Multiproduct dynamic lot-sizing model with coordinated replenishments

In this article we consider a multiproduct dynamic lot-sizing model. In addition to a separate setup cost for each product ordered, a joint setup cost is incurred when at least one product is ordered. We formulate the model as a concave minimization problem over a compact polyhedral set and present a finite branch and bound algorithm for finding an optimal ordering schedule. Superiority of the branch and bound algorithm to the existing exact procedures is demonstrated. We report computational experience with problems whose dimensions render the existing procedures computationally infeasible.     

On a large sample test for the traffic intensity in GI|G|s queue

A large sample test based on normal approximation for the traffic intensity parameter ρ in the cases of single and multiple-server queues has been proposed. The test procedure is developed without imposing steady-state assumptions and is applicable to queueing systems with general interarrival and service-time distributions.     

Minimizing mean absolute deviation of completion times about a common due date

We consider a single machine scheduling problem in which the objective is to minimize the mean absolute deviation of job completion times about a common due date. We present an algorithm for determining multiple optimal schedules under restrictive assumptions about the due date, and an implicit enumeration procedure when the assumptions do not hold. We also establish the similarity of this problem to the two parallel machines mean flow time problem.     

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.     

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.     

Bayes adaptive control of two-echelon inventory systems i: development for a special case of one-station lower echelon and monte carlo evaluation

Bayes adaptive control policies are developed in the present paper for the special case of a one-station lower echelon: a Poisson distribution of demand, whose mean is assumed to have a prior gamma distribution. The cost structure is of a common type. The ordering policy for the upper echelon, which minimizes expected cost, is replaced by a new type of policy, called Bayes prediction policy. This policy does not require tedious computations, of the sort required by dynamic programming solutions. The characteristics of the policies are studied by Monte Carlo simulation, and supplemented by further theoretical development.     

Values for optimum reject allowances

Industrial situations exist where it is necessary to estimate the optimum number of parts to start through a manufacturing process in order to obtain a given number of completed good items. The solution to this problem is not straightforward when the expected number of rejects from the process is a random variable and when there are alternative penalties associated with producing too many or too few items. This paper discusses various aspects of this problem as well as some of the proposed solutions to it. In addition, tables of optimum reject allowances based on a comprehensive model are presented.