Lori S. Franz

Scheduling medical residents to rotations: solving the large-scale multiperiod staff assignment problem

The resident scheduling problem is a specific case of the multiperiod staff assignment problem where individuals are assigned to a variety of tasks over multiple time periods. As in many staffing and training situations, numerous limitations and requirements may be placed on those assignments. This paper presents a procedure for addressing two major problems inherent in the determination of a solution to this type of problem: infeasibilities that naturally occur in the scheduling environment but are obscured by complexity; and the intractable nature of large-scale models with this structure. The procedure developed describes a systematic approach that allows decision makers to resolve system-inherent infeasibilities, and a heuristic based on rounding to develop good feasible solutions to the model. The procedure is illustrated via a case example of resident assignments for teaching and training modules in a university affiliated teaching hospital.

A simplified interactive multiple objective linear programming procedure

Abstract Differences in decision making styles and decision settings have motivated the development of a variety of interactive approaches to assist decision makers (DMs) in determining preferred solutions to multiple criteria decision making problems. This paper presents a Simplified Interactive Multiple Objective Linear Programming (SIMOLP) procedure which is designed to appeal to a broad range of DMs because of its simplicity and flexibility. Specifically, at any stage in the interactive process, the procedure attempts to 1. (1) minimize the inputs required from the DMs; 2. (2) provide DMs with a representative set of decision alternatives while simultaneously limiting the number of alternatives considered; and 3. (3) allow DMs to change their minds about previously eliminated alternatives. The procedure is illustrated with both graphical and numerical examples and computational experience is discussed.

Aggregate production planning using chance-constrained goal programming

Multiple objective models have frequently been proposed to assist in solving aggregate production planning problems. Although such models are an improvement over those with single objectives, demand is usually considered deterministic. For this reason, previous attempts at solving production problems have often lacked realism and could not be successfully applied in many real decision environments. This paper suggests a chance-constrained goal programming (CCGP) approach to production planning which allows the decision maker to specify both probabilistic product demands and production line operating characteristics more in keeping with actual situations. The CCGP approach is based on the sequential solution of a linear programming formulation, allowing efficient solution of large-scale real-world problems using commercially available LP codes. The procedure is demonstrated with a hypothetical example, and proper interpretation of goal achievement is discussed. The findings in the paper are applicable whet...

A mathematical model for scheduling and staffing multiclinic health regions

Abstract This paper describes the design and analysis of a multiobjective integer linear program for scheduling and staffing multiple clinics with itinerant health personnel in multiclinic regions. Specifically, the optimal assignment of physicians, nurse practitioners, nurses and/or nursing assistants to differing types of medical clinics with differing personnel needs is considered in conjunction with determination of individual clinic operating schedules. The scheduling model incorporates parameters such as distance between clinics, personnel availability, personnel time, demand for services, and the mix of personnel required to meet quality goals, minimize travel costs, and maximize staff preferences for certain assignments. The model is illustrated using data provided by family planning decision makers in a rural health care environment. Analysis of the results shows that the formulation is easily generalizable to multiple settings and that the essence of the scheduling decision can be represented by the mathematical programming framework. Because of the size of the problem, techniques for improving computational aspects are discussed. The model is designed to be used as a benchmark to enable the development of heuristic scheduling methods which can be used on a PC for near optimal scheduling.

An Interactive Procedure for Solving Multiple Objective Integer Linear Programming Problems

This research presents an interactive procedure for solving Multiple Objective Integer Linear Programming Problems (MOILP). The procedure uses preference information extracted during the interactive steps of the procedure to help the decision-maker (DM) find a preferred integer solution. The scenario considered here assumes that the DM cannot provide a quantitative specification of his (her) preferences in the form of a utility function. The demands imposed by the procedure upon the DM consist of requesting from him (her) the indication of the least preferred solution from a reduced set of candidate efficient solutions presented to him (her) for examination at each interaction. These candidate solutions are generated by the procedure utilizing a software package that solves single objective integer linear programming problems. In the last interaction, the DM is requested to select the most preferred solution from the reduced set that contains those solutions that are more attractive to him. A test problem is presented and solved following the indications of the procedure.

A binary-rounding heuristic for multi-period variable-task-duration assignment problems

Multi-period assignment problems seek to allocate employees to tasks as required across multiple time periods. This type of problem is a subset of three-dimensional assignment problems and is NP-complete. A binary-rounding heuristic, which allows the determination of a feasible zero-one solution from a feasible continuous solution was developed and applied to 72 test problems. The heuristic found the optimal solution to 68 of the 72 problems and was within 95% of the continuous optimum in the other four cases. The CPU time and iterations required were significantly reduced over those required by a pure integer solution process.

Group decision processes: MOLP procedures facilitating group and individual decision orientations

Abstract Three group decision facilitating procedures based on the SIMOLP methodology for solving multiple objective linear programming problems are presented. The procedures are evaluated with a set of test problems. The procedures are tested with a set of ten test problems and a set of simulated group decision makers, including simulated single-issue and inconsistent group members. Results of the computational evaluation show that all three procedures perform well with rational decision makers, and can be chosen according to the group orientation desired. In the case of inconsistent decision makers, however, the individually oriented third procedure may be less desirable.

A heuristic approximation for reducing problem size in network file allocation models

Abstract The design of distributed processing systems has increasingly drawn the attention of systems designers as more and more organizations recognize the advantages of decentralizing operations. However, determination of an optimal or preferred distributed data base configuration is a nontrivial task. A viable model for allocating files to nodes in a distributed system must consider the tradeoffs between costs and service and the unique characteristics of the system, including the planned redundancy inherent in the file organization. It also must be solvable within the current state of the art. This paper presents a mixed-integer linear programming model which allows assignment of replicated and/or partitioned files to the nodes of a distributed network while considering query, update and storage costs associated with the file assignments. The resulting model, though large, is solvable even for networks with a substantial number of nodes and links. Because the model relies on an average communication cost for determining file location, results are presented comparing the model performance to that of a model utilizing exact communication costs.

Coordinated transportation systems: An alternative approach to traditional independent systems

Abstract Public service agencies are servicing increasing numbers of clients as their operating funds continue to decrease. As a result, it is becoming more and more difficult for these agencies to maintain their effectiveness. This paper focuses upon shared transportation programs which is just one of the many cost-savings approaches public service agencies are beginning to implement. As alternatives to current transportation procedures, two coordinated transportation systems are presented, evaluated, and compared in a two agency-two vehicle system network scenario on the basis of total optimal vehicle route lengths. It is illustrated that significant cost savings can be achieved by coordinating transportation resources among local agencies. The main contributions of this paper are the two optimization models that will serve as benchmarks against which heuristic vehicle routing and scheduling models for coordinated transportation systems can be compared and tested. Such heuristics could then be incorporated into affordable software for use by local public service agencies.

A chance-constrained multiobjective model for mental health services planning

Mental health services planning, and particularly the planning for deinstitutionalization, is a very complex problem. This paper suggests a chance-constrained goal programming (CCGP) approach to mental health services planning. The CCGP approach is based on the sequential solution of a linear programming formulation, allowing efficient solution of large-scale planning problems using commercially available linear programming computer codes. The procedure is demonstrated with a case example and implementation of the approach is discussed.