Decision Making & Negotiations

We examine a queueing system with multiple primary servers and a fewer number of auxiliary servers. There are two classes of customers—those who require service from a primary server working alone and those who require service from a primary server who is assisted by an auxiliary server. Though the apparent Markovian state space is five-dimensional, we show that an aggregation results in an exact two-dimensional representation which is Markovian. Matrix geometric theory is used to obtain approximations for the mean delay and blocking probability of each customer type.

Many queueing situations such as computer, communications and emergency systems have the feature that customers may require service from several servers at the same time. They may thus be delayed until the required number of servers is avialable and servers may be idle when customers are waiting. We consider general server-completion-time distributions and derive approximation methods for the computation of the steady-state distribution of the number of customers in queue as well as the moments of the waiting-time distribution. Extensive computational results are reported.

This paper presents a successive approximation method for solving systems of nested functional equations which arise, e.g., when considering Markov renewal programs in which policies that are maximal gain or optimal under more selective discount — and average overtaking optimality criteria are to be found. In particular, a successive approximation method is given to find the optimal bias vector and bias-optimal policies. Applications with respect to a number of additional stochastic control models are pointed out.

How many patrol cars staffed with a single police officer are needed to provide equivalent police service to an existing system with n two-officer patrol cars? This question is explored for New York City using a multiple patrol car per call priority queueing model. It is shown that a one-officer patrol program is feasible, yet pitfalls exist which could adversely affect its performance. The paper details the process of data analysis and model building and emphasizes the subjective elements that remain in a highly technical OR study.

The performance of adult females on information acquisition tasks is shown to be related to their performance on information integration tasks; both are shown to be related to basic measures of cognitive ability derived from formal operations theory.

One of the primary concerns of urban police departments is the effective use of patrol cars. In large cities, police assigned to patrol cars typically account for more than 50% of total police manpower and their allocation has become particularly crucial in light of recent fiscal cutbacks.

In this paper, we analyze the behavior of equilibrium real interest rates in an identical consumer economy in which the preferences are represented by time additive logarithmic utility functions and production technologies are Cobb-Douglas with stochastic constant returns to scale. The following main results are established. (i) When there is no relative price uncertainty, it is shown that the equilibrium interest rate exhibits a mean reverting tendency. A nontrivial steady state distribution is found to exist for the equilibrium interest rate.

In many practical applications of multi-item inventory systems significant economies of scale can be exploited when coordinating replenishment orders for groups of items. This paper considers a continuous review multi-item inventory system with compound Poisson demand processes; excess demands are backlogged and each replenishment requires a lead time. There is a major setup cost associated with any replenishment of the family of items, and a minor (item dependent) setup cost when including a particular item in this replenishment. Moreover there are holding and penalty costs.

Consider a central depot (or plant) which supplies several locations experiencing random demands. Orders are placed (or production is initiated) periodically by the depot. The order arrives after a fixed lead time, and is then allocated among the several locations. (The depot itself does not hold inventory.) The allocations are finally received at the demand points after another lag. Unfilled demand at each location is backordered. Linear costs are incurred at each location for holding inventory and for backorders. Also, costs are assessed for orders placed by the depot.