Jointly constrained order quantities with all-units discounts

In this article we investigate situations where the buyer is offered discounted price schedules from alternative vendors. Given various discount schedules, the buyer must make the best buying decision under a variety of constraints, such as limited storage space and restricted inventory budgets. Solutions to this problem can be utilized by the buyer to improve profitability. EOQ models for multiple products with all-units discounts are readily solvable in the absence of constraints spanning the products. However, constrained discounted EOQ models lack convenient mathematical properties. Relaxing the product-spanning constraints produces a dual problem that is separable, but lack of convexity and smoothness opens the door for duality gaps. In this research we present a set of algorithms that collectively find the optimal order vector. Finally, we present numerical examples using actual data. to illustrate the application of the algorithms. © 1993 John Wiley & Sons, Inc.     

Simulation of stochastic activity networks using path control variates

This article details several procedures for using path control variates to improve the accuracy of simulation-based point and confidence-interval estimators of the mean completion time of a stochastic activity network (SAN). Because each path control variate is the duration of the corresponding directed path in the network from the source to the sink, the vector of selected path controls has both a known mean and a known covariance matrix. This information is incorporated into estimation procedures for both normal and nonnormal responses. To evaluate the performance of these procedures experimentally, we examine the bias, variance, and mean square error of the controlled point estimators as well as the average half-length and coverage probability of the corresponding confidence-interval estimators for a set of SANs in which the following characteristics are systematically varied: (a) the size of the network (number of nodes and arcs); (b) the topology of the network; (c) the percentage of activities with exponentially distributed durations; and (d) the relative dominance of the critical path. The experimental results show that although large improvements in accuracy can be achieved with some of these procedures, the confidence-interval estimators for normal responses may suffer serious loss of coverage probability in some applications.     

A proof for the longest-job-first policy in one-machine scheduling

We consider a one-machine scheduling problem with earliness and tardiness penalties. All jobs are assigned a common due date and the objective is to minimize the total penalty due to job earliness and tardiness. We are interested in finding the optimal combination of the common due-date value and the job sequence. Despite the fact that this problem in general is very hard to solve, we prove that there exists at least a common property for all optimal solutions: The first job in an optimal sequence is one of the longest jobs. We also prove that this property holds for a general class of unimodal penalty functions.     

Sole sourcing versus dual sourcing under stochastic demands and lead times

The use of a single vendor for each inventoried item is usually assumed in most of the inventory models. However, there are situations where the use of more than one vendor should be considered, especially when lead times are stochastic. This research presents a theoretical investigation of the effect of cost structures on the relative performance of sole-sourcing versus dual-sourcing inventory control policies. We show that except for cases where the ordering cost is high, the lead-time variability is low, or the customer service level is low, dual sourcing performs better than sole sourcing under the normally distributed demand and shifted-exponential lead times. Moreover, the computational results indicate the dual sourcing provides a better service level than sole sourcing at the optimal solutions, and that dual sourcing results in larger order quantities than sole sourcing, which suggests that attractive quantity discounts may not be in jeopardy when dual sourcing is employed. Finally, because it is generally known that multiple sourcing can enhance the competition among suppliers, material managers should consider splitting purchase orders when two equally qualified suppliers are available. © 1994 John Wiley & Sons, Inc.     

Estimation and prediction in a semi-markov model for evasive vehicle movement along a fixed path

In Turner and Holmes [8] a model for evasive vehicle movement along a fixed track is developed within the mathematical framework of a two-state semi-Markov process. They derive a number of analytical properties of the model. In this article we address problems concerning the estimation of parameters in the model and the construction of data-based prediction equations.     

On the number of games played in a best of (2n – 1) series

Let p(⩾0.5) denote the probability that team A beats B in a single game. The series continues until either A or B wins n games. Assuming that these games are independent replications, we study some features of the distribution of X_n, the number of games played in the series. It is shown that X_n is unimodal, has an IFRA distribution, and is stochastically decreasing in p. Close approximations to its mode, mean, and variance are given. Finally, it is shown that the maximum-likelihood estimator of p based on X_n is unique.     

Viability analysis: A formulation aid for all classes of network models

Nonviable network models have edges which are forced to zero flow simply by the pattern of interconnection of the nodes. The original nonviability diagnosis algorithm [4] is extended here to cover all classes of network models, including pure, generalized, pure processing, nonconserving processing, and generalized processing. The extended algorithm relies on the conversion of all network forms to a pure processing form. Efficiency improvements to the original algorithm are also presented.     

Single‐machine scheduling with deadlines to minimize the total weighted late work

We consider scheduling a set of jobs with deadlines to minimize the total weighted late work on a single machine, where the late work of a job is the amount of processing of the job that is scheduled after its due date and before its deadline. This is the first study on scheduling with the late work criterion under the deadline restriction. In this paper, we show that (i) the problem is unary NP‐hard even if all the jobs have a unit weight, (ii) the problem is binary NP‐hard and admits a pseudo‐polynomial‐time algorithm and a fully polynomial‐time approximation scheme if all the jobs have a common due date, and (iii) some special cases of the problem are polynomially solvable.     

Information security: Designing a stochastic‐network for throughput and reliability

Todas information and communication network requires a design that is secure to tampering. Traditional performance measures of reliability and throughput must be supplemented with measures of security. Recognition of an adversary who can inflict damage leads toward a game‐theoretic model. Through such a formulation, guidelines for network designs and improvements are derived. We opt for a design that is most robust to withstand both natural degradation and adversarial attacks. Extensive computational experience with such a model suggests that a Nash‐equilibrium design exists that can withstand the worst possible damage. Most important, the equilibrium is value‐free in that it is stable irrespective of the unit costs associated with reliability vs. capacity improvement and how one wishes to trade between throughput and reliability. This finding helps to pinpoint the most critical components in network design. From a policy standpoint, the model also allows the monetary value of information‐security to be imputed. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009