On the optimal policies of an exponential machine repair problem

We consider an exponential repair model with s machines and one repairman. The machines' failure rates are equal but the repair rate may change from machine to machine. The repairman repairs the failed machines one at a time and in the course of his work he may even interrupt repairing one machine and start another. We compare repair policies and prove an optimality result by means of stochastic order. The proof is based on representing the compared models simultaneously in a special way and comparing then the sample paths of the interesting stochastic processes.     

Offset Contracts as an Insurance Device in Building the National Security

A dynamic multi-stage decision-theoretic approach is introduced to establish the optimal offset and its incidence, the contract price arising from bargaining, and the scale of the acquisition. A new rationale is suggested for offsets in terms of their role as an insurance devise. Results are derived for the pricing of delivery contracts subject to offset claims and their national security implications. It is shown that the national security is strictly convex in the offset transaction. As to the incidence of the offset, the offset claim is shown to be capitalised in the delivery price. The bargaining price is shown to depend on the value of the product to be delivered for the national security, the relative negotiation power of the contracting partners and the social cost of public funds. The analysis highlights the expectation effects of offsets on the bargaining price and the scale of delivery. The results aid in explaining why offsets are widely used in procurement contracts for defence materiel. As they contribute to the national security, they should be allowed to survive and not be denied under competition laws.