Scheduling workers in a constricted area

A generalization of the equi-partitioning problem, termed the 2D-Partition Problem, is formulated. The motivation is an aircraft maintenance scheduling problem with the following characteristics. The complete maintenance overhaul of a single aircraft requires the completion of some 350 tasks. These tasks require a varying number of technicians working at the same time. For large subsets of these 350 tasks, the constraining resource is physical space—tasks must be completed in a physical space of limited size such as the cockpit. Furthermore, there is no precedence relationship among the tasks. For each subset, the problem is to schedule the tasks to minimize makespan. Let m denote the maximum number of technicians that can work at the same time in the physical area under consideration. We present optimization algorithms for m = 2 and 3. © 1996 John Wiley & Sons, Inc.     

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.     

Cumulative search-evasion games

Cumulative search-evasion games (CSEGs) are two-person zero-sum search-evasion games where play proceeds throughout some specified period without interim feedback to either of the two players. Each player moves according to a preselected plan. If (X_t, Y_t,) are the positions of the two players at time t, then the game's payoff is the sum over t from 1 to T of A(X_t, Y_t, t). Additionally, all paths must be “connected.” That is, the finite set of positions available for a player in any time period depends on the position selected by that player in the previous time period. One player attempts to select a mixed strategy over the feasible T-time period paths to maximize the expected payoff. The other minimizes. Two solution procedures are given. One uses the Brown-Robinson method of fictitious play and the other linear programming. An example problem is solved using both procedures.     

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.     

A poissonian binomial model with constrained parameters

The article examines ways of computing cumulative probabilities for a constrained Poissonian binomial distribution arising from a model of a weapon defense system.