This dissertation addresses some of the issues arising from the distribution of industrial gas. In the industrial gas business, the concept of vendor managed inventory (VMI) is practiced. Thus the supplier decides which customer gets delivery and the time that the delivery is made. This results in a win-win situation for both the vendors and customers as the customers get product when they need and the vendor gets to make deliveries with more flexibility thereby enabling cost benefits through grouping of customers. But, the VMI concept comes with its own problems that become difficult to solve when there are multiple supply points (vendors) and a large customer base for each vendor.

One such problem is the assignment of trailers (trucks) of different capacities to "tours" so that the total amount of product delivered is maximized while returning the least possible amount of product. This problem differs from most standard problems dealt with in the literature both in structure and in the constraints involved. The first part of this dissertation investigates the above-mentioned problem with the goal of making the solution fast and implementable. The problem is formulated as a mixed integer linear program (MILP) and solved using a "dynamic" branch and bound scheme. Innovative branching and bounding schemes that exploit the special structure of the problem are devised to enhance the speed of the algorithm. Computational experiments are done to test the effectiveness of the branching and bounding schemes as well as different fathoming tolerance strategies. Different objectives like "reference" cost (value of serving a customer) and "reference" cost with a second objective of volume returned are also tested on the branch and bound framework to compare differences in solutions and to attempt and establish links between them. Finally, the stochastic version of the problem is tackled. The stochasticity arises from the uncertainty (normally distributed) in the demand of customers on a tour. The objective function is modified to maximize expected volume delivered while minimizing the semi-variance of delivery volume (downside variance). An approximation procedure based on discretizing the distribution of each customer is developed to calculate the objective value. This value can then be employed within our already developed branch and bound methodology.

The second part of the dissertation considers the problem of reallocating trailers (trucks) between plants such that certain performance indicators like volume per trip, volume per mile, and average product returned are optimized over a time horizon. This problem differs from the standard fleet sizing (re-allocation) problem as it takes capacity of individual trailers into account. Trailers are categorized based on capacities and form part of "slates", which are designed to indicate the number of trailers of each category that have to be placed at different plants and the value of having those trailers. The value of each slate is calculated by a combination of simulation and the analysis of hierarchy procedure (AHP). The problem is modeled as a mixed integer program (MIP) and its solution chooses one slate for each plant that maximizes the total value of the selected slates. The solution to this problem forms a prelude to the trailer assignment model. In addition to the above-mentioned issues, cost to serve a customer plays an important role in distribution as well as other areas. It serves as a key metric that represents the value of serving a customer. The third and final part of the dissertation deals with refining the calculation of previously developed metric using concepts that include cooperative game theory.