The branch-and-bound technique of Little, et al. and Land and Doig is presented and then applied to two flow-shop scheduling problems. Computational results for up to 9 jobs are given for the 2-machine problem when the objective is minimizing the mean completion time. This problem was previously untreated. Results for up to 10 jobs, including comparisons with other techniques, are given for the 3-machine problem when the objective is minimizing the makespan.

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.

This paper gives a model in which two urban emergency service units (such as fire engines or ambulances) cooperate in responding to alarms or calls from the public in a specified region of a city. Given the home locations of the units and the spatial distribution of alarm rates, it is possible to specify which unit should respond to each alarm by defining a response area for each unit. The average response time to alarms and the workload of each unit are calculated as functions of the boundary that separates their response areas. The boundaries that minimize average response time and the ones that equalize workload are determined. Some boundaries can be dominated, in the sense that another boundary improves both workload balance and response time. The set of undominated boundaries is found.

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.

In response to an incoming fire alarm, someone must decide how many and which engine and ladder companies (firefighters and their apparatus) to dispatch to the scene. Traditional dispatching policies assume that all of the designated companies are available at the time the alarm is received. These policies do not consider the workload imposed on firefighters, and do not work well at the high alarm rates now characteristic of parts of large cities. Our procedure, designed for use in New York City's computed-aided Management Information and Control System, makes good initial dispatch decisions at all alarm rates. It uses response times to serious fires to measure performance and recognizes that the dispatcher has incomplete information about the seriousness of the incident when the decision is made. A simulation comparison of our procedure with the traditional policy was made using actual incidents from July 1972. Our procedure reduced the average second engine and second ladder response times to serious fires by 25 to 45 seconds, while keeping total workload essentially unchanged. This reduction, which is about 10--15% of the five and a half minutes obtained for the traditional policy, results primarily from our procedure's deciding how many to send based on historical information on the chance that an alarm from a given location at a given time of day is serious. For example, the fraction of fires in occupied structures getting an initial second engine rose from 65% with the traditional policy to 85% with our procedure, although both policies sent an initial second engine to the same fraction of all incidents. Our procedure also reduced the number of relocations of engine companies and ladder companies substantially. The approach we used should be valuable in the design of computer-aided dispatching systems in other cities. In particular, others may find it helpful to review the way in which the objective function is developed, the way particular aspects of the dispatch problem are treated, the provision of several parameters for tuning behavior, and features of the simulation testing.government services: fire, heuristic models, simulation: use in policy analysis