A characterization of the wald distribution

Suppose X is a random variable having an absolutely continuous distribution function F(x). We assume that F(x) has the Wald distribution. A relation between the probability density function of X⁻¹ with that of X is used to characterize the Wald distribution.     

Computation of constrained optimum quantities and reorder points for time-weighted backorder penalties

The purpose of this paper and the accompanying tables is to facilitate the calculation of constrained optimum order quantities and reorder points for an inventory control system where the criterion of optimality is the minimization of expected inventory holding, ordering, and time-weighted backorder costs. The tables provided in the paper allow the identification of the optimal solution when order quantities and/or reorder points are restricted to a set of values which do not include the unconstrained optimal solution.     

‘The only good jihadist is a dead jihadist’:Boko Haram and de-radicalization around Lake Chad

ABSTRACT

This article discusses the shortcomings of the “de-radicalization doctrine” in sub-Saharan Africa. The issues raised are illustrated by the war against Boko Haram, which involves Nigeria, Niger, Chad and Cameroon. Relying on interviews with security officers, insurgents, civil servants, displaced people, humanitarian workers and Muslim and Christian clerics in Nigeria, Niger and Chad since 2005, the investigation shows that the four states focused on repression rather than demobilisation programs in prison or outdoors. The Boko Haram crisis is mainly a story of mismanagement. The article thus challenges the assumptions of the “de-radicalization doctrine” in Muslim Africa South of the Sahara. First, attempts to de-radicalize jihadi terrorists tend to focus too much on religious fanaticism and the exegesis of the Quran. Secondly, they are neither feasible nor efficient. Finally, they obscure priorities that are more important to counter extremism and demobilize insurgents.     

On queueing systems with variable service capacities

In some queueing systems the total service capacity utilized at any given time is a variable under the control of a decision maker. Management doctrines are examined which prescribe the actual service capacity as a function of the queue length and the recent history of the system. Steady state probabilities, expected queue lengths and frequencies of change in capacity are evaluated for a wide class of possible control schemes. Optimization procedures are outlined.     

Allocation of resources to randomly occurring opportunities

An allocation problem is considered in lvhich different kinds of resources must be allocated to various activities, within a given time period. The opportunities for allo'cation appear randomly during this period. Certain assumptions about the values of possible allocations and the distribution of occurrences of opportunities lead to a dynamic programming formulation of the problem. This leads to a system of ordinary differential equations which are (in theory) solvable recursively, and can be solved numerically to any desired degree of precision. An example is given for the allocation of aircraft-carried weapons to targets of opportunity.     

An inventory model with finite-range stochastic lead times

This article considers an inventory model with constant demand and stochastic lead times distributed over a finite range. A generalization of the EOQ formula with backorders is derived and ranges for the decision variables are obtained. The results are illustrated with the case of uniformly distributed lead time.     

Production-location problems with demand considerations

The production-location problem of a profit maximizing firm is considered. A model is developed for a single firm, facing the joint problems of determining the optimal plant location, the optimal input mix, and the optimal plant size. A homothetic production function is used as the model of the production technologies, and the existence of a sequential “separability” between the production, or input mix, problem and the location problem is demonstrated.