No abstract

We study real-time demand fulfillment for networks consisting of multiple local warehouses, where spare parts of expensive technical systems are kept on stock for customers with different service contracts. Each service contract specifies a maximum response time in case of a failure and hourly penalty costs for contract violations. Part requests can be fulfilled from multiple local warehouses via a regular delivery, or from an external source with ample capacity via an expensive emergency delivery. The objective is to minimize delivery cost and penalty cost by smartly allocating items from the available network stock to arriving part requests. We propose a dynamic allocation rule that belongs to the class of one-step lookahead policies.To approximate the optimal relative cost, we develop an iterative calculation scheme that estimates the expected total cost over an infinite time horizon, assuming that future demands are fulfilled according to a simple static allocation rule. In a series of numerical experiments, we compare our dynamic allocation rule with the optimal allocation rule, and a simple but widely used static allocation rule. We show that the dynamic allocation rule has a small optimality gap and that it achieves an average cost reduction of 7.9% compared to the static allocation rule on a large test bed containing problem instances of real-life size.

No abstract

Summary:In this paper the tools are dveloped for forecasting and recruitment planning ln a graded manpower system. Basic features of the presented approach are:-the system contains several grades or job categories in which the employees stay for a certain time before being promoted or leaving the system, -promotability and leaving rate for any employee depend on time spent 1n the job category and personal qualifications (like education, experience, age), -recruitment 1S not necessarily restricted to the lowest level ln the system, -several planning aims and restrictions are allowed.The approach is based on a generalized Markov model for the dynamic behaviour of an individual employee. On this Markov model a forecasting procedure and a recruitment-scheduling procedure are based.

For semi‐Markov decision processes with discounted rewards we derive the well known results regarding the structure of optimal strategies (nonrandomized, stationary Markov strategies) and the standard algorithms (linear programming, policy iteration). Our analysis is completely based on a primal linear programming formulation of the problem.