Multi-item service constrained (s,S) policies for spare parts logistics systems

Many organizations providing service support for products or families of products must allocate inventory investment among the parts (or, identically, items) that make up those products or families. The allocation decision is crucial in today's competitive environment in which rapid response and low levels of inventory are both required for providing competitive levels of customer service in marketing a firm's products. This is particularly important in high-tech industries, such as computers, military equipment, and consumer appliances. Such rapid response typically implies regional and local distribution points for final products and for spare parts for repairs. In this article we fix attention on a given product or product family at a single location. This single-location problem is the basic building block of multi-echelon inventory systems based on level-by-level decomposition, and our modeling approach is developed with this application in mind. The product consists of field-replaceable units (i.e., parts), which are to be stocked as spares for field service repair. We assume that each part will be stocked at each location according to an (s, S) stocking policy. Moreover, we distinguish two classes of demand at each location: customer (or emergency) demand and normal replenishment demand from lower levels in the multiechelon system. The basic problem of interest is to determine the appropriate policies (s_i S_i) for each part i in the product under consideration. We formulate an approximate cost function and service level constraint, and we present a greedy heuristic algorithm for solving the resulting approximate constrained optimization problem. We present experimental results showing that the heuristics developed have good cost performance relative to optimal. We also discuss extensions to the multiproduct component commonality problem.     

Discrete equal‐capacity p‐median problem

This paper examines the discrete equal‐capacity p‐median problem that seeks to locate p new facilities (medians) on a network, each having a given uniform capacity, in order to minimize the sum of distribution costs while satisfying the demand on the network. Such problems arise, for example, in local access and transport area telecommunication network design problems where any number of a set of p facility units can be constructed at the specified candidate sites (hence, the net capacity is an integer multiple of a given unit capacity). We develop various valid inequalities, a separation routine for generating cutting planes that are specific members of such inequalities, as well as an enhanced reformulation that constructs a partial convex hull representation that subsumes an entire class of valid inequalities via its linear programming relaxation. We also propose suitable heuristic schemes for this problem, based on sequentially rounding the continuous relaxation solutions obtained for the various equivalent formulations of the problem. Extensive computational results are provided to demonstrate the effectiveness of the proposed valid inequalities, enhanced formulations, and heuristic schemes. The results indicate that the proposed schemes for tightening the underlying relaxations play a significant role in enhancing the performance of both exact and heuristic solution methods for this class of problems. © 2000 John & Sons, Inc. Naval Research Logistics 47: 166–183, 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     

Gittins-index heuristics for research planning

The classical work of Gittins, which resulted in the celebrated index result, had applications to research planning as an important part of its motivation. However, research planning problems often have features that are not accommodated within Gittins's original framework. These include precedence constraints on the task set, influence between tasks, stopping or investment options and routes to success in which some tasks do not feature. We consider three classes of Markovian decision models for research planning, each of which has all of these features. Gittins-index heuristics are proposed and are assessed both analytically and computationally. They perform impressively. © 1995 John Wiley & Sons, Inc.     

Evaluating the effects of machine breakdowns in stochastic scheduling problems

In most of the stochastic resource-allocation problems discussed in the literature it is supposed that the key resource, herein called the machine, is continuously available until all tasks are completed. Plainly, this will often be an unrealistic assumption. This paper supposes that intermittent availability of the machine is due to a breakdown proces, and describes various approaches to the evaluation of the effect of breakdowns. Firstly, for the case of geometric up times, conditions are given under which breakdowns have no effect on optimal allocation strategies. Secondly, two different procedures are given which yield an upper bound on the loss incurred when a processing strategy is adopted under the assumption of no breakdowns, when in fact breakdowns do occur. The first of these is based on Gittins's indices and is described for the case of geometric up times, and the second uses a bounding argument on the breakdown process.     

Relaxation method for the solution of the minimax location-allocation problem in euclidean space

A method previously devised for the solution of the p-center problem on a network has now been extended to solve the analogous minimax location-allocation problem in continuous space. The essence of the method is that we choose a subset of the n points to be served and consider the circles based on one, two, or three points. Using a set-covering algorithm we find a set of p such circles which cover the points in the relaxed problem (the one with m < n points). If this is possible, we check whether the n original points are covered by the solution; if so, we have a feasible solution to the problem. We now delete the largest circle with radius r_p (which is currently an upper limit to the optimal solution) and try to find a better feasible solution. If we have a feasible solution to the relaxed problem which is not feasible to the original, we augment the relaxed problem by adding a point, preferably the one which is farthest from its nearest center. If we have a feasible solution to the original problem and we delete the largest circle and find that the relaxed problem cannot be covered by p circles, we conclude that the latest feasible solution to the original problem is optimal. An example of the solution of a problem with ten demand points and two and three service points is given in some detail. Computational data for problems of 30 demand points and 1–30 service points, and 100, 200, and 300 demand points and 1–3 service points are reported.     

Some order relations in closed networks of queues with multiserver stations

Consider a closed network of queues of the “product-form” type, where each station has s servers (s ≥ 1 is identical for all stations). We show that the throughput function of the network is Schur concave with respect to the loading of the stations and arrangement increasing with respect to the assignment of server groups. Consequently, different loading/assignment policies can be compared under majorization/arrangement orderings and their relative merits decided according to the yields of throughput. The results can be used to support planning decisions in computer and production systems which are modeled as closed networks of queues.     

NUCLEAR MYTHOLOGY AND NUCLEAR USELESSNESS

Five Myths about Nuclear Weapons, by Ward Wilson. Houghton Mifflin Harcourt, 2013. 188 pages, $22.     

The road not taken: Conflict termination and guerrillaism in the American Civil War

Irrespective our views on the rationality of our opponent's continuing to conduct operations against us, unless utterly extirpated, he retains a vote on when and how conflict will end. This is because war is about power — compelling another actor to do something he would not otherwise do, or to cease doing something he would otherwise prefer to do. In planning for conflict termination we should account for the peculiarities of opponents who may decide not to quit when we have beat them fair and square. We do not desire that they cease conventional fighting, but that they cease fighting altogether.