Decision Making & Negotiations

A nonstationary Markov chain is weakly ergodic if the dependence on the state distribution on the starting state vanishes as time tends to infinity. A chain is strongly ergodic if it is weakly ergodic and converges in distribution. In this paper we show that the two ergodicity concepts are equivalent for finite chains under rather general (and widely verifiable) conditions. We discuss applications to probabalistic analyses of general search methods for combinatorial optimization problems (simulated annealing).

Based on observations made during an extensive study of police patrol operations in New York City, we examine the issues of the validity and utility of queueing models of service systems in which adaptive behavior by the (human) customers or servers is likely. We find that in addition to depending on the technical accuracy of its assumptions, the accuracy of such a model will also depend upon the level of managerial control of the system and adequacy of resources.

Evidence of excess volatilities of asset prices compared with those of market fundamentals is often attributed to speculative bubbles. This study demonstrates that bubbles could in theory lead to excess volatility, but it shows that certain variance bounds tests preclude bubbles as an explanation. The evidence ought to be attributed to model misspecification or inappropriate statistical tests. One important misspecification occurs if a researcher incorrectly specifies the time series properties of market fundamentals.

Most quantities of interest in discounted and undiscounted (semi-) Markov decision processes can be obtained by solving a system of functional equations. This paper derives bounds and variational characterizations for the solutions of such systems.

This paper considers a single-item, periodic-review inventory model with uncertain demands. In contrast to prior treatments of this problem we assume a finite production capacity per period. Assuming stationary data, a convex one-period cost function and a discrete demand distribution, we show (under a few additional unrestrictive assumptions) that a modified base-stock policy is optimal under the average-cost criterion; in addition, we characterize the optimal base-stock level.

This paper considers a single-item, periodic review inventory model with uncertain demands. We assume a finite production capacity in each period. With stationary data, a convex one-period cost function and a continuous demand distribution, we show (under a few additional unrestrictive assumptions) that a modified basic-stock policy is optimal under the discounted cost criterion, both for finite and infinite planning horizons. In addition we characterize the optimal base-stock levels in several ways.

We consider the problem of scheduling n jobs, each with a specific processing requirement, release time and due date on m uniform parallel machines. It is shown that a feasible schedule can be obtained by determining the maximum flow in a network, thus permitting the use of standard network flow codes. Using a specialized maximum flow procedure, the complexity reduces to O(tn3) operations when t is the number of distinct machine types.

Bernard Frieden and Lynne Sagalyn provide an in-depth analysis of several public-private partnerships that have resulted in several large downtown retail redevelopment projects. These projects were dependent in part on an improvement in underlying factors such as the revitalization of the downtown office market. But, more important, these projects owe their existence to innovative entrepreneurial urban policy. This essay shows how current city policies evolved from the experience gained from redevelopment efforts launched under federal auspices, including Great Society programs.