Single-period inventory models with demand uncertainty and quantity discounts: Behavioral implications and a new solution procedure

Quantity discounts are considered in the context of the single-period inventory model known as “the newsboy problem.” It is argued that the behavioral implications of the all-units discount schedule are more complex and interesting than the literature has suggested. Consideration of this behavior and the use of marginal analysis lead to a new method for solving this problem that is both conceptually simpler and more efficient than the traditional approach. This marginal-cost solution procedure is described graphically, an algorithm is presented, and an example is used to demonstrate that this solution procedure can be extended easily to handle complex discount schedules, such as some combined (simultaneously applied) purchasing and transportation cost discount schedules.     

Control-variate selection criteria

For multiresponse simulations requiring point and confidence-region estimators of the mean response, we propose control-variate selection criteria that minimize mean-square confidence-region volume in two situations: (a) Only the mean control vector is known, and standard linear control-variate estimation procedures are used. (b) Covariances among controls are also known and are incorporated into new linear control-variate estimation procedures. An example illustrates the performance of these selection criteria.     

Hu's precedence tree scheduling algorithm: A simple proof

This article presents a simple proof of Hu's algorithm for scheduling in minimum time a set of tasks constrained by precedence tree constraints, each task requiring a unit time to complete, and where m processors are available.     

On the relationship between the force ratio and the instantaneous casualty-exchange ratio for some lanchester-type models of warfare

A “local” condition of winning (in the sense that the force ratio is changing to the advantage of one of the combatants) is shown to apply to all deterministic Lanchester-type models with two force-level variables. This condition involves the comparison of only the force ratio and the instantaneous force-change ratio. For no replacements and withdrawals, a combatant is winning “instantaneously” when the force ratio exceeds the differential casualty-exchange ratio. General outcome-prediction relations are developed from this “local” condition and applied to a nonlinear model for Helmbold-type combat between two homogeneous forces with superimposed effects of supporting fires not subject to attrition. Conditions under which the effects of the supporting fires “cancel out” are given.