Time minimizing flows in directed networks

An important class of network flow problems is that class for which the objective is to minimize the cost of the most expensive unit of flow while obtaining a desired total flow through the network. Two special cases of this problem have been solved, namely, the bottleneck assignment problem and time-minimizing transportation problem. This paper addresses the more general case which we shall refer to as the time-minimizing network flow problem. Associated with each arc is an arc capacity (static) and a transferral time. The objective is to find a maximal flow for which the length (in time) of the longest path carrying flow is minimized. The character of the problem is discussed and a solution algorithm is presented.     

Econometric forecasting via discounted least squares

Simple direct smoothing formulas are derived for updating coefficient estimates and forecasts in a discounted least squares model. These formulas are the natural extensions of R. G. Brown's well-known smoothing formulas to a general econometric setting with arbitrary explanatory time series. The recursive updating process and its forecast error properties are illustrated via a simple, yet realistic numerical example.     

On the distribution of the optimal value for a class of stochastic geometric programs

An approach is presented for obtaining the moments and distribution of the optimal value for a class of prototype stochastic geometric programs with log-normally distributed cost coefficients. It is assumed for each set of values taken on by the cost coefficients that the resulting deterministic primal program is superconsistent and soluble. It is also required that the corresponding dual program has a unique optimal point with all positive components. It is indicated how one can apply the results obtained under the above assumptions to stochastic programs whose corresponding deterministic dual programs need not satisfy the above-mentioned uniqueness and positivity requirements.     

Multiple resource leveling in construction systems through variation of activity intensities

The resource leveling problem for a construction system producing a stream of output units is considered. The system is modeled using a critical-path-analysis activity network, from which an extended network is developed for an integrated planning effort of all output units. Activity intensity variables are defined which measure activity demand rates for resources and consequent activity durations for the production of each output unit. A heuristic approach consisting of an iterative nonlinear programming procedure is presented which computes activity durations (intensities) for the minimization of resource capacity costs subject to meeting construction due dates. The application to a major ship overhaul project is described, in which the procedure was used to level workloads of the various labor–trade shops.     

An algorithm for maximizing target achievement in the stochastic knapsack problem with normal returns

We consider the stochastic linear knapsack problem in which costs are known with certainty but returns are independent, normally distributed random variables. The objective is to maximize the probability that the overall return equals or exceeds a specified target value. A previously proposed preference order dynamic programming-based algorithm has been shown to be potentially suboptimal. We offer an alternative hybrid DP/branch-and-bound algorithm that both guarantees optimality and significantly outperforms generating the set of Pareto optimal returns.© 1993 John Wiley & Sons, Inc.     

A two-station stochastic inventory model with exact methods of computing optimal policies

A method is presented for calculating optimal inventory levels in a two-station transactions reporting inventory system. The criterion of optimality is the minimization of expected cost. The computational properties of the model are stressed and the solution method is precise. It is shown that when the model represents a central warehouse which supplies several retail outlets, stocks carried at the central location affect the capacity of the system to handle orders. Stocks carried at the retail level affect only the size of the retail order backlog.