Arrangement Increasing Resource Allocation
Consider a system composed of several units. The performance of each unit can be affected by providing a portion of a limited amount of costly resources available. An allocation of resources to a unit results in a unit’s response that depends on the level of resources allocated to it and some of its random parameters. In this paper we consider cases where each unit has one or two random parameters. The overall performance of the system is mapped by a function on the vector of responses generated by all the units in the system. Our interest is in identifying the conditions on the response function of the units, the system performance function and the random parameters under which the random system performance as a function of the resource allocation has stochastic arrangement increasing property. This allows one to substantially reduce the number of allocation that needs to be searched to identify an optimal allocation that maximizes the expected utility derived from the system response as a result of the resource allocation.
KeywordsAllocation Arrangement increasing Joint stochastic orders Joint stochastic increasing vector Stochastic functions
Mathematics Subject Classification (2010)60E15 62E10 90B05 90B25
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- Li C, Li X (2016a) Some new results on allocation of coverage limits and deductibles to mutually independent risks. To appear in Communications in Statistics - Theory and MethodsGoogle Scholar
- Li C, Li X (2016b) Sufficient conditions for ordering aggregate heterogeneous random claim amounts. Insur Math Econ 70:406–413Google Scholar
- Liyanage L, Shanthikumar JG (1993) Allocation through stochastic schur convexity and stochastic transposition increasingness. In: Shaked M, Tong YL (eds) Stochastic inequalities, vol 22. Institute of Mathematical Statistics, pp 253–273Google Scholar