Expected Penalty Cost Research Articles

A probabilistic programming model for blending aggregates

The paper introduces the formulation of a probabilistic programming model to find the optimum mix proportion of aggregates to meet the specific grading requirement in order to minimize the cost which consists of the material cost and the expected penalty cost. The model is probabilistic since the gradation, which is the major parameter, is a random variable. A linear programming model is first formulated. Using the LP solution as initial value, a direct search technique is then employed to solve the problem. The model is expected to be applicable to any problem of aggregates blending. In this paper, however, the mixing aggregates of an asphalt mixing plant is exemplified to test the applicability of the model.

A User-Oriented Software Reliability Model

A user-oriented reliability model has been developed to measure the reliability of service that a system provides to a user community. It has been observed that in many systems, especially software systems, reliable service can be provided to a user when it is known that errors exist, provided that the service requested does not utilize the defective parts. The reliability of service, therefore, depends both on the reliability of the components and the probabilistic distribution of the utilization of the components to provide the service. In this paper, a user-oriented software reliability figure of merit is defined to measure the reliability of a software system with respect to a user environment. The effects of the user profile, which summarizes the characteristics of the users of a system, on system reliability are discussed. A simple Markov model is formulated to determine the reliability of a software system based on the reliability of each individual module and the measured intermodular transition probabilities as the user profile. Sensitivity analysis techniques are developed to determine modules most critical to system reliability. The applications of this model to develop cost-effective testing strategies and to determine the expected penalty cost of failures are also discussed. Some future refinements and extensions of the model are presented.

The Transportation Problem with Stochastic Demand

The transportation problem with stochastic demand is considered when penalties are paid for each oversupplied and undersupplied unit of product. The transportation plan minimizing the total transportation costs plus total expected penalty cost of both kinds is to be found. The paper presents a method of solution which is preceded by a development that replaced the original cost function with a controlled linear approximation.