A multi-run interactive method for bicriterion optimization problems

This article introduces a new conceptual and methodological framework for the use of decision makers and their interactions with the computer in bicriterion decision making. The new method, called the multirun interactive method, attempts to estimate the prior of the decision maker on his uncertain preference nature using the minimum cross-entropy principle. A computational study is performed with four hypothesized prior distributions under various interaction conditions. Other important aspects related to the method, such as implementation of the method, decision making under certainty, decision making with multiple decision makers, and bicriterion integer programming, are also discussed.     

Optimal resource extraction with uncertain reserves

We consider the problem of finding a plan that maximizes the expected discounted return when extracting a nonrenewable resource having uncertain reserves. An extraction plan specifies the rate at which the resource is extracted as a function of time until the resource is exhausted or the time horizon is reached. The return per unit of resource extracted may depend on the rate of extraction, time, and the amount of resource previously extracted. We apply a new method called the generalized search optimization technique to find qualitative features of optimal plans and to devise algorithms for the numerical calculation of optimal plans.     

Inventory sharing under decentralized preventive transshipments

We consider preventive transshipments between two stores in a decentralized system with two demand subperiods. Replenishment orders are made before the first subperiod, and the stores may make transshipments to one another between the subperiods. We prove that the transshipment decision has a dominant strategy, called a control‐band conserving transfer policy, under which each store chooses a quantity to transship in or out that will keep its second‐subperiod starting inventory level within a range called a control band. We prove that the optimal replenishment policy is a threshold policy in which the threshold depends on the capacity level at the other store. Finally, we prove that there does not exist a transfer price that coordinates the decentralized supply chain. Our research also explains many of the differences between preventive and emergency transshipments, including differences in the optimal transfer policies and the existence or nonexistence of transfer prices that coordinate the system. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Estimating the probability that a simulated system will be the best

Consider a stochastic simulation experiment consisting of v independent vector replications consisting of an observation from each of k independent systems. Typical system comparisons are based on mean (long‐run) performance. However, the probability that a system will actually be the best is sometimes more relevant, and can provide a very different perspective than the systems' means. Empirically, we select one system as the best performer (i.e., it wins) on each replication. Each system has an unknown constant probability of winning on any replication and the numbers of wins for the individual systems follow a multinomial distribution. Procedures exist for selecting the system with the largest probability of being the best. This paper addresses the companion problem of estimating the probability that each system will be the best. The maximum likelihood estimators (MLEs) of the multinomial cell probabilities for a set of v vector replications across k systems are well known. We use these same v vector replications to form v^k unique vectors (termed pseudo‐replications) that contain one observation from each system and develop estimators based on AVC (All Vector Comparisons). In other words, we compare every observation from each system with every combination of observations from the remaining systems and note the best performer in each pseudo‐replication. AVC provides lower variance estimators of the probability that each system will be the best than the MLEs. We also derive confidence intervals for the AVC point estimators, present a portion of an extensive empirical evaluation and provide a realistic example. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 341–358, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10019     

The asymptotic joint distribution of the state occupancy times in an alternating renewal process

An alternating renewal process starts at time zero and visits states 1,2,…,r, 1,2, …,r 1,2, …,r, … in sucession. The time spent in state i during any cycle has cumulative distribution function F_i, and the sojourn times in each state are mutually independent, positive and nondegenerate random variables. In the fixed time interval [0,T], let U_i(T) denote the total amount of time spent in state i. In this note, a central limit theorem is proved for the random vector (U_i(T), 1 ≤ i ≤ r) (properly normed and centered) as T → ∞.     

Optimal replacement for fault-tolerant systems

We consider the optimal replacement problem for a fault tolerant system comprised of N components. The components are distingushable, and the state of the system is given by knowing exactly which components are operationl and which have failed. The individual component failure rates depend on the state of the entire system. We assume that the rate at which the system produces income decreases as the system deteriorates and the system replacement cost rises. Individual components cannot be replaced. We give a greedy-type algorithm that produces the replacement policy that maximizes the long-run net system income per unit time.