Abstract
In this paper we consider a firm that employs heterogeneous workers to meet demand for its product or service. Workers differ in their skills, speed, and/or quality, and they randomly leave, or turn over. Each period the firm must decide how many workers of each type to hire or fire in order to meet randomly changing demand forecasts at minimal expense. When the number of workers of each type can by continuously varied, the operational cost is jointly convex in the number of workers of each type, hiring and firing costs are linear, and a random fraction of workers of each type leave in each period, the optimal policy has a simple hire- up-to/fire-down-to structure. However, under the more realistic assumption that the number of workers of each type is discrete, the optimal policy is much more difficult to characterize, and depends on the particular notion of discrete convexity used for the cost function. We explore several different notions of discrete convexity and their impact on structural results for the optimal policy.
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References
Altman E, Gaujal B, Hordijk A (2000) Multimodularity, convexity, and optimizations properties. Math Oper Res 25:324–347
Armony M, Maglaris C (2003) On customer contact centers with a call-back option: customer decisions, routing rules, and system design. Oper Res 52:271–292
Bartholomew DJ, Forbes AF, McClean SI (1991) Statistical techniques for manpower planning, 2nd edn. Wiley, New York
Berman O, Larson RC (1994) Determining optimal pool size of a temporary call-in work force. Eur J Oper Res 73:55–64
Bordoloi SK, Matsuo H (2001) Human resource planning in knowledge-intensive operations: a model for learning with stochastic turnover. Eur J Oper Res 130:169–189
Borst S, Seri P (1999) Robust algorithms for sharing agents with multiple skills. Working paper, Bell Laboratories, Lucent Technologies, Murray Hill, NJ
Dixit A (1997) Investment and employment dynamics in the short run and the long run. Oxford Econ Pap 49:1–20
Eberly JC, van Mieghem JA (1997) Multi-factor dynamic investment under uncertainty. J Econ Theory 75:345–387
Fine CH, Freund RM (1990) Optimal investment in product-flexible manufacturing capacity. Manage Sci 36:449–466
Gans N, Koole G, Mandelbaum A (2003) Telephone call centers: tutorial, review, and research prospects. Manuf Serv Oper Manage 5:79–141
Gans N, Zhou Y-P (2002) Managing learning and turnover in employee staffing. Oper Res 50:991–1006
Hajek B (1985) Extremal splittings of point processes. Math Oper Res 10:543–556
Harrison JM, van Mieghem JA (1999) Multi-resource investment strategies: operational hedging under demand uncertainty. Eur J Oper Res 113:17–29
Harrison JM, Zeevi A (2003) A method for staffing large call centers based on stochastic fluid models (preprint)
Karlin S (1968) Total positivity, vol 1. Stanford University Press, Stanford
Koole G, Mandelbaum A (2002) Queueing models of call centers: an introduction. Ann Oper Res 113:41–59
Koole G, Pot A, Talim J (2003) Routing heuristics for multi-skill call centers. In: Proceedings of the 2003 winter simulation conference
Larson RC, Pinker EJ (2000) Staffing challenges in financial services. In: Melnick EL, Nayyar PR, Pinedo ML, Seshadri S (eds). Creating value in financial services: strategies, operations, and technologies, vol 17. Kluwer, Boston, pp 327–356
Mandelbaum A (2003) Call centers: research bibliography with abstracts. Downloadable from: http://ie.technion.ac.il/serveng
Murota K (2003) Discrete convex analysis. SIAM, Philadelphia
Murota K (2004) Note on multimodularity and L-convexity, report METR 2004-31. Department of Mathematical, Informatics The University of Tokyo, Tokyo, Japan
Misra S, Pinker E, Shumsky RA (2003) Sizing and structuring a slaesforce in the presence of job flexibility and experience-based learning (preprint)
Narongwanich W, Duenyas I, Birge JR (2003) Optimal portfolio of reconfigurable and dedicated capacity under uncertainty (preprint)
Netessine S, Dobson G, Shumsky RA (2002) Flexible service capacity: optimal investment and the impact of demand correlation. Oper Res 50:375–388
Perry M, Nilsson A (1994) Performance modeling of automatic call distributors: operator services staffing with heterogeneous positions. In: Proceedings of the 14th international teletraffic congress, ITC-14. Elsevier, Amsterdam, pp 1023–1032
Pinedo M, Seshadri S, Shanthikumar JG (2000) Call centers in financial services: strategies, technologies and operations. In: Melnick EL, Nayyar PR, Pinedo ML, Seshadri S (eds). Creating value in financial services: strategies, operations, and technologies, vol 18. Kluwer, Boston, pp 357–388
Pinker EJ, Larson RC (2003) Optimizing the use of contingent labor when demand is uncertain. Eur J Oper Res 144:39–55
Pinker EJ, Shumsky RA (2000) The efficiency-quality trade-off of cross-trained workers. Manuf Serv Oper Manage 2:32–48
Schmidt CP, Nahmias S (2003) Workforce planning under uncertainty (preprint)
Shumsky RA, Zhang F (2003) Dynamic capacity management with substitution (preprint)
van Mieghem JA (1998) Investment strategies for flexible resources. Manage Sci 44:1071–1078
van Mieghem JA (2002) Capacity portfolio investment and hedging: review and new directions (preprint)
van Mieghem JA, Rudi N (2002) Newsvendor networks: inventory management and capacity investment with discretionary activities. Manuf Serv Oper Manage 4:313–335
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Ahn, HS., Righter, R. & Shanthikumar, J.G. Staffing decisions for heterogeneous workers with turnover. Math Meth Oper Res 62, 499–514 (2005). https://doi.org/10.1007/s00186-005-0033-5
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DOI: https://doi.org/10.1007/s00186-005-0033-5