The efficiency of the simplex method: a survey

Article Abstract:

The most commonly used optimization model is the Linear Program (LP) Problem. George Dantzig's Simplex Solution for solving the LP Problem is a very efficient computational mechanism in use for almost 40 years, but some major aspects of its behavior are not fully understood. Its typical application is in planning, scheduling, allocation, and other decision-making aspects of industrial, military, and economic operations. Four aspects of Simplex Method efficiency are explored, including: (1) reports on practical applications in real-life LP settings, (2) results from 'Monte Carlo' experiments solving randomly-generated LP problems, (3) complexity results, and (4) theoretical study results.

Models, Linear programming, Monte Carlo method, Monte Carlo methods

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Power approximation for computing (s, S) policies using service level

Article Abstract:

An approximation for calculating reorder point and order quantity (s, S) inventory policies was conducted for single items undergoing periodic reviews. Ordering costs and replenishment lead times were fixed, holding costs were linear, and unfilled demand was backlogged. A gamma-service level measured average backlog in relation to average demand. Only the demand variance and the mean were needed to calculate the power approximation policies. The results of the approximation indicate that the gamma-service level usually was within one percent of the service level requirement, and that the expected total costs were within one percent of the optimal level.

Methods, Usage, Numerical analysis, Inventory control

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