Abstract
Stochastic scheduling problems are considered by using discounted dynamic programming. Both, maximizing pure rewards and minimizing linear holding costs are treated in one common Markov decision problem. A sufficient condition for the optimality of the myopic policy for finite and infinite horizon is given. For the infinite horizon case we show the optimality of an index policy and give a sufficient condition for the index policy to be myopic. Moreover, the relation between the two sufficient conditions is discussed.
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Baras JS, Dorsey AJ, Makowski AM (1985) Two competing queues with linear costs and geometric service requirements: Theμc-rule is often optimal. Adv Appl Probab 17:186–209
Baras JS, Ma DJ, Makowski AM (1985)Kcompeting queues with geometric service requirements and linear costs: Theμc-rule is always optimal. Syst Control Lett 6:173–180
Buyukkoc C, Varaiya P, Walrand J (1985) Thecμ rule revisited. Adv Appl Prob 17:237–238
Bell C (1971) Characterization and computation of optimal policies for operating an M/G/1 queueing system with removable server. Oper Res 19:208–218
Friis SH, Rieder U, Weishaupt J (1993) Optimal control of single-server queueing networks. ZOR-Methods and Models of Oper Res 37:187–205
Gittins JC (1989) Multi-armed bandit allocation indices. Wiley, Chichester
Harrison JM (1975a) A priority queue with discounted linear costs. Oper Res 23:260–269
Harrison JM (1975b) Dynamic scheduling of a multiclass queue: Discount optimality. Oper Res 23:270–282
Heyman DP, Sobel MJ (1984) Stochastic models in operations research, Vol. II. McGraw-Hill, New York
Righter R, Shanthikumar JG (1989) Scheduling multiclass single server queueing systems to stochastically maximize the number of successful departures. Prob Eng Inf Sciences 3:323–333
Tcha DW, Pliska SR (1977) Optimal control of single server queueing networks and multi-classM/G/1 queues with feedback. Oper Res 25:248–258
Weishaupt J (1992) Optimalitätsaussagen für stochastische Schedulingprobleme. Dissertation, Universität Ulm
Whittle P (1981) Arm-acquiring bandits. Ann Probab 9:284–292
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Weishaupt, J. Optimal myopic policies and index policies for stochastic scheduling problems. ZOR - Methods and Models of Operations Research 40, 75–89 (1994). https://doi.org/10.1007/BF01414030
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DOI: https://doi.org/10.1007/BF01414030