Economics Insights @ CBS

We investigate optimal production controls for a tandem two-machine system with an internal buffer and unreliable machines. First, numerical methods are used to generate optimal policies for specific examples. Then, based on diese numerical results, an approximate suboptimal control policy is developed that divides the state space into distinct regions and uses only simple hedging-point policies in each region. Algorithms to obtain hedging points are provided.

Manufacturing and service organizations routinely face the challenge of scheduling jobs, orders, or individual customers in a schedule that optimizes either (i) an aggregate efficiency measure, (ii) a measure of performance balance, or (iii) some combination of these two objectives. We address these questions for single-machine job scheduling systems with fixed or controllable due dates.

In 1991, D. J. Bertsimas and G. van Ryzin introduced and analyzed a model for stochastic and dynamic vehicle routing in which a single, uncapacitated vehicle traveling at a constant velocity in a Euclidian region must service demands whose time of arrival, location and on-site service are stochastic. The objective is to find a policy to service demands over an infinite horizon that minimizes the expected system time (wait plus service) of the demands. This paper extends our analysis in several directions.

We analyze a class of stochastic and dynamic vehicle routing problems in which demands arrive randomly over time and the objective is minimizing waiting time. In our previous analysis ([5] and [6]) on this problem, we needed to assume uniformly distributed demand locations and Poisson arrivals. In this paper, using quite different techniques, we are able to extend our results to the more realistic case where demand locations have an arbitrary distribution and arrivals follow a general renewal process.