Bus stop location on school bus routes

Abstracts

Static Shop Scheduling ESKEW JD (1973) Economic aspects of industrial scheduling. MSc Thesis, Georgia Institute of Technology. Copies available from RG Parker, School of Industrial and Systems Engineerlag, Georgia Institute of Technology, Atlanta, Georgia, U.S.A.

THE NATURE of this research centered about the static job-shop scheduling/ sequencing problem. The usual objective in such a problem is to determine sequences for a set of jobs through a set of facilities such that some measure is made optimal or near optimal. Traditional treatises of the problem have been concerned with the development of procedures which seek to minimize the completion time of all jobs, sometimes referred to as the scheduled time. However, this study has substantiated that such an objective may result in gross suboptimization where the objective is to minimize certain costs for the shop. Three cost measures were considered: (1) machine idle costs, (2) due-date penalty costs, and (3)job delay costs. A branch-and-bound type approach was developed such that sequences for each machine were determined where particular sequencing decisions were made based upon the minimization of an opportunity cost comprised of (1) and (2) above. After a complete sequencing solution is obtained, the algorithm attempts to right-shift or reschedule operations to reduce job delay costs. Substantial computational experience was accumulated such that the performance of the cost-based algorithm was compared with more conventional procedures. In addition, sensitivity tests were performed to gain insight into the effects of variations of certain shop/cost parameters. Abstracted by Robert G Parker, Georgia Institute of Technology, Atlanta, U.S.A.

Bus Stop Location on School Bus Routes GLEASON JM (1974) Bus stop location on school bus routes. Paper available from the author, College of Business Administration, Texas Tech University, Lubbock, Texas 79409,

U.S.A. VARIOUS APPROACHES to school bus routing have been reported in the literature. Typically, inputs to the models include information concerning the number of students to be loaded at each bus stop. Unfortunately, location of the bus stops (and, consequently, the number of students to be loaded at each stop) is usually determined on an "educated guess" or a "trial and error" basis. Two factors influence bus stop location decisions: (1) a minimum number of bus stops, and (2) acceptable walking distance to bus stops. As the number of bus stops on a route increases, travel time increases as a result of frequent stops and starts. Since one of the constraints in routing is a limit on the length of time students are required to spend on a bus, we would 242

Omega, Vol. 3, No. 2 prefer to shorten travel time on the routes as much as possible. Thus, we would prefer to establish a minimum number of bus stops, consistent with service to students on the route. Furthermore, most school bus routes are constrained by a limit on the maximum distance a student may walk in order to board a bus. Therefore, bus stops should be located such that the students need walk no more than a specified distance to reach a boarding point. This paper suggests a zero-one integer programming model which may be used to locate the minimum number of bus stops required to ensure that no student need walk more than a specified distance to board the bus. Abstracted by John M Gleason, Texas Tech University, Texas, U.S.A. Optimal

Bidding

in Sequential

Auctions

OREN SS and ROTHKOPF MH (1974) A model for choosing bidding strategy in a sequence of auctions when competitors are assumed to react. Copies available from the authors, Xerox Palo Alto Research Center, Paio Alto, California 94304, U.S.A.

MUCH OF the theory of competitive bidding and all of the early developments in that theory dealt with "one-shot" bidding situations in which it is appropriate for the bidder to attempt to maximize his expected profit from the present auction or simultaneous group of auctions. Recently, some models for optimum bidding in sequential auctions have been developed, most of these dealing with the internal effects within the bidding firm of winning or losing auctions and sharing the assumption that the competition will not react in later auctions to what the bidder has done in earlier auctions. Since the literature is filled with suggestions on how bidders should use information about the past behavior of competitors to determine their bids in present auctions, we have built a model of bidding in sequential auctions in which a bidder's competitors are assumed to react to his previous bids. We assume that bidders develop a behavioral model of how their competitors will react. This leads us to model the sequential bidding problem as a multistage control process in which the control is the bidder's strategy while the state characterizes the collective behavior of the competitors. In this model the state transition represents the competitors' reactions to the bidder's policy. Dynamic programming is used to derive an equation for the optimal infinite horizon bidding strategy. Next we develop an equation that must hold if each of a group of similarly situated competitors follows such a policy. When this equation is solved for a generalization of a previous model of "one-shot" auctions, the formula for the optimal "one-shot" policy is modified by the inclusion of a term that depends upon the magnitude of competitive reaction, the time between auctions, and the discount rate. Abstracted by Michael H Rothkopf, Xerox Palo Alto Research Center, Palo Alto, California, U.S.A. 243