Restless bandit marginal productivity indices, diminishing returns, and optimal control of make-to-order/make-to-stock M/G/1 queues

被引:31
作者
Niño-Mora, J [1 ]
机构
[1] Univ Carlos III Madrid, Dept Stat, E-28903 Getafe, Madrid, Spain
关键词
restless bandits; stochastic scheduling; index policies; indexability; control by price; semi-Markov decision processes; dynamic resource allocation; diminishing returns; marginal productivity; efficient frontier; convex optimization; bias; mixed criteria; make to order; make to stock; control of queues; production-inventory control; partial conservation laws; achievable performance;
D O I
10.1287/moor.1050.0165
中图分类号
C93 [管理学]; O22 [运筹学];
学科分类号
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要
This paper presents a framework grounded on convex optimization and economics ideas to solve by index policies problems of optimal dynamic allocation of effort to a discrete-state (finite or countable) binary-action (work/rest) semi-Markov restless bandit project, elucidating issues raised by previous work. Its contributions include: (i) the concept of a restless bandit's marginal productivity index (MPI), characterizing optimal policies relative to general cost and work measures; (ii) the characterization of indexable restless bandits as those satisfying diminishing marginal returns to work, consistently with a nested family of threshold policies; (iii) sufficient indexability conditions via partial conservation laws (PCLs); (iv) the characterization of the MPI as an optimal marginal productivity rate relative to feasible active-state sets; (v) application to semi-Markov bandits under several criteria, including a new mixed average-bias criterion; and (vi) PCL-indexability analyses and MPIs for optimal service control of make-to-order/make-to-stock queues with convex holding costs, under discounted and average-bias criteria.
引用
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页码:50 / 84
页数:35
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