We present a collection of results in the broad area of stochastic optimization. Our basic model is that of dynamic resource allocation via customer acceptance control. We begin by modelling optimal acceptance to a discrete-capacity service-on-demand system where customers arrive with differing demands and revenues. With strong restrictions on customer types we establish the optimal policy under general arrival processes. With weaker restrictions we establish monotonicity properties under stationary arrivals. We than look at a deterministic demand-curve approach to the same problem; resource allocation over time. We solve the problem of non-overlapping customer demands, for a number of different demand curves. Our main work concerns selling perishable goods via customer acceptance control. We look at the optimal boundary between accepting and declining customers of different types. Existing papers demonstrate this threshold but fail to observe its surprisingly linear nature. We study the problem of finding the best linear threshold and see that, as a heuristic, it performs very well. Our study of linear thresholds educes an interesting problem: sample-path analysis. The problem concerns the evolution of segments of the sample-path in inventory-time space with regions of different downward drift. We succeed in fully characterising the studied sample path segments, finding a remarkable dual use of an interesting identity. In the final chapters, we look at two further problems of stochastic optimization. The first is an innovative approach to modelling future demand, utilizing previous price requests. Using these dynamic demand estimations we demonstrate monotonicity properties of the optimal pricing policy. The second problem is the famous parking problem first introduced by Rényi in the fifties. We study a Markov chain queuing model for the availability of parking spaces. We derive the pay-offs from the class of very natural threshold policies, with respect to an ‘average distance from venue’ objective.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:604120 |
| Date | January 2008 |
| Creators | Hodge, D. J. |
| Publisher | University of Cambridge |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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