zbMATH — the first resource for mathematics

Service system design for managing interruption risks: a backup-service risk-mitigation strategy. (English) Zbl 1404.90057
Summary: This paper considers a system of immobile service facilities that provide service to a set of customers, which can be demand points, population zones, etc. The customers create congestion at facilities because of stochastic demands and service times. Each service facility is interrupted frequently, and the recovery process for each interruption starts after an assessment period. Both recovery and assessment processes last for uncertain periods. The backup-service strategy, together with appropriate adjustment of facility locations and service capacities, is used to mitigate interruption risks, that is, each customer is assigned to a backup facility to get service when the primary facility is interrupted. The goal is to determine open service facilities and their service capacities, and to assign customers to primary and backup facilities in order to maximize an aggregated performance measure, which is a balanced sum of the customers’ and the system owner’s criteria. The problem is formulated as an integer non-linear optimization model and solved by a Lagrangian-relaxation algorithm. The numerical experiments illustrate the high efficiency of the algorithm. Several managerial implications are also provided.

90B22 Queues and service in operations research
Full Text: DOI
[1] Aboolian, R.; Berman, O.; Drezner, Z., Location and allocation of service units on a congested network, IIE Transactions, 40, 4, 422-433, (2008)
[2] Aboolian, R.; Berman, O.; Krass, D., Profit maximizing distributed service system design with congestion and elastic demand, Transportation Science, 46, 2, 247-261, (2012)
[3] Ahmadi-Javid, A., Berman, O., & Hoseinpour, P. (2018). Location and capacity planning of facilities with general service-time distributions using conic optimization. arXiv:1809.00080.
[4] Ahmadi-Javid, A.; Ramshe, N., Linear formulations and valid inequalities for a classic location problem with congestion: A robust optimization application, Optimization Letters, (2018), forthcoming
[5] Ahmadi-Javid, A., & Hoseinpour, P. (2017). Convexification of queueing formulas by mixed-integer second-order cone programming: An application to a discrete location problem with congestion. arXiv:1710.05794.
[6] Ahmadi-Javid, A.; Seyedi, P.; Syam, S., A survey of healthcare facility location, Computers & Operations Research, 79, 223-263, (2017) · Zbl 1391.90365
[7] Amiri, A., The design of service systems with queueing time cost, workload capacities and backup service, European Journal of Operational Research, 104, 1, 201-217, (1998) · Zbl 0955.90016
[8] Atencia, I., A discrete-time queueing system with server breakdowns and changes in the repair times, Annals of Operations Research, 235, 1, 37-49, (2015) · Zbl 1334.60189
[9] Baron, O.; Berman, O.; Krass, D., Facility location with stochastic demand and constraints on waiting time, Manufacturing & Service Operations Management, 10, 3, 484-505, (2008)
[10] Belotti, P.; Kirches, C.; Leyffer, S.; Linderoth, J.; Luedtke, J.; Mahajan, A., Mixed-integer nonlinear optimization, Acta Numerica, 22, 1-131, (2013) · Zbl 1291.65172
[11] Berman, O.; Drezner, Z., The multiple server location problem, Journal of Operational Research Society, 58, 1, 91-99, (2007) · Zbl 1155.90414
[12] Berman, O.; Krass, D., Stochastic location models with congestion, (Laporte, G.; Nickel, S.; Saldanha-da-Gama, F., Location science, (2015), Springer), 443-485
[13] Berman, O.; Krass, D.; Wang, J., Locating service facilities to reduce lost demand, IIE Transactions, 38, 11, 933-946, (2006)
[14] Bertsekas, D. P., Nonlinear programming, (1999), Athena Scientific: Athena Scientific Belmont · Zbl 1015.90077
[15] Boffey, B.; Galvao, R.; Espejo, L., A review of congestion models in the location of facilities with immobile servers, European Journal of Operational Research, 178, 3, 643-662, (2007) · Zbl 1163.90417
[16] Boualem, M., Insensitive bounds for the stationary distribution of a single server retrial queue with server subject to active breakdowns, Advances in Operations Research, (2014), Article ID: 985453 · Zbl 1291.90063
[17] Bussieck, M. R.; Vigerske, S., MINLP solver software, Wiley encyclopedia of operations research and management science, (2010), Wiley
[18] Deepak, T. G.; Krishnamoorthy, A.; Narayanan, V. C.; Vineetha, K., Inventory with service time and transfer of customers and/inventory, Annals of Operations Research, 160, 1, 191-213, (2008) · Zbl 1221.90014
[19] Down, D. G.; Lewis, M. E., Dynamic load balancing in parallel queueing systems: Stability and optimal control, European Journal of Operational Research, 168, 2, 509-519, (2006) · Zbl 1101.90017
[20] Dudin, A.; Jacob, V.; Krishnamoorthy, A., A multi-server queueing system with service interruption, partial protection and repetition of service, Annals of Operations Research, 233, 1, 101-121, (2015) · Zbl 1327.90048
[21] Elhedhli, S., Service system design with immobile servers, stochastic demand, and congestion, Manufacturing and Service Operations Management, 8, 1, 92-97, (2006)
[22] Fisher, M. L., The Lagrangian relaxation method for solving integer programming problems, Management Science, 50, 12, 1861-1871, (2004)
[23] Geoffrion, A. M., Lagrangian relaxation for integer programming, (Jünger, M.; Liebling, Th. M.; Naddef, D.; Nemhauser, G. L.; Pulleyblank, W. R.; Reinelt, G.; Rinaldi, G.; Wolsey, L. A., 50 years of integer programming 1958-2008, (2010), Springer), 243-281 · Zbl 1187.90010
[24] Govindan, K.; Fattahi, M.; Keyvanshokooh, E., Supply chain network design under uncertainty: A comprehensive review and future research directions, European Journal of Operational Research, 263, 1, 108-141, (2017) · Zbl 1380.90041
[25] Grossmann, I. E.; Viswanathan, J.; Vecchietti, A.; Raman, R.; Kalvelagen, E., GAMS/DICOPT: A discrete continuous optimization package, (2002), GAMS Development Corporation
[26] He, Q. M.; Neuts, M. F., Two M/M/1 queues with transfers of customers, Queueing Systems, 42, 4, 377-400, (2002) · Zbl 1013.90044
[27] Hogan, K.; ReVelle, C., Concepts and applications of backup coverage, Management Science, 32, 11, 1434-1444, (1986)
[28] Hoseinpour, P.; Ahmadi-Javid, A., A profit-maximization location-capacity model for designing a service system with risk of service interruptions, Transportation Research, Part E: Logistics and Transportation Review, 96, 113-134, (2016)
[29] Hoseinpour, P.; Ahmadi-Javid, A., Designing service system networks with interruption risks, International Transactions in Operational Research, (2017)
[30] Jacob, V.; Krishnamoorthy, A., Analysis of customer-induced interruption and retrial of interrupted customers, American Journal of Mathematical and Management Sciences, 34, 4, 343-366, (2015)
[31] Jacob, V.; Chakravarthy, S. R.; Krishnamoorthy, A., On a customer-induced interruption in a service system, Stochastic Analysis and Applications, 30, 6, 949-962, (2012) · Zbl 1262.68023
[32] Jan, S.; Mooney, G.; Ryan, M.; Bruggemann, K.; Alexander, K., The use of conjoint analysis to elicit community preferences in public health research: A case study of hospital services in South Australia, Australian and New Zealand journal of Public Health, 24, 1, 64-70, (2000)
[33] Keyvanshokooh, E.; Ryan, S. M.; Kabir, E., Hybrid robust and stochastic optimization for closed-loop supply chain network design using accelerated Benders decomposition, European Journal of Operational Research, 249, 1, 76-92, (2016) · Zbl 1346.90136
[34] Kim, S., A column generation heuristic for congested facility location problem with clearing functions, Journal of the Operational Research Society, 64, 12, 1780-1789, (2013)
[35] Krishnamoorthy, A.; Nair, S. S.; Narayanan, V. C., Production inventory with service time and interruptions, International Journal of Systems Science, 46, 10, 1800-1816, (2015) · Zbl 1332.90011
[36] Krishnamoorthy, A.; Pramod, P. K.; Chakravarthy, S. R., Queues with interruptions: A survey, TOP, 22, 1, 290-320, (2014) · Zbl 1305.60095
[37] Krishnamoorthy, A.; Sivadasan, J.; Lakshmy, B., Queues with interruption in random environment, Annals of Operations Research, 233, 1, 201-219, (2015) · Zbl 1325.90027
[38] Krishnamoorthy, A.; Sivadasan, J.; Lakshmy, B., On an M/G/1 queue with vacation in random environment, (Proceedings of International Conference on Information Technologies and Mathematical Modelling, (2015), Springer), 250-262
[39] Kumar, B. K.; Rukmani, R.; Thanikachalam, A.; Kanakasabapathi, V., Performance analysis of retrial queue with server subject to two types of breakdowns and repairs, Operational Research, 18, 2, 521-559, (2018)
[40] LeBlanc, L. J.; Simmons, R. V., Continuous models for capacity design of large packet-switched telecommunication networks, ORSA Journal on Computing, 1, 4, 271-286, (1989) · Zbl 0825.90394
[41] Little, J. D., A proof for the queuing formula: L = λW, Operations Research, 9, 3, 383-387, (1961) · Zbl 0108.14803
[42] Narasimhan, S.; Pirkul, H.; Schilling, D. A., Capacitated emergency facility siting with multiple levels of backup, Annals of Operations Research, 40, 1, 323-337, (1992) · Zbl 0782.90062
[43] Newman, R. G., A conjoint analysis in outpatient clinic preferences, Journal of Health Care Marketing, 4, 1, 41-49, (1984)
[44] Pirkul, H.; Schilling, D., The capacitated maximal covering location problem with backup service, Annals of Operations Research, 18, 1, 141-154, (1989) · Zbl 0707.90066
[45] Pirkul, H.; Schilling, D. A., The siting of emergency service facilities with workload capacities and backup service, Management Science, 34, 7, 896-908, (1988)
[46] Rajagopalan, S.; Yu, H. L., Capacity planning with congestion effects, European Journal of Operational Research, 134, 2, 365-377, (2001) · Zbl 0990.90007
[47] Riccio, L. J., Management science in New York’s department of Sanitation, Interfaces, 14, 2, 1-13, (1984)
[48] Saccani, N.; Johansson, P.; Perona, M., Configuring the after-sales service supply chain: A multiple case study, International Journal of Production Economics, 110, 1, 52-69, (2007)
[49] Sherali, H. D.; Choi, G.; Tuncbilek, C. H., A variable target value method for no differentiable optimization, Operations Research Letters, 26, 1, 1-8, (2000) · Zbl 0958.90091
[50] Silva, F.; Serra, D., Locating emergency services with different priorities: The priority queuing covering location problem, Journal of Operational Research Society, 59, 9, 1229-1238, (2008) · Zbl 1176.90363
[51] Snyder, L. V.; Atan, Z.; Peng, P.; Rong, Y.; Schmitt, A. J.; Sinsoysal, B., OR/MS models for supply chain disruptions: A review, IIE Transactions, 48, 2, 89-109, (2016)
[52] Syam, S. S., A multiple server location-allocation model for service system design, Computers & Operations Research, 35, 7, 2248-2265, (2008) · Zbl 1180.90079
[53] Tadj, L.; Ke, J. C., A single and batch service queue with random breakdowns, International Journal of Services Sciences, 5, 2, 116-132, (2014)
[54] Taleb, S.; Aissani, A., Preventive maintenance in an unreliable M/G/1 retrial queue with persistent and impatient customers, Annals of Operations Research, 247, 1, 291-317, (2016) · Zbl 1358.90037
[55] Vidyarthi, N.; Jayaswal, S., Efficient solution of a class of location-allocation problems with stochastic demand and congestion, Computers & Operations Research, 48, 20-30, (2014) · Zbl 1348.90424
[56] Vidyarthi, N.; Kuzgunkaya, O., The impact of directed choice on the design of preventive healthcare facility network under congestion, Health Care Management Science, 18, 4, 459-474, (2014)
[57] Wang, Q.; Batta, R.; Rump, C. M., Algorithms for a facility location problem with stochastic customer demand and immobile servers, Annals of operations Research, 111, 1, 17-34, (2002) · Zbl 1013.90023
[58] Wang, Q.; Batta, R.; Rump, C. M., Facility location models for immobile servers with stochastic demand, Naval Research Logistics, 51, 1, 137-152, (2004) · Zbl 1055.90046
[59] Yang, D. Y.; Ke, J. C., Cost optimization of a repairable M/G/1 queue with a randomized policy and single vacation, Applied Mathematical Modelling, 38, 21, 5113-5125, (2014) · Zbl 1428.90047
[60] Yang, D. Y.; Chang, F. M.; Ke, J. C., On an unreliable retrial queue with general repeated attempts and J optional vacations, Applied Mathematical Modelling, 40, 4, 3275-3288, (2016)
[61] Zhang, Y.; Berman, O.; Verter, V., Incorporating congestion in preventive healthcare facility network design, European Journal of Operations Research, 198, 3, 922-935, (2009) · Zbl 1176.90390
[62] Zhang, Y.; Berman, O.; Verter, V., The impact of client choice on preventive healthcare facility network design, OR Spectrum, 34, 2, 349-370, (2012) · Zbl 1239.90069
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.