Robert M. Nauss

The 0–1 knapsack problem with multiple choice constraints☆

Abstract In this paper we consider the 0–1 knapsack problem with multiple choice constraints appended. Such a problem may arise in a capital budgeting context where only one project may be selected from a particular group of projects. Thus the problem is to choose one project from each group such that the budgetary constraint is satisfied and the maximum return is realized. We formulate two branch and bound algorithms which use two different relaxations as the primary bounding relaxations. In addition, theoretical results are given for a simple reduction in the number of variables in the problem.

Optimal sequencing in the presence of setup times for tow/barge traffic through a river lock

Abstract Queues of tow/barges form when a river lock is rendered inoperable due to lock malfunction, a tow/barge accident or adverse lock operating conditions. In this paper, we develop model formulations that allow the queue to be cleared using a number of differing objectives. Of particular interest is the presence of different setup times between successive passages of tow/barges through the lock. Dependent on the objective chosen, we are able to show that certain ordering protocols may be used to markedly reduce the sequencing search space for N tow/barges from the order of N ! to 2 N . We present accompanying linear and nonlinear integer programming formulations and carry out computational experiments on a representative set of problems.

Investigating Strategic Alternatives for Improving Service in an Inland Waterway Transportation System

A series of five locks form a transportation bottleneck in the upper Mississippi River navigation system. With optimizing models, statistical modeling and computer simulation, the authors explore the effects of alternative scheduling regimes and infrastructure changes to improve performance of an inland waterway transportation system. In this paper, the authors show the value of triangulating and integrating analysis with different research paradigms in order to explore the effects of alternative strategies for improving performance of a major transportation system.

The elastic generalized assignment problem

The generalized assignment problem (GAP) has been studied by numerous researchers over the past 30 years or so. Simply stated, one must find a minimum-cost assignment of tasks to agents such that each task is assigned to exactly one agent and such that each agents resource capacity is honoured. The problem is known to be NP-hard. In this paper, we study the elastic generalized assignment problem (EGAP). The elastic version of GAP allows agent resource capacity to be violated at additional cost. Another version allows undertime costs to be assessed as well if an agents resource capacity is not used to its full extent. The EGAP is also NP-hard. We describe a special-purpose branch-and-bound algorithm that utilizes linear programming cuts, feasible solution generators, Lagrangean relaxation and subgradient optimization. We present computational results on a large collection of randomly generated ‘hard’ problems with up to 4000 binary variables.

Computer support for operator assignment and dispatching in an urban transit system

Abstract The St. Louis Metropolitan Transit Authority, as part of a systematic program to improve maintenance on its buses, is attempting to have operators drive the same vehicle each day. A simulation model was developed for testing the feasibility of the system and testing heuristic rules for parking buses to prevent blockages at scheduled departure times. A mathematical programming procedure is used for assigning buses to runs. An interactive computer system supports parking and dispatching. This article describes the three tools and relates experience with their use.

Decision Support For Staffing, Outsourcing And Project Scheduling In Mis Strategic Plans

Abstract Implementing MIS plans requires simultaneous consideration of staffing, outsourcing and project scheduling. As organizations introduce new systems and phase out legacy systems, they weigh alternatives regarding the transfer of applications to new platforms, outsourcing of applications, development of applications in-house, and outsourcing of the development of applications. They also recruit new talent and develop new competence in existing staff. When MIS plans are too ambitious, schedules must be altered or additional resources must be acquired. To deal with these complexities, a mixed integer programming model was developed for the information services division of a state governmental agency. It enabled a thorough study of the economies of different combinations of full-time staff, contract workers and outsourcing to implement MIS plans. In this paper, we present the model and relate experience with its use.

Triangulation of Modeling Methodologies for Strategic Decisions in an Inland Waterway Transportation System

We show how optimizing models, computer simulation, and expert opinion were integrated to investigate the potential performance of a waterway navigation system under different scheduling regimes and infrastructure changes. Analytical models are used to derive scheduling rules that balance efficiency against equity. Discrete-event simulation is used to assess system performance under various infrastructural changes (helper boats, expanded locks) and traffic management schemes (such as load leveling, priority scheduling, or self-regulation by the barge industry). Expert opinion is sought to address concerns of stakeholders and shed light on industry reactions to different policy alternatives. We show the importance of triangulation involving different modeling and philosophical approaches in generating relevant information for development of solution strategies.

Staffing geographically distributed service facilities with itinerant personnel

We address the problem of designing and staffing service facilities for a geographically distributed population of independent customers. Capacitated gravity models are used to represent a customers selection of service facility. Analytical models and simulation are used to estimate service levels that would occur with alternative staffing levels and hours of operation. Integer programming is used to determine staffing patterns. We illustrate how these tools are used in concert to plan the statewide location and operation of drivers examination centers with combinations of fixed and itinerant staff.

On the use of internal rate of return in linear and integer programming

Internal rate of return (IRR) is used as a criterion many investment decisions. For example many issuers of new municipal debt evaluate competitive bids on the basis of IRR. We incorporate IRR into mathematical programming formulations in such a way that the resulting problem becomes linear. This linearization permits linear programming and integer linear programming algorithms to be brought to bear on problems which had heretofore been solved in an iterative, time consuming fashion.

Generating optimal true interest cost bids for new municipal bond competitive issues

Abstract In 1984 over