Congestion-based leadtime quotation and pricing for revenue maximization with heterogeneous customers. (English) Zbl 1269.60074
The present paper deals with a queueing model where two customer classes compete for a given resource and each customer upon arrival is dynamically presented with a menu of price and leadtime pairs. The customers select their preferred pairs from the menu and the server is obligated to meet the given leadtime. Customers have convex-concave delay costs. The firm does not have information on a given customer’s type, so the offered menus must be incentive compatible. A menu quotation policy is given and proven to be asymptotically optimal under traditional large-capacity heavy-traffic scaling.
Reviewer: János Sztrik (Debrecen)
MSC:
| 60K30 | Applications of queueing theory (congestion, allocation, storage, traffic, etc.) |
| 60K25 | Queueing theory (aspects of probability theory) |
References:
| [1] | Afèche, P.: Incentive-compatible revenue management in queuing systems: optimal strategic delay and other delay tactics. Working paper, Rotman School of Management, Toronto, Canada (2010) |
| [2] | Akan, M., Ata, B., Olsen, T.L.: Congestion-based leadtime quotation for heterogeneous customers with convex–concave delay costs: optimality of a cost-balancing policy based on convex hull functions. Oper. Res. (2012, forthcoming) · Zbl 1263.90019 |
| [3] | Akan, M., Ata, B., Dana, J.: Revenue management by sequential screening. Working paper (2008) · Zbl 1330.91078 |
| [4] | Antonides, G., Verhoef, P.C., van Aalst, M.: Consumer perception and evaluation of waiting time: a field experiment. J. Consum. Psychol. 12(3), 193–202 (2002) · doi:10.1207/S15327663JCP1203_02 |
| [5] | Ata, B., Kumar, S.: Heavy traffic analysis of open processing networks with complete resource pooling: asymptotic optimality of discrete review policies. Ann. Appl. Probab. 15(1), 331–391 (2005) · Zbl 1071.60081 · doi:10.1214/105051604000000495 |
| [6] | Ata, B., Olsen, T.L.: Near-optimal dynamic leadtime quotation and scheduling under convex–concave customer delay costs. Oper. Res. 57(3), 753–768 (2008) · Zbl 1233.90177 · doi:10.1287/opre.1080.0608 |
| [7] | Besbes, O., Maglaras, C.: Revenue optimization for a make-to-order queue in an uncertain market environment. Oper. Res. 57(6), 1438–1450 (2009) · Zbl 1233.90111 · doi:10.1287/opre.1080.0645 |
| [8] | Borst, S., Mandelbaum, A., Reiman, M.I.: Dimensioning large call centers. Oper. Res. 52(1), 17–34 (2004) · Zbl 1165.90388 · doi:10.1287/opre.1030.0081 |
| [9] | Çelik, S., Maglaras, C.: Dynamic pricing and lead-time quotation for a multiclass make-to-order queue. Manag. Sci. 54, 1132–1146 (2008) · Zbl 1232.90140 · doi:10.1287/mnsc.1070.0836 |
| [10] | Chatterjee, S., Slotnick, S.A., Sobel, M.J.: Delivery guarantees and the interdependence of marketing and operations. Prod. Oper. Manag. 11(3), 393–410 (2002) · doi:10.1111/j.1937-5956.2002.tb00193.x |
| [11] | Charnsirisakskul, K., Griffin, P., Keskinocak, P.: Order selection and scheduling with lead-time flexibility. IIE Trans. 36, 697–707 (2004) · doi:10.1080/07408170490447366 |
| [12] | Charnsirisakskul, K., Griffin, P., Keskinocak, P.: Pricing and scheduling decisions with lead-time flexibility. Eur. J. Oper. Res. 171(1), 153–169 (2006) · Zbl 1091.90016 · doi:10.1016/j.ejor.2004.07.062 |
| [13] | Csorgo, M., Horvath, L.: Weighted Approximations in Probability and Statistics. Wiley, New York (1993) |
| [14] | Dellaert, N.P.: Due-date setting and production control. Int. J. Prod. Econ. 23, 59–67 (1991) · doi:10.1016/0925-5273(91)90048-X |
| [15] | Duenyas, I.: Single facility due-date setting with multiple customer classes. Manag. Sci. 41(4), 608–619 (1995) · Zbl 0836.90075 · doi:10.1287/mnsc.41.4.608 |
| [16] | Duenyas, I., Hopp, W.J.: Quoting customer lead times. Manag. Sci. 41(1), 43–57 (1995) · Zbl 0829.90049 · doi:10.1287/mnsc.41.1.43 |
| [17] | Duran, S., Gülcü, A., Keskinocak, P., Swann, J.L.: Leadtime quotation and order acceptance when demand depends on service performance. Working paper, Georgia Institute of Technology, Atlanta, GA (2006) |
| [18] | Easton, F.F., Moodie, D.R.: Pricing and lead time decisions for make-to-order firms with contingent orders. Eur. J. Oper. Res. 116(2), 305–318 (1999) · Zbl 1007.91519 · doi:10.1016/S0377-2217(98)00101-5 |
| [19] | Frederick, S., Loewenstein, G., O’Donoghue, T.: Time discounting and time preference: a critical review. J. Econ. Lit. 40, 350–401 (2002) · doi:10.1257/002205102320161311 |
| [20] | Gurvich, I., Whitt, W.: Scheduling flexible servers with convex delay costs in many-server service systems. Manuf. Serv. Oper. Manag. 11(2), 237–253 (2007) |
| [21] | Ha, A.: Incentive-compatible pricing for a service facility with joint production and congestion externalities. Manag. Sci. 44, 1623–1636 (1998) · Zbl 0989.90045 · doi:10.1287/mnsc.44.12.1623 |
| [22] | Ha, A.: Optimal pricing that coordinates queues with customer-chosen service requirements. Manag. Sci. 47(7), 915–930 (2001) · Zbl 1232.90147 · doi:10.1287/mnsc.47.7.915.9806 |
| [23] | Hassin, R., Haviv, M.: To Queue or Not to Queue: Equilibrium Behavior in Queueing Systems. International Series in Operations Research & Management Science. Kluwer Academic, Norwell (2003) · Zbl 1064.60002 |
| [24] | Kahneman, D., Tversky, A.: Advances in prospect theory: cumulative representation of uncertainty. J. Risk Uncertain. 5, 297–324 (1992) · Zbl 0775.90106 · doi:10.1007/BF00122574 |
| [25] | Katta, A.-K., Sethuraman, J.: Pricing strategies and service differentiation in queues–a profit maximization perspective. Working paper, Columbia University, New York, NY (2005) |
| [26] | Kapuscinski, R., Tayur, S.: Reliable due-date setting in a capacitated mto system with two customer classes. Oper. Res. 55, 56–74 (2007) · Zbl 1167.90541 · doi:10.1287/opre.1060.0339 |
| [27] | Keskinocak, P., Ravi, R., Tayur, S.: Scheduling and reliable lead time quotation for orders with availability intervals and lead time sensitive revenues. Manag. Sci. 47(2), 264–279 (2001) · Zbl 1232.90211 · doi:10.1287/mnsc.47.2.264.9836 |
| [28] | Keskinocak, P., Tayur, S.: Due-date management policies. In: Simchi-Levi, D., David Wu, S., Max Shen, Z. (eds.) Handbook of Quantitative Supply Chain Analysis: Modeling in the E-Business Era. International Series in Operations Research and Management Science, pp. 485–553. Kluwer Academic, Norwell (2004) · Zbl 1105.90313 |
| [29] | Kumar, S., Randhawa, R.S.: Exploiting market size in service systems. Manuf. Serv. Oper. Manag. 12(3), 511–526 (2010) · doi:10.1287/msom.1090.0282 |
| [30] | Leclerc, F., Schmitt, B.H., Dube, L.: Waiting time and decision making: is time like money? J. Consum. Res. 22(1), 110–119 (1995) · doi:10.1086/209439 |
| [31] | Lederer, P.J., Li, L.D.: Pricing, production, scheduling, and delivery-time competition. Oper. Res. 45(3), 407–420 (1997) · Zbl 0890.90020 · doi:10.1287/opre.45.3.407 |
| [32] | Maglaras, C.: Revenue management for a multiclass single-server queue via a fluid model analysis. Oper. Res. 54(5), 914–932 (2006) · Zbl 1167.90545 · doi:10.1287/opre.1060.0305 |
| [33] | Maglaras, C., Zeevi, A.: Pricing and capacity sizing for systems with shared resources: approximate solutions and scaling relations. Manag. Sci. 49(8), 1018–1038 (2003) · doi:10.1287/mnsc.49.8.1018.16402 |
| [34] | Maglaras, C., Zeevi, A.: Pricing and design of differentiated services: approximate analysis and structural insights. Oper. Res. 53(2), 242–262 (2005a) · Zbl 1165.91371 · doi:10.1287/opre.1040.0172 |
| [35] | Maglaras, C., Zeevi, A.: Effects of substitution and customer choice on heavy-traffic. Working paper, Columbia University, New York, NY (2005b) · Zbl 1165.91371 |
| [36] | Mandelbaum, A., Stolyar, A.L.: Scheduling flexible servers with convex delay costs: heavy-traffic optimality of the generalized c{\(\mu\)}-rule. Oper. Res. 52(6), 836–855 (2004) · Zbl 1165.90402 · doi:10.1287/opre.1040.0152 |
| [37] | Marchand, M.G.: Priority pricing. Manage. Sci., Theory Ser. 20(7), 1131–1140 (1974) · Zbl 0314.90008 · doi:10.1287/mnsc.20.7.1131 |
| [38] | Mendelson, H., Whang, S.: Optimal incentive-compatible priority pricing for the m/m/1 queue. Oper. Res. 38(5), 870–883 (1990) · Zbl 0723.90023 · doi:10.1287/opre.38.5.870 |
| [39] | Palaka, K., Erlebacher, S., Kropp, D.H.: Lead-time setting, capacity utilization, and pricing decisions under lead-time dependent demand. IIE Trans. 30(2), 151–163 (1998) |
| [40] | Plambeck, E.L.: Optimal leadtime differentiation via diffusion approximations. Oper. Res. 52, 213–228 (2004) · Zbl 1165.90405 · doi:10.1287/opre.1030.0089 |
| [41] | Plambeck, E.L., Ward, A.R.: Optimal control of high-volume assemble-to-order systems with maximum leadtime quotation and expediting. Queueing Syst. 60(1–2), 1–69 (2008) · Zbl 1156.90304 · doi:10.1007/s11134-008-9085-6 |
| [42] | Plambeck, E.L., Kumar, S., Harrison, J.M.: A multiclass queue in heavy traffic with throughput time constraints: asymptotically optimal dynamic controls. Queueing Syst. 39, 23–54 (2001) · Zbl 1002.90015 · doi:10.1023/A:1017983532376 |
| [43] | Rao, S., Petersen, E.R.: Optimal pricing of priority services. Oper. Res. 46(1), 46–56 (1998) · Zbl 0987.90023 · doi:10.1287/opre.46.1.46 |
| [44] | Rogers, L.C.G., Williams, D.: Diffusions, Markov Processes and Martingales. Cambridge University Press, Cambridge (2000) · Zbl 0977.60005 |
| [45] | Royden, H.: Real Analysis, 3rd edn. McMillan, New York (1988) · Zbl 0704.26006 |
| [46] | Shen, Z.-J., Su, X.: Customer behavior modeling in revenue management and auctions: a review and new research opportunities. Prod. Oper. Manag. 16(6), 713–728 (2007) · doi:10.1111/j.1937-5956.2007.tb00291.x |
| [47] | Stolyar, A.L.: Maxweight scheduling in a generalized switch: state space collapse and workload minimization in heavy traffic. Ann. Appl. Probab. 14(1), 1–53 (2004) · Zbl 1057.60092 · doi:10.1214/aoap/1075828046 |
| [48] | Tang, K., Tang, J.: Time-based pricing and leadtime policies for a build-to-order manufacturer. Prod. Oper. Manag. 11(3), 374–392 (2002) · doi:10.1111/j.1937-5956.2002.tb00192.x |
| [49] | Van Mieghem, J.A.: Dynamic scheduling with convex delay costs: the generalized c{\(\mu\)} rule. Ann. Appl. Probab. 5, 809–833 (1995) · Zbl 0843.90047 · doi:10.1214/aoap/1177004706 |
| [50] | Van Mieghem, J.A.: Price and service discrimination in queuing systems: incentive compatibility of gc{\(\mu\)} scheduling. Manag. Sci. 46(9), 1249–1267 (2000) · Zbl 1232.90157 · doi:10.1287/mnsc.46.9.1249.12238 |
| [51] | Wang, L., Kapuscinski, R.: Joint price and due date quotation: monopolistic and competitive cases. Working paper, University of Michigan, Ann Arbor, MI (2007) |
| [52] | Weng, Z.K.: Manufacturing lead times, system utilization rates and lead-time-related demand. Eur. J. Oper. Res. 89(2), 259–268 (1996) · Zbl 0913.90150 · doi:10.1016/0377-2217(95)00268-5 |
| [53] | Whitt, W.: Stochastic-Process Limits. Springer, Berlin (2002) · Zbl 0993.60001 |
| [54] | Wolff, R.W.: Stochastic Modeling and the Theory of Queues. Prentice Hall, New York (1989) · Zbl 0701.60083 |
| [55] | Yahalom, T., Harrison, J.M., Kumar, S.: Designing and pricing incentive compatible grades of service in queuing systems. Working paper, Stanford University, Stanford, CA (2006) |
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