Heuristic Methods for the Capacitated Location- Allocation Problem with Stochastic Demand
The proper number and appropriate locations of service centers can save cost, raise revenue and gain more satisfaction from customers. Establishing service centers is high-cost and difficult to relocate. In long-term planning periods, several factors may affect the service. One of the most critical factors is uncertain demand of customers. The opened service centers need to be capable of serving customers and making a profit although the demand in each period is changed. In this work, the capacitated location-allocation problem with stochastic demand is considered. A mathematical model is formulated to determine suitable locations of service centers and their allocation to maximize total profit for multiple planning periods. Two heuristic methods, a local search and genetic algorithm, are used to solve this problem. For the local search, five different chances to choose each type of moves are applied. For the genetic algorithm, three different replacement strategies are considered. The results of applying each method to solve numerical examples are compared. Both methods reach to the same best found solution in most examples but the genetic algorithm provides better solutions in some cases.
[1] L. Cooper, “Location-allocation problems,” Oper. Res., vol. 11, no. 3, pp. 331-343, June 1963.
[2] M. F. Goodchild, “ILACS: A Location-Allocation Model for Retail Site Selection,” J. Retailing, vol. 60, no. 1, pp. 84-100, Spring 1984.
[3] K. Gokbayrak and A. S. Kocaman, “A distance-limited continuous location-allocation problem for spatial planning of decentralized systems,” Comput. Oper. Res., vol. 88, pp. 15-29, Dec. 2017.
[4] J. Brimberg and S. Salhi, “A continuous location-allocation problem with zone-dependent fixed cost,” Ann. Oper. Res., vol. 136, pp. 99-115, Apr. 2005.
[5] S. M. Mousavi and S. T. A. Niaki, “Capacitated location allocation problem with stochastic location and fuzzy demand: A hybrid algorithm,” Appl. Math. Model., vol. 37, pp. 5109-5119, Apr. 2013.
[6] A. M. Fathollahi Fard and M. Hajaghaei-Keshteli, “A tri-level location-allocation model for forward/reverse supply chain,” Appl. Soft Comput., vol. 62, pp. 328-346, Jan. 2018.
[7] S. Khodaparasti, M. E. Bruni, P. Beraldi, H. R. Maleki, and S. Jahedi, “A multi-period location-allocation model for nursing home network planning under uncertainty,” Oper. Res. Health Care, vol. 18, pp. 4-15, Sept. 2018.
[8] P. Ghasemi, K. Khalili-Damghani, A. Hafezalkotob, and S. Raissi, “Uncertain multi-objective multi-commodity multi-period multi-vehicle location-allocation model for earthquake evacuation planning,” Appl. Math. Comput., vol. 350, pp. 105-132, June 2019.
[9] H. Baharmand, T. Comes, and M. Lauras, “Bi-objective multi-layer location-allocation model for the immediate aftermath of sudden-onset disasters,” Transport. Res. E-Log, vol. 127, pp. 86-110, July 2019.
[10] P. R. Jenkins, B. J. Lunday, and M. J. Robbins, “Robust, multi-objective optimization for the military medical evacuation location-allocation problem,” Omega, Jul. 2019, Art. no. 102088.
[11] D. Weible, P. Salamon, I. B. Christoph-Schulz, and G. Peter, “How do political, individual and contextual factors affect school milk demand? Empirical evidence from primary schools in Germany,” Food Policy, vol. 43, pp. 148-158, Dec. 2013.
[12] N. I. Benjamin and B. Lin, “Influencing factors on electricity demand in Chinese nonmetallic mineral products industry: A quantile perspective,” J. Clean. Prod., vol. 243, Jan. 2020, Art. no. 118584.
[13] B. W. Inganga, A. Njeru, K. Omburi, and O. I. Tirimba, “Factor affecting customer demand of financial services offered by commercial banks in Nairobi country,” Int. J. Sci. Res. Publ., vol. 4. no. 11, pp. 1-25 Nov. 2014.
[14] J. Cano-Belmán and H. Meyr, “Deterministic allocation models for multi-period demand fulfillment in multi-stage customer hierarchies,” Comput. Oper. Res., vol. 101, pp. 76-92, Jan. 2019.
[15] K. Afrin, B. Nepal, and L. Monplaisir, “A data-driven framework to new product demand prediction: Integrating product differentiation and transfer learning approach,” Expert Syst. Appl., vol. 108, pp. 246-257, Oct. 2018.
[16] T. V. Nguyen, L. Zhou, A. Y. L. Chong, Boying Li, and X. Pu, “Predicting customer demand for remanufacturing products: A data-mining approach,” Eur. J. Oper. Res., to be published.
[17] A. Ghodratnama, H. R. Arbabi, and A. Azaron, “Production planning in industrial townships modeled as hub location-allocation problems considering congestion in manufacturing plants,” Comput. Ind. Eng., vol. 129, pp. 479-501, Mar. 2019.
[18] S. Yan, J. Lin, Y. Chen, and F. Xie, “Rental bike location and allocation under stochastic demands,” Comput. Ind. Eng., vol. 107, pp. 1-11, May 2017.
[19] K. Wang, B. Makond, and S. Liu, “Location and allocation decisions in a two-echelon supply chain with stochastic demand – A genetic algorithm based solution,” Expert Syst. Appl., vol. 38, pp. 6125-6131, May 2011.
[20] M. Alizadeh, J. Ma, N. Mahdavi-Amiri, and M. Marufuzzaman, “A stochastic programming model for a capacitated location-allocation problem with heterogeneous demands,” Comput. Ind. Eng., vol. 137, Nov. 2019. Art. no. 106055.
[21] N. Vidyarthi and S. Jayaswal, “Efficient solution of a class of location-allocation problems with stochastic demand and congestion,” Comput. Oper. Res., vol. 48, pp. 20-30, Aug. 2014.
[22] E. Özceylan, A. Uslu, M. Erbaş, C. Çetinkaya, and S. K. İşleyen, “Optimizing the location-allocation problem of pharmacy warehouses: A case study in Gaziantep,” Int. J. Optimiz. Control, vol. 7, no. 1, pp. 117-129, 2017.
[23] M. Kaveh and M. S. Mesgari, “Improved biogeography-based optimization using migration process adjustment: An approach for location-allocation of ambulances,” Comput. Ind. Eng., vol. 135, pp. 800-813, Sept. 2019.
[24] B. R. Sarker, B. Wu, and K. P. Paudel, “Optimal number and location of storage hubs and biogas production reactors in farmland with allocation of multiple feedstocks,” Appl. Math. Model., vol. 55, pp. 447-465, Mar. 2018.
[25] Y. Lin, H. Jia, Y. Yang, G. Tian, F. Tao, and L. Ling, “An improved artificial bee colony for facility allocation problem of end-of-life vehicles recovery network,” J. Clean. Prod., vol. 205, pp. 134-144, Dec. 2018.
[26] F. Barzinpour and V. Esmaeilli, “A multi-objective relief chain location distribution model for urban disaster management,” Int. J. Adv. Manuf. Technol., vol. 70, pp. 1291-1302, Feb. 2014.
[27] B. Sharma, M. Ramkumar, N. Subramanian, and B. Malhotra, “Dynamic temporary blood facility location-allocation during and post-disaster periods,” Ann. Oper. Res., 2017.
[28] J. H. Halland, “Genetic Algorithms,” Sci. Am., vol. 267, pp. 66-72, 1992.
[29] Location Routing Problem, June 2019. (Online). Available: http://fc.isima.fr/~lacomme/lrp/lrp.html
[1] L. Cooper, “Location-allocation problems,” Oper. Res., vol. 11, no. 3, pp. 331-343, June 1963.
[2] M. F. Goodchild, “ILACS: A Location-Allocation Model for Retail Site Selection,” J. Retailing, vol. 60, no. 1, pp. 84-100, Spring 1984.
[3] K. Gokbayrak and A. S. Kocaman, “A distance-limited continuous location-allocation problem for spatial planning of decentralized systems,” Comput. Oper. Res., vol. 88, pp. 15-29, Dec. 2017.
[4] J. Brimberg and S. Salhi, “A continuous location-allocation problem with zone-dependent fixed cost,” Ann. Oper. Res., vol. 136, pp. 99-115, Apr. 2005.
[5] S. M. Mousavi and S. T. A. Niaki, “Capacitated location allocation problem with stochastic location and fuzzy demand: A hybrid algorithm,” Appl. Math. Model., vol. 37, pp. 5109-5119, Apr. 2013.
[6] A. M. Fathollahi Fard and M. Hajaghaei-Keshteli, “A tri-level location-allocation model for forward/reverse supply chain,” Appl. Soft Comput., vol. 62, pp. 328-346, Jan. 2018.
[7] S. Khodaparasti, M. E. Bruni, P. Beraldi, H. R. Maleki, and S. Jahedi, “A multi-period location-allocation model for nursing home network planning under uncertainty,” Oper. Res. Health Care, vol. 18, pp. 4-15, Sept. 2018.
[8] P. Ghasemi, K. Khalili-Damghani, A. Hafezalkotob, and S. Raissi, “Uncertain multi-objective multi-commodity multi-period multi-vehicle location-allocation model for earthquake evacuation planning,” Appl. Math. Comput., vol. 350, pp. 105-132, June 2019.
[9] H. Baharmand, T. Comes, and M. Lauras, “Bi-objective multi-layer location-allocation model for the immediate aftermath of sudden-onset disasters,” Transport. Res. E-Log, vol. 127, pp. 86-110, July 2019.
[10] P. R. Jenkins, B. J. Lunday, and M. J. Robbins, “Robust, multi-objective optimization for the military medical evacuation location-allocation problem,” Omega, Jul. 2019, Art. no. 102088.
[11] D. Weible, P. Salamon, I. B. Christoph-Schulz, and G. Peter, “How do political, individual and contextual factors affect school milk demand? Empirical evidence from primary schools in Germany,” Food Policy, vol. 43, pp. 148-158, Dec. 2013.
[12] N. I. Benjamin and B. Lin, “Influencing factors on electricity demand in Chinese nonmetallic mineral products industry: A quantile perspective,” J. Clean. Prod., vol. 243, Jan. 2020, Art. no. 118584.
[13] B. W. Inganga, A. Njeru, K. Omburi, and O. I. Tirimba, “Factor affecting customer demand of financial services offered by commercial banks in Nairobi country,” Int. J. Sci. Res. Publ., vol. 4. no. 11, pp. 1-25 Nov. 2014.
[14] J. Cano-Belmán and H. Meyr, “Deterministic allocation models for multi-period demand fulfillment in multi-stage customer hierarchies,” Comput. Oper. Res., vol. 101, pp. 76-92, Jan. 2019.
[15] K. Afrin, B. Nepal, and L. Monplaisir, “A data-driven framework to new product demand prediction: Integrating product differentiation and transfer learning approach,” Expert Syst. Appl., vol. 108, pp. 246-257, Oct. 2018.
[16] T. V. Nguyen, L. Zhou, A. Y. L. Chong, Boying Li, and X. Pu, “Predicting customer demand for remanufacturing products: A data-mining approach,” Eur. J. Oper. Res., to be published.
[17] A. Ghodratnama, H. R. Arbabi, and A. Azaron, “Production planning in industrial townships modeled as hub location-allocation problems considering congestion in manufacturing plants,” Comput. Ind. Eng., vol. 129, pp. 479-501, Mar. 2019.
[18] S. Yan, J. Lin, Y. Chen, and F. Xie, “Rental bike location and allocation under stochastic demands,” Comput. Ind. Eng., vol. 107, pp. 1-11, May 2017.
[19] K. Wang, B. Makond, and S. Liu, “Location and allocation decisions in a two-echelon supply chain with stochastic demand – A genetic algorithm based solution,” Expert Syst. Appl., vol. 38, pp. 6125-6131, May 2011.
[20] M. Alizadeh, J. Ma, N. Mahdavi-Amiri, and M. Marufuzzaman, “A stochastic programming model for a capacitated location-allocation problem with heterogeneous demands,” Comput. Ind. Eng., vol. 137, Nov. 2019. Art. no. 106055.
[21] N. Vidyarthi and S. Jayaswal, “Efficient solution of a class of location-allocation problems with stochastic demand and congestion,” Comput. Oper. Res., vol. 48, pp. 20-30, Aug. 2014.
[22] E. Özceylan, A. Uslu, M. Erbaş, C. Çetinkaya, and S. K. İşleyen, “Optimizing the location-allocation problem of pharmacy warehouses: A case study in Gaziantep,” Int. J. Optimiz. Control, vol. 7, no. 1, pp. 117-129, 2017.
[23] M. Kaveh and M. S. Mesgari, “Improved biogeography-based optimization using migration process adjustment: An approach for location-allocation of ambulances,” Comput. Ind. Eng., vol. 135, pp. 800-813, Sept. 2019.
[24] B. R. Sarker, B. Wu, and K. P. Paudel, “Optimal number and location of storage hubs and biogas production reactors in farmland with allocation of multiple feedstocks,” Appl. Math. Model., vol. 55, pp. 447-465, Mar. 2018.
[25] Y. Lin, H. Jia, Y. Yang, G. Tian, F. Tao, and L. Ling, “An improved artificial bee colony for facility allocation problem of end-of-life vehicles recovery network,” J. Clean. Prod., vol. 205, pp. 134-144, Dec. 2018.
[26] F. Barzinpour and V. Esmaeilli, “A multi-objective relief chain location distribution model for urban disaster management,” Int. J. Adv. Manuf. Technol., vol. 70, pp. 1291-1302, Feb. 2014.
[27] B. Sharma, M. Ramkumar, N. Subramanian, and B. Malhotra, “Dynamic temporary blood facility location-allocation during and post-disaster periods,” Ann. Oper. Res., 2017.
[28] J. H. Halland, “Genetic Algorithms,” Sci. Am., vol. 267, pp. 66-72, 1992.
[29] Location Routing Problem, June 2019. (Online). Available: http://fc.isima.fr/~lacomme/lrp/lrp.html
@article{"International Journal of Business, Human and Social Sciences:79678", author = "Salinee Thumronglaohapun", title = "Heuristic Methods for the Capacitated Location- Allocation Problem with Stochastic Demand", abstract = "The proper number and appropriate locations of service centers can save cost, raise revenue and gain more satisfaction from customers. Establishing service centers is high-cost and difficult to relocate. In long-term planning periods, several factors may affect the service. One of the most critical factors is uncertain demand of customers. The opened service centers need to be capable of serving customers and making a profit although the demand in each period is changed. In this work, the capacitated location-allocation problem with stochastic demand is considered. A mathematical model is formulated to determine suitable locations of service centers and their allocation to maximize total profit for multiple planning periods. Two heuristic methods, a local search and genetic algorithm, are used to solve this problem. For the local search, five different chances to choose each type of moves are applied. For the genetic algorithm, three different replacement strategies are considered. The results of applying each method to solve numerical examples are compared. Both methods reach to the same best found solution in most examples but the genetic algorithm provides better solutions in some cases.", keywords = "Location-allocation problem, stochastic demand, local search, genetic algorithm. ", volume = "14", number = "6", pages = "510-6", }
