A timetabling problem is formulated as a large integer linear programming problem in 0-1 variables. A solution method based on Lagrangean relaxation coupled with subgradient optimization is presented. The solution met...
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A timetabling problem is formulated as a large integer linear programming problem in 0-1 variables. A solution method based on Lagrangean relaxation coupled with subgradient optimization is presented. The solution method also incorporates a branch and bound procedure which takes advantage of special ordered sets of variables. We present computational results for a large timetabling problem involving 900 subjects in a one-year graduate program.
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 ...
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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 integerprogramming 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.
In this paper, oil spills occurring near shore in semienclosed waterways are viewed as emergency events. A partial set covering model, similar to those developed for firehouse location analysis, is applied to the prob...
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In this paper, oil spills occurring near shore in semienclosed waterways are viewed as emergency events. A partial set covering model, similar to those developed for firehouse location analysis, is applied to the problem of locating oil spill response equipment. The model includes both assessments of the relative probability of occurrence and the impact after occurrence of various spill types. A multiple objective approach enables the decisionmaker to evaluate strategies without confounding the probability of occurrence with the impact of occurrence.
When auditing payments for medical services by a third party, estimates of payments erroneously made are frequently based on statistical samples. When such procedures are used by government agencies to audit Medicaid ...
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When auditing payments for medical services by a third party, estimates of payments erroneously made are frequently based on statistical samples. When such procedures are used by government agencies to audit Medicaid payments, hearing officers often base provider restitution on the lower end of an interval estimate, which is a function of sample size. Several methods are tested for maximizing the total restitution obtained from multiple audits subject to a constraint on the total cost of the auditing.
One of the most important ways for today's banks to improve productivity is to speed up collection of funds of out-of-town (or “transit”) checks. A computerized integerprogramming model for transit check cleari...
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One of the most important ways for today's banks to improve productivity is to speed up collection of funds of out-of-town (or “transit”) checks. A computerized integerprogramming model for transit check clearing has been developed and implemented at the Maryland National Bank, Baltimore. This model has improved the efficiency of transit check clearing and resulted in yearly savings in excess of $100,000.
integerprogramming techniques were used to determine the order in which to build office buildings and when to put the space on the market for a seven-building, 90-acre, mixed-use real estate project in Texas. The out...
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integerprogramming techniques were used to determine the order in which to build office buildings and when to put the space on the market for a seven-building, 90-acre, mixed-use real estate project in Texas. The output of the optimization provided development managers with the schedule for opening each building, the amount of space to be leased each year in each building, and the annual cash flows to the owner.
For Air Products and Chemicals, Inc., inventory management of industrial gases at customer locations is integrated with vehicle scheduling and dispatching. Their advanced decision support system includes on-line data ...
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For Air Products and Chemicals, Inc., inventory management of industrial gases at customer locations is integrated with vehicle scheduling and dispatching. Their advanced decision support system includes on-line data entry functions, customer usage forecasting, a time/distance network with a shortest path algorithm to compute intercustomer travel times and distances, a mathematical optimization module to produce daily delivery schedules, and an interactive schedule change interface. The optimization module uses a sophisticated Lagrangian relaxation algorithm to solve mixed integer programs with up to 800,000 variables and 200,000 constraints to near optimality. The system, first implemented in October, 1981, has been saving between 6% to 10% of operating costs.
A flexible manufacturing system (FMS) is an integrated, computer-controlled complex of automated material handling devices and numerically controlled machine tools that can simultaneously process medium-sized volumes ...
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A flexible manufacturing system (FMS) is an integrated, computer-controlled complex of automated material handling devices and numerically controlled machine tools that can simultaneously process medium-sized volumes of a variety of part types. FMSs are becoming an attractive substitute for the conventional means of batch manufacturing, especially in the metal-cutting industry. This new production technology has been designed to attain the efficiency of well-balanced, machine-paced transfer lines, while utilizing the flexibility that job shops have to simultaneously machine multiple part types. Some properties and constraints of these systems are similar to those of flow and job shops, while others are different. This technology creates the need to develop new and appropriate planning and control procedures that take advantage of the system's capabilities for higher production rates.
This paper introduces a line of research on capacity-constrained multi-stage production scheduling problems. The first section introduces the problem area as it arises from a failure of MRP systems. Then a review of t...
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This paper introduces a line of research on capacity-constrained multi-stage production scheduling problems. The first section introduces the problem area as it arises from a failure of MRP systems. Then a review of the literature and an analysis of the type of problems that exist are presented in §2. Section 3 outlines linear and mixed integer-linear programming formulations. These formulations compute the required production lead times according to the demands on available capacity, thereby reducing in-process inventory compared to the usual practice in MRP. A discussion of how to use the LP version is included. However, the size of the problems in practice implies that more efficient solution techniques must be found. The final topic of this paper, Product Structure Compression, is introduced as a method to reduce the size of the problem without losing optimality.
This paper is concerned with the problem of scheduling tasks on a system consisting of two parallel processors in order that makespan be minimized. In particular, we treat a variety of modifications to this basic them...
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This paper is concerned with the problem of scheduling tasks on a system consisting of two parallel processors in order that makespan be minimized. In particular, we treat a variety of modifications to this basic theme, including the cases of identical, proportional, and unrelated processors. In addition, a heuristic scheme is suggested when precedence constraints exist where such constraints may be assignment dependent. Substantial computational experience is reported in all cases where it would appear that relatively large problems can be handled routinely.
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