Minimizing the makespan in open‐shop scheduling problems with a convex resource consumption function

We consider open‐shop scheduling problems where operation‐processing times are a convex decreasing function of a common limited nonrenewable resource. The scheduler's objective is to determine the optimal job sequence on each machine and the optimal resource allocation for each operation in order to minimize the makespan. We prove that this problem is NP‐hard, but for the special case of the two‐machine problem we provide an efficient optimization algorithm. We also provide a fully polynomial approximation scheme for solving the preemptive case. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Budget allocation under uncertainty and the costs of war and insecurity

This study presents a framework and models for the analysis of government budget allocation into defense and civilian expenditures in situations of uncertainty about the incidence of war. The models display the intricate relationships between security levels, subjective probabilities of the occurrence of war, and potential war damages. We show that poor countries tend to perceive greater probabilities of war than their richer rivals, and that the psychological burden of insecurity is larger when the country’s wealth is larger and when its preference for security is higher. We apply our models to the Israeli–Syrian arms race and show that the higher rate of growth of Israel’s gross domestic product relative to that of Syria is expected to lead to an increase in Syria’s perception of the likelihood of war and to a decrease in Israel’s perception of such a likelihood. We also show that if Syria’s regime becomes ideologically more extreme, the monetary cost of maintaining Israel’s security at the level that it enjoyed prior to the change will be very high, whereas the monetary cost of maintaining Israel’s welfare will be moderate.