A Stochastic Model for the Measurement of Electricity Outage Costs

The measurement of customer outage costs has recently become an important subject of research for the electric utilities. This paper uses a stochastic dynamic model as the starting point in developing a market-based method for the evaluation of outage costs. Specifically, the model postulates that once an electricity outage occurs, all production activity stops. Full production is resumed once the electricity outage is over. This process repeats itself indefinitely. The business customer maximizes his expected discounted profits (the expected value of the firm), taking into account his limited ability to respond to repeated random electricity outages. The model is applied to 11 industrial branches in Israel. The estimates exhibit a large variation across branches.

A Single Bottleneck System with Binomial Yields and Rigid Demand

This paper considers a "single bottleneck system": a multistage production system where all setups except one are zero. The stage with nonzero setup is defined to be the bottleneck; it may be thought of as the critical resource whose throughput largely determines the throughput of the entire system, as a envisioned by the OPT philosophy. Production is in lots with uncertain (binomial) yields and demand needs to be satisfied in full, thus possibly necessitating multiple production runs. We show how the optimal control problem can be reduced to that of optimal lotsizing a single stage.random yield, binomial distribution, rigid demand, bottleneck

Modeling the search for the least costly opportunity

With the continuing growth in the number of opportunities available at virtual stores over the Internet there is also a growing demand for the services of computer programs capable of scanning a large number of stores in a very short time. We assume that the cost associated with each scan is linear in the number of stores scanned, and that the resulting list of price quotes is not always satisfactory to the customer, in which case an additional scan is performed, and so on. In such a reality the customer, wishing to minimize her expected cost, must specify the requested sample size and a rule (control limit) to stop the search. In the context of search theory, the above search model can be categorized as "fixed-sample-size, sequential, with infinite horizon". According to this model the expected search cost is a function of two decision variables: the sample size and the control limit. We prove that for arbitrary sample size the expected search cost is either quasi-convex or strictly decreasing in the control limit, and that the optimal expected search cost is quasi-convex in the sample size. These properties allow an efficient calculation of the optimal policy. We also develop analytic formulas to calculate the cost's variance, allowing customers to choose a slightly higher expected cost if there is a considerable decrease in the variance. Finally, we present detailed examples for price quotes that are distributed uniformly or exponentially.Search theory Comparison shopping agents Optimal stopping rule