Application of renewal theory to continuous sampling plans

Renewal theory is used to study the effectiveness of a class of continuous sampling plans first introduced by Dodge. This approach provides a simple way of viewing and computing the long-run Average Outgoing Quality (AOQ) and its maximum AOQL. More importantly, it is used to study the average outgoing quality in a short production run through an approximation formula AOQ^*(t). Formulas for AOQ and AOQ^*(t) are provided. By simulation, it is found that AOQ^*(t) is sufficiently accurate in situations corresponding to actual practice.     

Minimum cost sampling plans using bayesian methods

This article considers a general method for acceptance/rejection decisions in lot-by-lot sampling situations. Given arbitrary cost functions for sampling, accepting, and rejecting (where the cost can depend on the quality of the item) and a prior distribution on supplier quality, formulas are derived that lead to the minimal cost single-staged inspection plan. For the Bernoulli case, where each item is classified as acceptable or defective, the formulas simplify immensely. A computer code for solving the Bernoulli case is given.     

Heuristic modeling of supply availabilities in large networks

The objective of this article is to describe heuristic solutions to the problem of modeling inventories at each node of a large network in the context of a computer simulation model of that network. The heuristic solutions are compared with the mathematical solution which is too unwieldy for use in a simulation model. The Weibull cumulative distribution is used as an approximation for the heuristic models. We question whether the good performance of the Weibull is coincidence or perhaps mathematically justifiable.     

Estimating critical path and arc probabilities in stochastic activity networks

This article describes a new procedure for estimating parameters of a stochastic activity network of N arcs. The parameters include the probability that path m is the longest path, the probability that path m is the shortest path, the probability that arc i is on the longest path, and the probability that arc i is on the shortest path. The proposed procedure uses quasirandom points together with information on a cutset ? of the network to produce an upper bound of O[(log K)^N?|?|+1/K] on the absolute error of approximation, where K denotes the number of replications. This is a deterministic bound and is more favorable than the convergence rate of 1/K^1/2 that one obtains from the standard error for K independent replications using random sampling. It is also shown how series reduction can improve the convergence rate by reducing the exponent on log K. The technique is illustrated using a Monte Carlo sampling experiment for a network of 16 relevant arcs with a cutset of ? = 7 arcs. The illustration shows the superior performance of using quasirandom points with a cutset (plan A) and the even better performance of using quasirandom points with the cutset together with series reduction (plan B) with regard to mean square error. However, it also shows that computation time considerations favor plan A when K is small and plan B when K is large.     

Recent articles on partial backorders: Comment

This note points out the omission of a simple but vital constraint in the recent articles on partial backlogging. Also, a simple intuitive interpretation of the “backorder” inequality of [2], [3], and [4] is provided.     

A (Q,R) inventory model with lost sales and erlang-distributed lead times

The exact expression is derived for the average stationary cost of a (Q,R) inventory system with lost sales, unit Poisson demands, Erlang-distributed lead times, fixed order cost, fixed cost per unit lost sale, linear holding cost per unit time, and a maximum of one order outstanding. Explicit expressions for the state probabilities and a fast method of calculating them are obtained for the case of Q greater than R. Exponential lead times are analyzed as a special case. A simple cyclic coordinate search procedure is used to locate the minimum cost policy. Examples of the effect of lead time variability on costs are given.     

A heuristic with tie breaking for certain 0–1 integer programming models

A heuristic for 0–1 integer programming is proposed that features a specific rule for breaking ties that occur when attempting to determine a variable to set to 1 during a given iteration. It is tested on a large number of small- to moderate-sized randomly generated generalized set-packing models. Solutions are compared to those obtained using an existing well-regarded heuristic and to solutions to the linear programming relaxations. Results indicate that the proposed heuristic outperforms the existing heuristic except for models in which the number of constraints is large relative to the number of variables. In this case, it performs on par with the existing heuristic. Results also indicate that use of a specific rule for tie breaking can be very effective, especially for low-density models in which the number of variables is large relative to the number of constraints.     

Causative matrix technique for deriving interim period transition probabilities in nonstationary markov process

The Markov assumption that transition probabilities are assumed to be constant over entire periods has been applied in economic and social structures, for example, in the analysis of income and wage distributions. In many cases, however, nonstationary transition probabilities exist over different periods. Based on causative matrix technique, this study shows a binomial approximation for obtaining nonstationary interim transition probabilities under undisturbance when the first and the last transition matrices are known.