Optimal Continuous Review Policies for Two Product Inventory Systems with Joint Setup Costs

Minimum average cost ordering policies for continuously reviewed two product inventory systems with joint setup costs are sought. Disappointly, the optimal policy, even in a simple symmetric case, is not always simple: For some values of cost and demand parameters, a policy that would be difficult to implement is optimal. Markov Renewal Programming is used to find the region in parameter space where a given policy is optimal.

Optimality of Myopic Inventory Policies for Several Substitute Products

Multiproduct inventory systems with proportional ordering costs and stochastic demands are studied. New conditions are obtained under which a myopic ordering policy (a policy of minimizing expected cost in the current period alone) is optimal for a sequence of periods for all initial inventory levels. An important one of these, the substitute property, holds when the myopic policy is such that increasing the initial inventory of one product does not increase the quantity ordered of any product. Conditions on the one period expected holding and shortage cost function, which are of independent interest in nonlinear programming, are shown to imply the substitute property. Applications of these conditions to models with storage or investment limitations and to a multiechelon model are given. Under backlogging the usual extension to a fixed delivery lag is obtained. Some non-stationary cases are also treated.

Response to Communication on Rand-HUD Fire Models

The Communication from Rodrick and Deborah Wallace repeats allegations that they have made in print [Wallace, D. 1977. New York city fire crisis, part one, the system is falling apart. Heights and Valley News (May) 10--11; Wallace, R., D. Wallace. 1977. Studies on the Collapse of Fire Service in New York City 1972--1976: The Impact of Pseudoscience in Public Policy (pamphlet), Univ. Press of America, Washington, D.C.] and in various forums for more than three years. Their critique is not of Chaiken's paper, "Transfer of Emergency Service Deployment Models to Operating Agencies," (Chaiken, J. 1978. Transfer of emergency service deployment models to operating agencies. Management Sci. 24 (7) 719--731.) but rather they use the appearance of that paper as an occasion to comment again on the application of Rand's fire deployment models in New York City during the period from 1972 to 1976. Readers of Chaiken's paper who are not familiar with this history are likely to wonder how his paper, which barely mentions New York City, inspired the Wallaces' comments in this Communication.