A Foreward Simplex Method for Staircase Linear Programs

Article Abstract:

Modelling planning problems that extend over many time periods as linear programs lead to a special structure called a 'staircase' or 'dynamic' linear program. In this special structure, the nonzero coefficients of the linear program appear in blocks along the 'main diagonal' of the coefficient matrix. Such problems are commonly found in economic planning, structural design, agricultural planning, dynamic traffic assignment, production planning, and scheduling models. Forward algorithms provide an approach to solving these dynamic problems by solving successively longer finite horizon subproblems, terminating when a stopping rule can be invoked (or a decision horizon found). Such algorithms are available for a large number of specific models. Here we discuss the implementation and testing of a forward algorithm for solving general dynamic (staircase) linear programs. Tests reported indicate that the solution time is linear in the number of periods of the staircase problem, as compared to a quadratic or cubic relationship for standard linear programming codes. Computational decision horizons are often found, and are responsible for the good performance of the algorithm. (Reprinted by Permission of Publisher.)

Linear programming, Business planning, Dynamic programming, Large-Scale Systems

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Two Heuristics for the Deterministic, Single Operator, Multiple Machine, Multiple Run Cyclic Scheduling Problem

Article Abstract:

Multi-machine assignments are common in the textile, tooling, and moding industries. Two types of interference models are discussed. Random interference models describe problems when the call for service is stochastic. Deterministic models describe the situation when time between breakdowns and service times is assumed to be known. Charts, graphs and formulas help define external manual time, automatic processing time and cycle time. Both heuristics are coded in Fortran on a CDX-6600 computer. A deterministic model describes the situation when time between breakdowns and services times is assumed to be

Industrial productivity, Production control, Productivity, Software Design, Heuristic Methods, Scheduling Applications

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Oligopoly Models for Optimal Advertising When Production Costs Obey a Learning Curve

Article Abstract:

Oligopoly studies in economics generally confine themselves to one or two firms. Analyses involving three to ten firms are extremely interesting but very difficult. The problem of characterizing an optimal advertising policy over time in this environment is an important question in the field of marketing. Discrete differential game models are used to find Nash equilibrium solutions. Computer solutions to the resulting differential equations are plotted for various parameter settings. Numerical results are presented in tables and graphs.

Marketing, Game theory, Modeling, Data modeling software, Optimization, Marketing Applications, Advertising (Industry)

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