Evaluation of force structures under uncertainty

A model, for assessing the effectiveness of alternative force structures in an uncertain future conflict, is presented and exemplified. The methodology is appropriate to forces (e.g., the attack submarine force) where alternative unit types may be employed, albeit at differing effectiveness, in the same set of missions. Procurement trade-offs, and in particular the desirability of special purpose units in place of some (presumably more expensive) general purpose units, can be addressed by this model. Example calculations indicate an increase in the effectiveness of a force composed of general purpose units, relative to various mixed forces, with increase in the uncertainty regarding future conflicts.     

On the optimal allocation of crewmen aboard a warship

In the temporarily isolated situation in which a warship finds itself during a mission. not only spare parts, but also “spare” crewmen in various categories of specialization must he on board. Mathematical models for the probabilities of mission survival for personnel and for personnel and materiel jointly are proposed. A practical example is worked out: the optimal allocation of spare crewmen to different categories of specialization is calculated.     

Sequencing n jobs on two machines with setup,processing and removal times separated

The paper extends the machine flow-shop scheduling problem by separating processing time into setup, processing and removal times.     

Applications of renewal theory in analysis of the free-replacement warranty

Under a free-replacement warranty of duration W, the customer is provided, for an initial cost of C, as many replacement items as needed to provide service for a period W. Payments of C are not made at fixed intervals of length W, but in random cycles of length Y = W + γ(W), where γ(W) is the (random) remaining life-time of the item in service W time units after the beginning of a cycle. The expected number of payments over the life cycle, L, of the item is given by M_Y(L), the renewal function for the random variable Y. We investigate this renewal function analytically and numerically and compare the latter with known asymptotic results. The distribution of Y, and hence the renewal function, depends on the underlying failure distribution of the items. Several choices for this distribution, including the exponential, uniform, gamma and Weibull, are considered.     

M/M/1 queues with interdependent arrival and service processes

We study via simulation an M/M/1 queueing system with the assumption that a customer's service time and the interarrival interval separating his arrival from that of his predecessor are correlated random variables having a bivariate exponential distribution. We show that positive correlation reduces the mean and variance of the total waiting time and that negative correlation has the opposite effect. By using spectral analysis and a nonparametric test applied to the sample power spectra associated with certain simulated waiting times we show the effect to be statistically significant.     

A parallel sequencing algorithm for minimizing total cost

The problem of sequencing jobs on parallel processors when jobs have different available times, due dates, penalty costs and waiting costs is considered. The processors are identical and are available when the earliest job becomes available and continuously thereafter. There is a processor cost during the period when the processor is available for processing jobs. The proposed algorithm finds the sequence (or sequences) with minimum total cost (sum of waiting, penalty and processor costs.). A proof of the algorithm and numerical results are given.     

Flowshop sequencing problem with ordered processing time matrices: A general case

The ordered matrix flow shop problem with no passing of jobs is considered. In an earlier paper, the authors have considered a special case of the problem and have proposed a simple and efficient algorithm that finds a sequence with minimum makespan for a special problem. This paper considers a more general case. This technique is shown to be considerably more efficient than are existing methods for the conventional flow shop problems.     

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.     

A lost sales (S — 1, S) perishable inventory system with renewal demand

This article analyzes a one-to-one ordering perishable inventory model with renewal demands and exponential lifetimes. The leadtimes are independently and exponentially distributed and the demands that occur during stock out periods are lost. Although the items are assumed to decay at a constant rate, the output process is not renewal and the Markov renewal techniques are successfully employed to obtain the operating characteristics. The problem of minimizing the long run expected cost rate is discussed and numerical values of optimal stock level are also provided. © 1996 John Wiley & Sons, Inc.