In the scheduling situation considered here, we are given a set of routes, each associated with a particular school. A single bus is assigned to each route, picking up the students and arriving at their school within a specified time window. The scheduling problem is to find the fewest buses needed to cover all the routes while meeting the time window specifications. We present two integer programming formulations of the scheduling problem and apply them to actual data from New Haven, Connecticut for two different years, as well as to 30 randomly generated problems. Linear programming relaxations of these integer programs were found to produce integer solutions more than 75 percent of the time. In the remaining cases, we found that the few fractional values can be adjusted to integer values without increasing the number of buses needed. Our method reduces the number of buses needed by about 25 percent compared to the manual solutions developed by the New Haven school bus scheduler.programming: integer, applications, programming: linear relaxation of integer programs, education systems: operations
In deciding how many units to dispatch to an incoming alarm of unknown seventy the fire department is faced with a dilemma: If too few units are sent initially the extra units needed will be delayed; if too many units are sent, the extra units make a needless response and are temporarily unavailable for subsequent alarms. In this paper, we present a Markovian decision model for this problem. The model leads to a simple decision rule that considers three key factors: (1) the probability that the incoming alarm is serious (the greater the probability the more units dispatched); (2) the expected alarm rate in the area surrounding the alarm (the greater the alarm rate, the fewer units dispatched); and (3) the number of units available in the area surrounding the alarm (the more units available, the more units dispatched). We compare the decision rule to policies commonly in use and find that it results in significant improvements in response time to serious fires.government services: fire, probability: Markov decision models, simulation: use in policy analysis
Management commitment and counseling of workers about NIHL may be key factors in program effectiveness. A combination of qualitative and quantitative methods appears to be useful for assessing HCPs.
Experimental design methods have been widely applied to problems in manufacturing, but little attention has been given to applying these tools to service problems. In the world of direct marketing, the traditional approach is called A=B testing and involves changing one factor at a time. In this article we address the problem of improving direct mail response at Mother Jones magazine, employing a 16-run two-level fractional factorial design that tests seven factors simultaneously. We compare this design to other possible design choices, discuss sample size determination, and show how we labeled factors to isolate likely two-factor interactions. We discuss the results and conclusions of our study and the benefits to Mother Jones magazine.
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