Doctoral Dissertations

Date of Award

12-1999

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Management Science

Major Professor

Charles Noon

Committee Members

Melissa R. Bowers, Chanaka Edirisinghe, Bruce A. Ralston

Abstract

The Deterministic Repeatable Inventory Routing Problem (DRIRP) is a combination of a Vehicle Routing Problem and an Inventory ManagementProblem. It is the problem of finding a set of vehicle routes and delivery/pickup amounts servicing customers with deterministic production rates. The customers have limited local storage and thus a visit must be scheduled before the stockout or overflow level is reached. The objective of the problem is to minimize the per unit cost of picking up the product.Moreover, the problem is constrained to finding solutions that are repeatable in a cyclic fashion. This means that, once established, an optimal routingstrategy can be implemented over a long planning horizon as long as the problem data remains the same, The DRIRP model can be applied to a number of real world problems including off-shore barge scheduling.Several models, ranging from a single-vehicle single-visit to a complex multi-vehicle multi-visit model are developed. Each of these models increases the complexity and range of the solutions that can be considered by an analyst while the basic problem instance remains the same.The DRIRP is in a general class of mathematically difficult problem that cannot be solved in polynomial time. However, this research examines several techniques to help solve particular instances and models of the problem. These include variable elimination techniques, continuous variable bounding logic, and a cutting plane approach based on polyhedral theory.The various techniques improve the lower bound of the LP relaxation, thus improving the efficiency and run-time of the branch-and-bound technique used to solve the Mixed Integer Program.The approaches are tested on sample test problems obtained from areal world industrial operation. Preliminary results show that the problem is indeed very difficult but the solution methodology developed in this dissertation can be applied to barge scheduling. Moreover, these models and solution techniques further expand the set of feasible solutions that can be considered and allow larger problems to be solved.

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