Service levels in distribution systems with random customer order size

An approximate method for measuring the service levels of the warehouse-retailer system operating under (s, S) policy is presented. All the retailers are identical and the demand process at each retailer follows a stationary stuttering Poisson process. This type of demand process allows customer orders to be for a random number of units, which gives rise to the undershoot quantity at both the warehouse and retailer levels. Exact analyses of the distribution of the undershoot quantity and the number of orders place by a retailer during the warehouse reordering lead time are derived. By using this distribution together with probability approximation and other heuristic approaches, we model the behavior of the warehouse level. Based on the results of the warehouse level and on an existing framework from previous work, the service level at the retailer level is estimated. Results of the approximate method are then compared with those of simulation. © 1995 John Wiley & Sons, Inc.     

A bayesian approach to environmental stress screening

The article presents a Bayesian analysis for the environmental stress screening problem. The decision problem of deriving optimal stress screen durations is solved. Given a screen duration, the optimal stress level can also be determined. Indicators of the quality of a screen of any duration are derived. A statistical model is presented which allows a posterior density for the rate of early failures of the production process to be calculated. This enables the user to update his opinion about the quality of the process. © 1994 John Wiley & Sons, Inc.     

A two-machine repair model with variable repair rate

A two-unit cold standby production system with one repairman is considered. After inspection of a failed unit the repairman chooses either a slow or a fast repair rate to carry out the corresponding amount of work. At system breakdown the repairman has an additional opportunity to switch to the fast rate. If there are no fixed costs associated with system breakdowns, then the policy which minimizes longrun average costs is shown to be a two-dimensional control limit rule. If fixed costs are incurred every time the system breaks down, then the optimal policy is not necessarily of control limit type. This is illustrated by a counterexample. Furthermore, we present several performance measures for this maintenance system controlled by a two-dimensional control limit rule. © 1993 John Wiley & Sons, Inc.     

A search game with a protector

A classic problem in Search Theory is one in which a searcher allocates resources to the points of the integer interval [1, n] in an attempt to find an object which has been hidden in them using a known probability function. In this paper we consider a modification of this problem in which there is a protector who can also allocate resources to the points; allocating these resources makes it more difficult for the searcher to find an object. We model the situation as a two‐person non‐zero‐sum game so that we can take into account the fact that using resources can be costly. It is shown that this game has a unique Nash equilibrium when the searcher's probability of finding an object located at point i is of the form (1 − exp (−λ_ix_i)) exp (−μ_iy_i) when the searcher and protector allocate resources x_i and y_i respectively to point i. An algorithm to find this Nash equilibrium is given. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47:85–96, 2000     

The LP/POMDP marriage: Optimization with imperfect information

A new technique for solving large‐scale allocation problems with partially observable states and constrained action and observation resources is introduced. The technique uses a master linear program (LP) to determine allocations among a set of control policies, and uses partially observable Markov decision processes (POMDPs) to determine improving policies using dual prices from the master LP. An application is made to a military problem where aircraft attack targets in a sequence of stages, with information acquired in one stage being used to plan attacks in the next. © 2000 John Wiley & Sons, Inc., Naval Research Logistics 47: 607–619, 2000     

Exact analysis of (R,s, S) inventory control systems with lost sales and zero lead time

We study an (R, s, S) inventory control policy with stochastic demand, lost sales, zero lead‐time and a target service level to be satisfied. The system is modeled as a discrete time Markov chain for which we present a novel approach to derive exact closed‐form solutions for the limiting distribution of the on‐hand inventory level at the end of a review period, given the reorder level (s) and order‐up‐to level (S). We then establish a relationship between the limiting distributions for adjacent values of the reorder point that is used in an efficient recursive algorithm to determine the optimal parameter values of the (R, s, S) replenishment policy. The algorithm is easy to implement and entails less effort than solving the steady‐state equations for the corresponding Markov model. Point‐of‐use hospital inventory systems share the essential characteristics of the inventory system we model, and a case study using real data from such a system shows that with our approach, optimal policies with significant savings in inventory management effort are easily obtained for a large family of items.     

On the reduction of total‐cost and average‐cost MDPs to discounted MDPs

This article provides conditions under which total‐cost and average‐cost Markov decision processes (MDPs) can be reduced to discounted ones. Results are given for transient total‐cost MDPs with transition rates whose values may be greater than one, as well as for average‐cost MDPs with transition probabilities satisfying the condition that there is a state such that the expected time to reach it is uniformly bounded for all initial states and stationary policies. In particular, these reductions imply sufficient conditions for the validity of optimality equations and the existence of stationary optimal policies for MDPs with undiscounted total cost and average‐cost criteria. When the state and action sets are finite, these reductions lead to linear programming formulations and complexity estimates for MDPs under the aforementioned criteria.© 2017 Wiley Periodicals, Inc. Naval Research Logistics 66:38–56, 2019     

Evolutionary determinants of war

This paper considers evolutionarily stable decisions about whether to initiate violent conflict rather than accepting a peaceful sharing outcome. Focusing on small sets of players such as countries in a geographically confined area, we use the concept of evolutionary stability in finite populations. We find that players’ evolutionarily stable preferences widen the range of peaceful resource allocations that are rejected in favor of violent conflict, compared to the Nash equilibrium outcomes. Relative advantages in fighting strength are reflected in the equilibrium set of peaceful resource allocations.     

Learning to Fight and Fighting to Learn: Practitioners and the Role of Unit Publications in VIII Fighter Command 1943–1944

A military cannot hope to improve in wartime if it cannot learn. Ideally, in wartime, formal learning ceases and the application of knowledge begins. But this is optimistic. In 1942, USAAF Eighth Air Force assumed it had the means necessary for victory. In reality, its technique and technology were only potentially – rather than actually – effective. What remained was to create the practice of daylight bombing – to learn. This article (1) recovers a wartime learning process that created new knowledge, (2) tests existing tacit hypotheses in military adaptation research, and (3) offers additional theoretical foundation to explain how knowledge is created in wartime