Recent articles on partial backorders: Comment

This note points out the omission of a simple but vital constraint in the recent articles on partial backlogging. Also, a simple intuitive interpretation of the “backorder” inequality of [2], [3], and [4] is provided.     

Inventory management with advance capacity information

An important aspect of supply chain management is dealing with demand and supply uncertainty. The uncertainty of future supply can be reduced if a company is able to obtain advance capacity information (ACI) about future supply/production capacity availability from its supplier. We address a periodic‐review inventory system under stochastic demand and stochastic limited supply, for which ACI is available. We show that the optimal ordering policy is a state‐dependent base‐stock policy characterized by a base‐stock level that is a function of ACI. We establish a link with inventory models that use advance demand information (ADI) by developing a capacitated inventory system with ADI, and we show that equivalence can only be set under a very specific and restrictive assumption, implying that ADI insights will not necessarily hold in the ACI environment. Our numerical results reveal several managerial insights. In particular, we show that ACI is most beneficial when there is sufficient flexibility to react to anticipated demand and supply capacity mismatches. Further, most of the benefits can be achieved with only limited future visibility. We also show that the system parameters affecting the value of ACI interact in a complex way and therefore need to be considered in an integrated manner. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

Lateral capacity exchange and its impact on capacity investment decisions

We study the problem of capacity exchange between two firms in anticipation of the mismatch between demand and capacity, and its impact on firm's capacity investment decisions. For given capacity investment levels of the two firms, we demonstrate how capacity price may be determined and how much capacity should be exchanged when either manufacturer acts as a Stackelberg leader in the capacity exchange game. By benchmarking against the centralized system, we show that a side payment may be used to coordinate the capacity exchange decisions. We then study the firms' capacity investment decisions using a biform game framework in which capacity investment decisions are made individually and exchange decisions are made as in a centralized system. We demonstrate the existence and uniqueness of the Nash equilibrium capacity investment levels and study the impact of firms' share of the capacity exchange surplus on their capacity investment levels.© 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Technical note: Worst‐case performance of power‐of‐two policies for serial inventory systems with incremental quantity discounts

This study presents power‐of‐two policies for a serial inventory system with constant demand rate and incremental quantity discounts at the most upstream stage. It is shown that an optimal solution is nested and follows a zero‐inventory ordering policy. To prove the effectiveness of power‐of‐two policies, a lower bound on the optimal cost is obtained. A policy that has a cost within 6% of the lower bound is developed for a fixed base planning period. For a variable base planning period, a 98% effective policy is provided. An extension is included for a system with price dependent holding costs. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

A note on the constrained shortest-path problem

The subject of this note is the validity of the algorithm described by Aneja and Nair to solve the constrained shortest-path problem.     

Scheduling stochastic jobs on a single machine subject to breakdowns

A single machine is available to process a collection of stochastic jobs. There may be technological constraints on the job set. The machine sometimes breaks down. Costs are incurred and rewards are earned during processing. We seek strategies for processing the jobs which maximize the total expected reward earned.     

Damage calculations for unreliable warheads

For large numbers of perfectly reliable, optimally targeted warheads the square-root law approximates the expected fraction damage achieved on an area target. In this paper a more exact expression is derived for this damage fraction which Holds for all numbers of warheads. This expression is shown to converge to the square-root law when a large number of warheads are fired. The more exact expression is used in a procedure to calculate expected damage when warheads are unreliable, and this procedure is shown to be superior to a modified square-root approximation which has been used previously.     

Duality for quasi-concave programs with application to economics

A duality theory is developed for mathematical programs with strictly quasi-concave objective functions to be maximized over a convex set. This work broadens the duality theory of Rockafellar and Peterson from concave (convex) functions to quasi-concave (quasi-convex) functions. The theory is closely related to the utility theory in economics. An example from economic planning is examined and the solution to the dual program is shown to have the properties normally associated with market prices.     

The optimum design of multivariate acceptance sampling plans

A model is developed which may be used to determine the expected total cost of quality control per inspection lot under acceptance sampling by variables where several characteristics are to be simultaneously controlled. Optimization of the model is accomplished through the application of a conventional search procedure. The sensitivity of the model and the optimum solution to the shape of the underlying probability distributions is discussed and associated analyses are presented through an example.