An inventory model with finite-range stochastic lead times

This article considers an inventory model with constant demand and stochastic lead times distributed over a finite range. A generalization of the EOQ formula with backorders is derived and ranges for the decision variables are obtained. The results are illustrated with the case of uniformly distributed lead time.     

A characterization of the wald distribution

Suppose X is a random variable having an absolutely continuous distribution function F(x). We assume that F(x) has the Wald distribution. A relation between the probability density function of X⁻¹ with that of X is used to characterize the Wald distribution.     

The capital supply curve in capacity expansion models: Some economic and algorithmic aspects

Capacity expansion models typically minimize the discounted cost of acquisition and operation over a given planning horizon. In this article we generalize this idea to one in which a capital supply curve replaces the usual discount rate. A capital supply curve is a means to model financial outlook, investment limits, and risk. We show that when such a curve is included in a capacity expansion model, it will, under certain conditions, provide a less capital intensive solution than one which incorporates a discount rate. In this article, we also provide an algorithm that solves capacity expansion models that incorporate a capital supply curve. The attractive feature of this algorithm is that it provides a means to utilize the “discount rate” models efficiently. Throughout, we give applications in power generation planning and computational experience for this application is also presented.     

Inequalities involving the lifetime of series and parallel systems

Let {Xⁱ} be independent HNBUE (Harmonic New Better Than Used in Expectation) random variables and let {Yⁱ} be independent exponential random variables such that E{Xⁱ}=E{Yⁱ} It is shown that \documentclass{article}\pagestyle{empty}\begin{document}$ E\left[{u\left({\mathop {\min \,X_i}\limits_{l \le i \le n}} \right)} \right] \ge E\left[{u\left({\mathop {\min \,Y_i}\limits_{l \le i \le n}} \right)} \right] $\end{document} for all increasing and concave u. This generalizes a result of Kubat. When comparing two series systems with components of equal cost, one with lifetimes {Xⁱ} and the other with lifetimes {Yⁱ}, it is shown that a risk-averse decision-maker will prefer the HNBUE system. Similar results are obtained for parallel systems.     

A class of inventory models with customer impatience

Classical inventory models generally assume either no backlogging of demands or unlimited backlogging. This paper treats the case wherein backlogged customers are willing to wait for a random period of time for service. A broad class of such models is discussed, with a more complete analysis performed on a simple subclass. Steady state equations are derived and solved assuming exponentially distributed interarrival times of customers, order delivery lead times, and customer patience.     

A note on a paper by houston and huffman

This paper calls attention to an experimental design which enhances the efficiency of the technique described by B. F. Houston and R. A. Huffman [3]. This alternative design is a modification of the simplex lattice design developed by Scheffé [6] for the mixture problem. While not possessing the optimal statistical properties of the central composite design proposed in [3], such as minimum bias and minimum variance, this modified design is optimum with respect to the number of design points employed; hence, it is the minimum cost design. Further, the design proposed in this note is excellent for use in multiple-block experimentation, which is very often required with constrained systems.     

Determining optimal growth paths in logistics operations

This paper considers a logistics system modelled as a transportation problem with a linear cost structure and lower bounds on supply from each origin and to each destination. We provide an algorithm for obtaining the growth path of such a system, i. e., determining the optimum shipment patterns and supply levels from origins and to destinations, when the total volume handled in the system is increased. Extensions of the procedure for the case when the costs of supplying are convex and piecewise linear and for solving transportation problems that are not in “standard form” are discussed. A procedure is provided for determining optimal plant capacities when the market requirements have prespecified growth rates. A goal programming growth model where the minimum requirements are treated as goals rather than as absolute requirements is also formulated.     

An optimum t-test for the scale parameter of an extreme-value distribution

A Student's t-test proposed by Ogawa is considered for the hypothesis Ho: σ=σo against the alternative hypothesis H₁: σ ≠ σo, where σ is the scale parameter of the Extremevalue distribution of smallest values with known location parameter μ. The test is based on a few sample quantiles chosen from a large sample so as to give asymptotically maximum power to the test when the number of sample quantiles is fixed. A table which facilitates the computation of the test statistic is given. Several schemes for determining the ranks of the sample quantiles by the optimal spacings are compared and the effect of the bias of the estimate of σ on the test is investigated through a Monte Carlo study.     

Optimal location of public facilities

Location of both public and private facilities has become an important consideration in today's society. Progress in solution of location problems has been impeded by difficulty of the fixed charge problem and the lack of an efficient algorithm for large problems. In this paper a method is developed for solving large-scale public location problems. An implicit enumeration scheme with an imbedded transportation algorithm forms the basis of the solution technique.