Safe distances

This work highlights the problem in military operations of setting safety limits for friendly forces, neutral forces, or civilians, to avoid sustaining unnecessary casualties both in wartime and in training. We present and investigate an analytic model which both enables the quantitative understanding of the inherent problems, and which furnishes a reasonably flexible tool in the hands of the analyst. Characteristic numerical results are displayed and analyzed: They show in particular that prevailing crude approximations are inadequate. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 259–269, 2001     

Lot sizes under continuous demand: The backorder case

We study a deterministic lot-size problem, in which the demand rate is a (piecewise) continuous function of time and shortages are backordered. The problem is to find the order points and order quantities to minimize the total costs over a finite planning horizon. We show that the optimal order points have an interleaving property, and when the orders are optimally placed, the objective function is convex in the number of orders. By exploiting these properties, an algorithm is developed which solves the problem efficiently. For problems with increasing (decreasing) demand rates and decreasing (increasing) cost rates, monotonicity properties of the optimal order quantities and order intervals are derived.     

Probabilistic a priori routing-location problems

In many routing-location models customers located at nodes of a network generate calls for service with known probabilities. The customers that request service in a particular day are served by a single server that performs a service tour visiting these customers. The order of providing service to customers for each potential list of calls is uniquely defined by some a priori fixed basic sequence of all the customers (a priori tour). The problems addressed in this article are to find an optimal home location or an optimal basic sequence for the server so as to minimize the expectation of a criterion. The following criteria are considered: the total waiting time of all the customers, the total length of the tour, the maximal waiting time of a customer, the average traveled length per customer, and the average waiting time per customer. We present polynomial-time algorithms for the location problems. For the routing problems we present lower bounds that can be calculated efficiently (in polynomial time) and used in a branch-and-bound scheme. © 1994 John Wiley & Sons, Inc.     

Equipment replacement under technological change

For infinite-horizon replacement economy problems it is common practice to truncate the problem at some finite horizon. We develop bounds on the error due to such a truncation. These bounds differ from previous results in that they include both revenues and costs. Bounds are illustrated through a numerical example from a real case in vehicle replacement. © 1994 John Wiley & Sons, Inc.     

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.     

On excess-, current-, and total-life distributions of phase-type renewal processes

Consider a renewal process whose interrenewal-time distribution is phase type with representation (α, T). We show that the (time-dependent) excess-life distribution is phase type with representation (α′, T), where α′ is an appropriately modified initial probability vector. Using this result, we derive the (time-dependent) distributions for the current life and the total life of the phase-type renewal process. They in turn enable us to obtain the equilibrium distributions for the three random variables. These results simplify the computation of the respective distribution functions and consequently enhance the potential use of renewal theory in stochastic modeling—particularly in inventory, queueing, and reliability applications. © 1992 John Wiley & Sons, Inc.     

A set-processing algorithm for scheduling staff on 4-day or 3-day work weeks

This paper presents an efficient algorithm for scheduling a single-category work force on 4-day or 3-day work weeks. Employees work 4 or 3 days each week, have A out of every B weekends off, and work no more than 5 consecutive days in a work stretch on 4-day work weeks and no more than 4 days in a work stretch on 3-day work weeks. Such conditions often prevail in 7-day-a-week organizations such as hospitals, manufacturing plants, and retail stores. We determine the minimum number of workers required to satisfy the scheduling constraints under any pattern of daily requirements. Then we present the algorithm for assigning days off for each worker, thereby determining the work schedules. We show that the algorithm, by construction, will necessarily satisfy the scheduling constraints. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 839–853, 1998     

A dynamic-programming approach to continuous-review obsolescent inventory problems

Inventory models of modern production and service operations should take into consideration possible exogenous failures or the abrupt decline of demand resulting from obsolescence. This article analyzes continuous-review versions of the classical obsolescence problem in inventory theory. We assume a deterministic demand model and general continuous random times to obsolescence (“failure”). Using continuous dynamic programming, we investigate structural properties of the problem and propose explicit and workable solution techniques. These techniques apply to two fairly wide (and sometimes overlapping) classes of failure distributions: those which are increasing in failure rate and those which have finite support. Consequently, several specific failure processes in continuous time are given exact solutions. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 757–774, 1997     

Maintaining systems with heterogeneous spare parts

We consider the problem of optimally maintaining a stochastically degrading, single‐unit system using heterogeneous spares of varying quality. The system's failures are unannounced; therefore, it is inspected periodically to determine its status (functioning or failed). The system continues in operation until it is either preventively or correctively maintained. The available maintenance options include perfect repair, which restores the system to an as‐good‐as‐new condition, and replacement with a randomly selected unit from the supply of heterogeneous spares. The objective is to minimize the total expected discounted maintenance costs over an infinite time horizon. We formulate the problem using a mixed observability Markov decision process (MOMDP) model in which the system's age is observable but its quality must be inferred. We show, under suitable conditions, the monotonicity of the optimal value function in the belief about the system quality and establish conditions under which finite preventive maintenance thresholds exist. A detailed computational study reveals that the optimal policy encourages exploration when the system's quality is uncertain; the policy is more exploitive when the quality is highly certain. The study also demonstrates that substantial cost savings are achieved by utilizing our MOMDP‐based method as compared to more naïve methods of accounting for heterogeneous spares.     

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.