science, 7 (1):63-71 (2004).
[33] Bansal, V.K., Application of geographic information systems in construction safety planning. International Journal of Project Management, 29 (1):66-77 (2011).
[34] Keyser, J.J., Book review. The Journal of Hand Surgery, 39 (8):1649-1650 (2014).
[35] Minutha, A., and Sannasiddanannavar, S.S., Planning for public health care services in Nanjangud Taluk a spatial analysis using GIS, Indian Streams Research Journal 4 (2):1-5 (2014).
[36] McLafferty, S.L., GIS and health care. Annual review of public health, 24 (1):25-42 (2003).
[37] Lovett, A., Haynes, R., Sünnenberg, G., and Gale, S., Car travel time and accessibility by bus to general practitioner services: a study using patient registers and GIS. Social Science & Medicine, 55 (1):97-111 (2002).
[38] Grekousis, G., and Photis, Y.N., Analyzing highrisk emergency areas with GIS and neural networks: The case of Athens, Greece. The Professional Geographer, 66 (1):124-137 (2014).
[39] Sanders, L.J., Aguilar, G.D., and Bacon, C.J., A spatial analysis of the geographic distribution of musculoskeletal and general practice healthcare clinics in Auckland, New Zealand. Applied Geography, 44:69-78 (2013).
[40] Huang, B., Dignan, M., Han, D., and Johnson, O., Does distance matter? Distance to mammography facilities and stage at diagnosis of breast cancer in Kentucky. The Journal of Rural Health, 25 (4):366- 371 (2009).
[41] Pearce, J., Witten, K., Hiscock, R., and Blakely, T., Are socially disadvantaged neighbourhoods deprived of health-related community resources? International journal of epidemiology, 36 (2):348- 355 (2007).
[42] Klein, M.B., Kramer, C.B., Nelson, J., Rivara, F.P., Gibran, N.S., and Concannon, T., Geographic access to burn center hospitals. JAMA, 302 (16):1774-1781 (2009).
[43] Farahani, R.Z., Asgari, N., Heidari, N., Hosseininia, M., and Goh, M., Covering problems in facility location: A review. Computers & Industrial Engineering, 62 (1):368-407 (2012).
[44] Caprara, A., Toth, P., and Fischetti, M., Algorithms for the set covering problem. Annals of Operations Research, 98 (1-4):353-371(2000).
[45] Li, X., Zhao, Z., Zhu, X., and Wyatt, T., Covering models and optimization techniques for emergency response facility location and planning: a review. Mathematical Methods of Operations Research, 74 (3):281-310 (2011).
[46] Beasley, J.E., An algorithm for set covering problem. European Journal of Operational Research, 31 (1):85-93 (1987).
[47] Hakimi, S.L.,Optimum locations of switching centers and the absolute centers and medians of a graph. Operations research, 12 (3):450-459 (1964).
[48] Kariv, O., and Hakimi, S.L., An algorithmic approach to network location problems. II: The pmedians. SIAM Journal on Applied Mathematics, 37 (3):539-560 (1979).