Mixed Integer Goal Programming Research Articles

A nonlinear mixed integer goal programming model for the two-machine closed flow shop

This paper presents a nonlinear mixed integer goal programming model of the deterministic, static two-machine closed flow shop (CFS) problem. The model incorporates two sets of goals that are of importance to the production manager: cost goals and production goals. The cost goals are setup costs, finished goods holding costs, machine idle costs, and work-in-process inventory costs. The production goals are makespan, mean tardiness, mean flow time, capacity between runs and end shop capacity.

An extended multi-objective replacement model for flexible automation investments

A multi-objective replacement model is developed for flexible automation investments, for use in a decision-support-system environment. The model is based on a general mixed integer goal programming (GP) formulation. The objectives of the model are to derive an optimal implementation sequence for new CNC modules and tooling, replacement schedule for current equipment and production plans for transition and later periods in the planning horizon. Several types of flexibility are considered, in addition to tooling costs and standardization issues. The GP model minimizes a weighted function of the deviational variables for direct profitability, as well as other strategic goals of the firm.

A new formulation and solution of the flowshop scheduling problem with no in-process waiting

To date, all models reported in the literature relating to the flowshop sequencing problem with no in-process waiting, have been based on single objective optimization. This paper presents a mixed integer goal programming model of the generalized N job, M machine standard flowshop problem with no in-process waiting, i.e. no intermediate queues. Instead of optimization being based on a single objective, the most satisfactory sequence is derived subject to user specified selection of the pre-emptive goals: makespan, flowtime, and machine idle time. Computational results of sample problems illustrating the advantage of a multiple criteria selection method are shown.

A mixed-integer goal programming model for nursing service budgeting.

This paper presents a mixed-integer goal programming model for expense budgeting in a hospital nursing department. The model incorporates several different objectives based upon such considerations as cost containment and providing appropriate nursing hours for delivering quality nursing care. Also considered are possible trade-offs among full-time, part-time and overtime nurses on weekdays as well as weekends. The budget includes vacation, sick leave, holiday, and seniority policies of a hospital and various constraints on a hospital nursing service imposed by nursing unions. The results are based upon data from a study hospital and indicate that the model is practical for budgeting in a hospital nursing department.

Multiple objective capital budgeting within the university

The problem of selecting capital projects in universities is compounded by the existence of conflicting multiple objectives on the part of different groups within the university community. Administrators, faculty members, students and politicians all have different goals and projects which they feel are important to the university and themselves. Because of the multiple objective dimension of the capital budgeting process goal programming becomes an appropriate solution approach. However, because of the indivisibility of some capital projects, mixed integer goal programming, a variation of the traditional GP model, must be employed. The solution approach is demonstrated via an illustrative case example. Model goals in the example (which are prioritized by the top administrative officers of the university) exist for capital budget and operating expenses, building and laboratory construction, accreditation, political interest and area performance.

A mixed-integer goal programming model for capital budgeting within a police department

A difficult problem for most police departments is allocating limited dollars for capital expenditures in the most efficient manner possible. Because of the varied objectives of police services as perceived by police administrators, government officials and citizens, traditional allocation criteria, such as cost-benefit analysis, are not viable. As such, this paper proposes the use of mixed-integer goal programming as a methodology for selecting police expenditure items given a limited budget and multiple, conflicting objectives. In order to demonstrate this technique, a case example involving 18 potential expenditure items for a moderately-sized police department will be employed. This example model will be solved using a predetermined priority structure, and the results interpreted. Several alternative priority structures that reflect the objectives of different interest groups will then be tested in order to demonstrate the flexibility of this approach.

A branch and bound algorithm with constraint partitioning for integer goal programming problems

Using constraint partitioning and variable elimination, the authors have recently developed an efficient algorithm for solving linear goal programming problems. However, many goal programs require some or all of the decision variables to be integer valued. This paper shows how the new partitioning algorithm can be extended with a modified branch and bound strategy to solve both pure and mixed type integer goal programming problems. A potential problem in combining the partitioning algorithm and the branch and bound search scheme is presented and resolved.

A Multiple Objective Approach to Space Planning for Academic Facilities

This paper addresses the office layout problem where existing offices vary considerably as to relevant criteria and yet permanent walls make it impractical to remodel existing spaces. The major objective of this study was the equitable reassignment of 144 offices to 289 faculty and staff members in 6 academic departments with the College of Administrative Science at The Ohio State University. Since the building contains 5 floors and a wide diversity of office quality, six conflicting objectives have been recognized. In order to adequate address these multiple objectives, a large mixed-integer goal programming model was formulated. A companion interactive computer program was also developed to evaluate the performance of each solution with respect to these objectives. The goal programming model served to evaluate several layout strategies and identify the tradeoffs implicit in the problem. The interactive computer program helped translate these insights into a final compromise solution. There are two interesting findings of the study. The first one is desirability of allowing the decision makers to be in command of the solution process. This may be particularly important when several decision makers must compete for the same resources. Another finding is that a linear programming code is sufficient for this particular formulation of a mixed-integer model. Although the model contains over 1,700 integer variables, a very few non-integer values were generated. This avoided the computational burden of a mixed-integer code. The model presented here has its generic roots in the so-called “assignment problems,” with the added feature of recognizing multiple objectives. It is felt that with the proper modifications, the ideas presented here may well be extended to location-distribution and other types of assignment problems. These models have been applied to the layout of the College, with the final implementation having occurred during the Summer Quarter, 1978.

Machine scheduling with mixed integer goal programming

Machine scheduling with mixed integer goal programming