Consumer Behavior

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).

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.

This paper presents an allocation model for a perishable product, distributed from a regional center to a given set of locations with random demands. We consider the combined problem of allocating the available inventory at the center while deciding how these deliveries should be performed. Two types of delivery patterns are analyzed: the first pattern assumes that all demand points receive individual deliveries; the second pattern subsumes the frequently occuring case in which deliveries in multistop routes traveled by a fleet of vehicles. Computational experience is reported.

In many resource allocation problems, the objective is to allocate discrete resource units to a set of activities so as to maximize a concave objective function subject to upper bounds on the total amounts allotted to certain groups of activities. If the constraints determine a polymatroid and the objective is linear, it is well known that the greedy procedure results in an optimal solution. In this paper we extend this result to objectives that are "weakly concave," a property generalizing separable concavity.

In the classical maximal flow problem, the objective is to maximize the supply to a single sink in a capacitated network. In this paper we consider general capacitated networks with multiple sinks: the objective is to optimize a general "concave" preference relation on the set of feasible supply vectors. We show that an optimal solution can be obtained by a marginal allocation procedure. An efficient implementation results in an adaptation of the augmenting path algorithm. We also discuss an application of the procedure for an investment company that deals in oil and gas ventures.