Dynamic and stochastic models with freight distribution applications

Anton Jan Kleywegt, Purdue University

Abstract

This research is motivated by the need for decision support tools to manage complex freight distribution operations. The fact that freight distribution is such an important economic activity, makes this research both worthwhile and rewarding. In the first part of this research, a generic resource allocation problem in a dynamic and stochastic environment is studied. This problem is motivated by the issues facing a manager of a transportation operation regarding the acceptance of loads and the dispatching of a vehicle. Because it has applications in many other areas, such as the scheduling of batch processors, the selling of assets, and the selection of investment projects, it is called the Dynamic and Stochastic Knapsack Problem (DSKP). The DSKP is analyzed for both the infinite horizon and the finite horizon cases. It is shown that an optimal acceptance rule is given by a threshold rule. The optimal stopping time is also easily determined, and has the convenient property that under typical conditions, only times right after a demand has been accepted need to be considered as potential stopping times. Efficient algorithms for computing optimal solutions are proposed. These algorithms compute the value corresponding to each state of the process only once, in contrast with the classical iterative algorithms that are used to solve dynamic programming problems. It is established that the optimal value and optimal threshold have a number of interesting monotonicity and convexity properties. In the second part of this research, a distribution problem with a number of terminals and a fleet of vehicles is studied. This problem is called the Dynamic and Stochastic Distribution Problem (DSDP). A Markov decision process model is developed, and optimal policies are characterized. It is shown that the classical algorithms for solving Markov decision processes converge if applied to the DSDP, in spite of the fact that the DSDP does not satisfy all the assumptions made in the traditional convergence proofs. An algorithm that exploits the structure of the DSDP is developed. The proposed algorithm consistently outperforms the classical algorithms in computational experiments.

Degree

Ph.D.

Advisors

Papastavrou, Purdue University.

Subject Area

Industrial engineering|Operations research|Systems design

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