A zero-one (0-1) linear programming formulation of multiproject and job-shop scheduling problems is presented that is more general and computationally tractable than other known formulations. It can accomodate a wide range of iwal-world situations including multiple resource c'.nstraints, due dates, job splitting, resource substitutabiilty, and concurrency and nonconcurrency of job performance requirements. Three possible objective functions are discussed: minimizing total throughput time for all projects: minimizing the time by which all projects are completed (i.e., minimizing makespan); and minimizing total lateness or lateness penalty for all projects. however, another look at the problem from a mathematical programming point of view seems in order, especially in light of recent developments in 0-I programming [7,9,18,25]. INTRODUCTIONThe -;chcduling problens cunsidered here deal with det,,idnng when a job should be processed, given limited e'.ailabilitius of rcources, e.g., rmen, equiptwnL, and facilities. The words .ob adI project will be used Lhvuugliout to denote the two levels of work aggregation being considered. A project consOi.tr of a set of jobs.In Luthei literaturc describing acht-d4ling research, the following equivalent descriptors way be found: Equations are developed to ensure that a schedule meets the foliowing constraints when they are imposed:

The problem addressed in this paper is the selection of the shortest path through a directed, acyclic network where the arc lengths are independent random variables. This problem has received little attention although the deterministic version of the problem has been studied extensively. The concept of a path optimality index is introduced as a performance measure for selecting a path of a stochastic network. A path optimality index is defined as the probability a given path is shorter than all other network paths. This paper presents an analytic derivation of path optimality indices for directed, acyclic networks. A new network concept, Uniformly Directed Cutsets (UDCs), is introduced. UDCs are shown to be important to the efficient implementation of the prescribed analytic procedure. There are strong indications that stochastic shortest route analysis has numerous applications in operations research and management science. Potential application areas include, equipment replacement analysis, reliability modeling, maximal flow problems, stochastic dynamic programming problems, and PERT-type network analysis.

This paper describes a procedure for evaluating pro posed startup policies that define the initial condi tions and the truncation point in a simulation ex periment. The evaluation procedure involves the tabulation of bias, variance, and mean square error of the sample mean over a fixed range of truncation points and initial conditions. For each policy, the tabulated values are averaged with respect to an empirical truncation-point distribution based on independent model runs. These results are used to construct confidence intervals for the steady-state mean with the same average length for all policies; the corresponding average confidence interval cover age can then be used to compare policies. To illustrate the procedure, several well-known policies are evaluated for two finite-state Markovian queueing systems—α single-server queue with a capac ity of 15 and a machine-repair system with 3 repair- men and 14 machines. The results for both systems indicate that the best initial condition is the most frequently observed value (the mode) of the steady- state distribution of the number-in-system process, and that the judicious selection of an initial condi tion is more effective than truncation in improving the performance of the sample mean as an estimator of the steady-state mean.

To reduce the effects of initial conditions on the results of a simulation experiment, several authors have proposed startup policies that specify how to minimize the warmup period and identify the truncation point beyond which observations are to be recorded and analyzed. Other approaches to this probZem have used results from time-series analysis and queueing theory. This paper surveys research on the simulation startup problem; a companion paper which follows presents a procedure for evaluating startup policies when the mean of the truncated sample is to be used to estimate the steady-state mean of the underlying process.