Location-allocation for distribution to a uniform demand with transshipments

This article analyzes the location-allocation problem for distribution from a single fixed origin via transshipment terminals to a continuous uniformly distributed demand. Distribution through terminals concentrates flows on the origin-to-terminal links and transportation economies of scale encourage the use of larger vehicles. Analytical expressions are derived for the optimal terminal locations, the optimal allocation of destinations to terminals, and the optimal transportation cost. Continuous analytic models assume either an allocation, by partitioning the service region into sectors, or terminal locations. This is unlikely to produce an optimal distribution system. The optimal cost is compared to the cost for suboptimal location-allocation combinations. Results indicate that the location decision is not too important if destinations are allocated optimally and that allocation to the nearest terminal may be poor, even with optimal locations. © 1992 John Wiley & Sons, Inc.     

Optimal inventory policies for substitutable commodities with stochastic demand

In this article we consider a stochastic model for two products which have a single-period inventory structure and which can be used as substitutes for each other should the need arise. Substitution will occur with probability one, but at perhaps a different revenue level. We prove that the expected profit function is concave, allowing us to find optimal stocking levels for the two products. We compare optimum inventory levels for the case of single substitution with that where there is no substitution. It is demonstrated for the case of single substitution that total optimum order quantities can actually increase or decrease with the substitution revenue.     

Optimal refueling sequence for a mixed fleet with limited refuelings

Consider a fleet of vehicles comprised of K₁ identical tankers and K₂ identical nontankers (small aircraft). Tankers are capable of refueling other tankers as well as nontankers. The problem is to find that refueling sequence of the tankers that maximizes the range simultaneously attainable by all K₂ nontankers. A recent paper established that the “unit refueling sequence,” comprised of one tanker refueling at each of K₁ refueling operations, is optimal. The same paper also proffered the following conjecture for the case that the number of refueling operations is constrained to be less than the number of tankers: A nonincreasing refueling sequence is optimal. This article proves the conjecture.     

Modeling lead-time demand for lumpy demand and variable lead time

Slow-moving items that occasionally exhibit large demand transactions are known as lumpy demand items. In modeling lumpy demand patterns, it is often assumed that the arrival of customer orders follows a Poisson process and that the order sizes are given by the geometric distribution. This gives rise to a stuttering Poisson (sP) model of lumpy demand. If lead times are constant, the result is a stuttering Poisson model of lead-time demand. Heretofore, authors such as Ward [18] and Mitchell, Rappold, and Faulkner [12] have assumed constant lead times and thus stopped at the sP model. We develop this model further by introducing the effect of lead-time variability. For illustration, we use the normal and the gamma distributions as characterizations of lead time. The resulting models of lead-time demand are referred to as the geometric Poisson normal (GPN) and the geometric Poisson gamma (GPG). For both these models, the article derives tractable expressions for calculating probabilities. Errors introduced by using the sP, constant lead-time model instead of the exact, variable lead-time model are also illustrated.     

Replacing continuous demand with discrete demand in a competitive location model

Location models commonly represent demand as discrete points rather than as continuously spread over an area. This modeling technique introduces inaccuracies to the objective function and consequently to the optimal location solution. In this article this inaccuracy is investigated by the study of a particular competitive facility location problem. First, the location problem is formulated over a continuous demand area. The optimal location for a new facility that optimizes the objective function is obtained. This optimal location solution is then compared with the optimal location obtained for a discrete set of demand points. Second, a simple approximation approach to the continuous demand formulation is proposed. The location problem can be solved by using the discrete demand algorithm while significantly reducing the inaccuracies. This way the simplicity of the discrete approach is combined with the approximated accuracy of the continuous-demand location solution. Extensive analysis and computations of the test problem are reported. It is recommended that this approximation approach be considered for implementation in other location models. © 1997 John Wiley & Sons, Inc.     

Production-location problems with demand considerations

The production-location problem of a profit maximizing firm is considered. A model is developed for a single firm, facing the joint problems of determining the optimal plant location, the optimal input mix, and the optimal plant size. A homothetic production function is used as the model of the production technologies, and the existence of a sequential “separability” between the production, or input mix, problem and the location problem is demonstrated.     

Optimal policies for a multi-echelon inventory system with demand forecasts

Consider an inventory system consisting of two installations, the stocking point and the field. Each period two decisions must be made: how much to order from outside the system and how much to ship to the field. The first decision is made based on the total amounts of stock then at the two installations. Next a forecast of the demand in the current period is sent from the field to the stocking point. Based upon a knowledge of the joint distribution of the forecast and the true demand, and the amounts of stock at the two installations, a decision to ship a certain amount of stock to the field is taken. The goal is to make these two decisions so as to minimize the total n-period cost for the system. Following the factorization idea of Clark and Scarf (1960), the optimal n period ordering and shipping policy, taking into account the accuracy of the demand forecasts, can be derived so as to make the calculation comparable to those required by two single installations.     

Periodic-review inventory models with inventory-level-dependent demand

Demand for some items can depend on the inventory level on display, a phenomenon often exploited by marketing researchers and practitioners. The implications of this phenomenon have received scant attention in the context of periodic-review inventory control models. We develop an approach to model periodic-review production/inventory problems where the demand in any period depends randomly, in a very general form, on the starting inventory level. We first obtain a complete analytical solution for a single-period model. We then investigate two multiperiod models, one with lost sales and the other with backlogging, whose optimal policies turn out to be myopic. Some extensions are also discussed. © 1994 John Wiley & Sons, Inc.     

Inventory systems with imperfect demand information

An inventory system is described in which demand information may be incorrectly transmitted from the field to the stocking point. The stocking point employs a forwarding policy which attempts to send out to the field a quantity which, in general, is some function of the observed demand. The optimal ordering rules for the general n-period problem and the steady state case are derived. In addition orderings of the actual reorder points as functions of the errors are presented, as well as some useful economic interpretations and numerical illustrations.     

Joint pricing and ordering policy for exponentially decaying inventory with known demand

This paper is concerned with the problem of simultaneously setting price and production levels for an exponentially decaying product. Such products suffer a loss in utility which is proportional to the total quantity of stock on hand. A continuous review, deterministic demand model is considered. The optimal ordering decision quantity is derived and its sensitivity to changes in perishability and product price is considered. The joint ordering pricing decision is also computed and consideration of parametric changes of these decisions indicates a non-monotonic response for optimal price to changes in product decay. Issues of market entry and extensions to a model with shortages are also analyzed.     

Estimating negative binomial demand for retail inventory management with unobservable lost sales

The importance of effective inventory management has greatly increased for many major retailers because of more intense competition. Retail inventory management methods often use assumptions and demand distributions that were developed for application areas other than retailing. For example, it is often assumed that unmet demand is backordered and that demand is Poisson or normally distributed. In retailing, unmet demand is often lost and unobserved. Using sales data from a major retailing chain, our analysis found that the negative binomial fit significantly better than the Poisson or the normal distribution. A parameter estimation methodology that compensates for unobserved lost sales is developed for the negative binomial distribution. The method's effectiveness is demonstrated by comparing parameter estimates from the complete data set to estimates obtained by artificially truncating the data to simulate lost sales. © 1996 John Wiley & Sons, Inc.     

Alternate methods of project scheduling with limited resources

The applicability of critical path scheduling is limited by the inability of the algorithm to cope with conflicting resource demands. This paper is an assessment of the effectiveness of many of the heuristic extensions to the critical path method which resolve the conflicts that develop between the resources demanded by an activity and those available. These heuristic rules are evaluated on their ability to solve a large multiproject scheduling problem.     

Simultaneous production of market‐specific and global products: A two‐stage stochastic program with additional demand after recourse

This paper analyzes the simultaneous production of market‐specific products tailored to the needs of individual regions and a global product that could be sold in many regions. We assume that the global product costs more to manufacture, but allows the decision concerning the allocation of products to regions to be delayed until after the manufacturing process has been completed. We further assume that there is additional demand after the region allocation but prior to delivery, extending the two‐stage stochastic program with recourse to include additional stochastic demand after the recourse. This scenario arises, for example, when there is additional uncertainty during a delivery delay which might occur with transoceanic shipments. We develop conditions for optimality assuming a single build‐allocate‐deliver cycle and stochastic demand during both the build and deliver periods. The optimal policy calls for the simultaneous production of market‐specific and global products, even when the global product is substantially more costly than the market‐specific product. In addition, we develop bounds on the performance of the optimal policy for the multicycle problem. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 438–461, 2003     

Recursive evaluation of order-up-to-S policies for two-echelon inventory systems with compound Poisson demand

We consider an inventory system with one warehouse and N retailers. All installations apply different order-up-to-S policies. Transportation times are constant and the retailers face compound Poisson demand. We provide a simple recursive procedure for the evaluation of holding and shortage costs for different control policies. © 1996 John Wiley & Sons, Inc.     

Stochastic duels with multiple hits and limited ammunition supply

Ancker's stochastic duels with limited ammunition supply are extended to cases where a kill is obtained through repetitive multiple hits with two firing modes, single-shot firing and pattern firing. Examples with negative exponential firing time and geometric ammunition supply are given.     

Serial production lines with unreliable machines and limited repair

The output of an N-stage line with unlimited buffer space between stages is a function of the number of repair crews assigned to the line and the failure and repair rates of the individual stages. Rules for assigning crews that are examined include preference for slow stages and randomization. It is shown that appropriate randomization maximizes output in the 2 stage, 1 crew case. Furthermore, in a large system with slower stages having slower repair rates, the best way to dedicate repairmen is to assign one man to each slow stage in so far as possible and to pair remaining stages in combinations of slowest-fastest, next slowest-next fastest, etc.     

基于心理战专业化的装备心理战技术——以雷达装备心理战技术为例

心理战是现代战争的主要作战形式之一,但目前的心理战主要以舆论宣传为主,与其他作战技术结合较少,向专业化作战方向发展缓慢。本文首先从装备心理战发展的必要性入手,提出了装备心理战的基本概念,并分析了其特征内涵;其次,构建了装备心理战的技术体系,梳理了装备心理战技术的应用与发展过程;最后,结合雷达装备心理战技术,举例说明特型干扰技术带来的心理战效果。装备心理战利用心理战原理,瞄准人机交互环节,推动了心理战与装备技术的高度融合。它的发展不仅可以从内驱动角度牵引装备技术发展,还可以深层次提升装备与操作人员的整体作战效能。希冀本研究能够对军队装备技术发展和军事训练提供一定参考。     

An economic sequential screening procedure for limited failure populations

An economic sequential screening procedure is considered for limited failure populations in which defective items fail soon after they are put in operation and nondefective ones never fail during the technical life of the items. A cost model is constructed that involves screening test cost and external failure cost. A sequential scheme that minimizes the expected cost is derived from the solution of a dynamic programming formulation and the optimal decision at each stage is obtained in a closed form. © 1994 John Wiley & Sons, Inc.