Preemptive Goal Programming Research Articles

A preemptive goal programming method for aggregating OWA operator weights in group decision making

This paper reveals that OWA operator weights cannot be aggregated by the weighted arithmetic or geometric average method in group decision making. A preemptive goal programming method (PGPM) is proposed for aggregating OWA operator weights, which is an extension of the minimax disparity approach developed earlier by the same authors. The effectiveness of PGPM is illustrated with a numerical example.

Cross-border logistics with fleet management: A goal programming approach

In this paper, we introduce the cross-border logistics problem with fleet management. A major phenomenon of implementation of open-door policy in China is the move of Hong Kong-based manufacturers' production lines to China, crossing the border to take advantages of lower production costs, lower wages and lower rental costs. The finished products are then transshipped to Hong Kong, an efficient logistics hub well-equipped with reliable transportation facility, for exporting. We present a preemptive goal programming model for multi-objective cross-border logistics problem, in which three objectives are optimized hierarchically. We also describe a framework for incorporating decision-makers' opinions for determination of goal priorities and target values. A set of Hong Kong data have been used to test the effectiveness and efficiency of the proposed model. Results demonstrate the decision-makers can find the flexibility and robustness of the proposed model by adjusting the goal priorities with respect to the importance of each objective.

SU‐FF‐T‐355: Performance Evaluations of a Preemptive Approach in IMRT Planning

Purpose: Preemptive Goal Programming (PGP) facilitates the use of soft‐constraints in a hierarchical manner for solving complex inverse planning problems. It is a highly effective multicriteria strategy for IMRT planning. However, in order to ensure good numerical performance, a robust constrained optimization algorithm with a practical strategy for handling degeneracy is required. This study identifies cases when PGP introduces challenging problems that do not hold a conventional constraint qualification. Numerical performance for such problems is evaluated using nonlinear planning metrics (DVH, EUD, and NTCP). Method and Materials: PGP, as implemented in our in‐house planning system, solves a series of nonlinear least‐squares problems by a sequential quadratic programming (SQP) algorithm provided with precise Jacobians by an automatic differentiation algorithm. In the presence of constraint degeneracy, an elastic mode (feasibility bound relaxation) is used to ensure a positive step taken at all iterations. Dosimetric as well as numerical performance is evaluated for dose (or EUD) escalation cases with critical organ dose constraints. Reformulation of constraints is also studied as a potential way of reducing degeneracy in these problems. Results: Optimization levels involving strongly active constraints showed degeneracy near optimality, thus requiring use of the elastic mode for convergence. This mode exhibited robust convergence (typically <∼100 iterations) for all IMRT cases studied. Highly nonlinear models (NTCP or EUD with high +/−powers) were handled well by SQP. A strategy of constraint reformulation showed a monotonic decrease in merit function value and its dosimetric performances were comparable to those without reformulation. Conclusion: The optimization task of escalating target dose is limited by binding dose constraints of OARs, which can also create degeneracy in PGP. This study shows SQP with an elastic mode exhibits a stable convergence using the dose‐volume, EUD and NTCP metrics. Numerical performances can be further stabilized by reformulating degenerate constraints.

SU‐FF‐T‐122: Progressive Articulation of Radiotherapy Planning Goals Based On Soft‐Constraints

Purpose: Inverse‐planning in radiation therapy is involved with multicriteria decision‐making problems as it aims to achieve multiple planning goals that are conflicting with each other in target(s) or surrounding healthy tissues. To facilitate an intuitive and explicit way of articulating planning goals, the concept of soft‐constraints has been implemented into our in‐house IMRT planning system using a Goal Programming (GP) technique. In addition, traditional linear GP has been extended to handle nonlinear goal functions so that the nonlinear metrics highly relevant to clinical protocols (such as DVH, EUD, TCP, and NTCP) can be directly utilized in the planning process. Method and Materials: In order to achieve a high convergence speed of the optimization, a gradient‐based, nonlinear constraint search algorithm has been used in the implementation of nonlinear GP. The system is designed to handle multiple goals either by a weighted‐sum approach (Archimedean GP) or lexicographic ordering (Preemptive GP). For some planning criteria exhibiting poor numerical performance for gradient searches (e.g., min, max, DVH), surrogate models have been used in such a way that the general idea of soft‐constraint is consistently maintained. Results: For clinical IMRT cases, the nonlinear GP provides a fast and practical approach to articulate planning goals. Moreover, prioritization of planning goals based on their importance significantly simplifies the RT multicriteria problem representations. The Lagrangian Multiplier values obtained after each level of optimization facilitate informed decisions on goal tradeoffs between different priority levels. Conclusion: The soft constraint concept has been implemented for clinically relevant nonlinear criteria in RT inverse planning. Due to the fast search convergence exhibited by the present system, the planning process can be interactive with the decision maker in setting or adjusting appropriate goal levels, leading to progressive tailoring of the individual plan results. Supported in part by NIH grant R01‐CA59827.

A DECISION SUPPORT SYSTEM FOR SUPPLIER SELECTION PROCESS

Today's global business environment, characterized by unprecedented competitive pressures and sophisticated customers that demand speedy solution creates a bigger set of potential suppliers to evaluate and to choose from. To deal with the complexities of the supplier selection process, an integration of Quality Function Deployment (QFD), Analytical Hierarchy Process (AHP) and Preemptive Goal Programming (PGP) techniques is proposed. A QFD matrix is used to display the degree of relationship between each pair of requirement for suppliers and supplier evaluating criterion. This paper employs the AHP first to measure the relative importance weighting for each of the requirements in the QFD process. Secondly, it is used to assess the evaluating score for each of the candidate suppliers for each particular supplier-evaluating criterion. PGP is built to deal with some suppliers' constraints such that the total value of purchase (TVP) becomes maximum and the total cost of purchase (TCP) minimum.

Manufacturing supply chain design and evaluation

Successful supply chain management calls for robust supply chain design and evaluation tools. Many published papers focused on high level strategic aspects of supply chain design and the results are usually generic guidelines for business executives rather than specific tools for plant managers. In this paper, we present a decision-based methodology for supply chain design that a plant manager can use to select suppliers. The methodology utilizes the techniques of analytic hierarchy process and preemptive goal programming. Supply chain operations reference model level I performance metrics are incorporated into the methodology as the decision criteria. In addition, a set of performance metrics is developed to evaluate the overall supply chain effectiveness, which allows direct comparison of different supply chain designs.

Product-driven supply chain selection using integrated multi-criteria decision-making methodology

Effective supply chain design calls for robust analytical models and design tools. Previous works in this area are mostly Operation Research oriented without considering manufacturing aspects. Recently, researchers have begun to realize that the decision and integration effort in supply chain design should be driven by the manufactured product, specifically, product characteristics and product life cycle. In addition, decision-making processes should be guided by a comprehensive set of performance metrics. In this paper, we relate product characteristics to supply chain strategy and adopt supply chain operations reference (SCOR) model level I performance metrics as the decision criteria. An integrated analytic hierarchy process (AHP) and preemptive goal programming (PGP) based multi-criteria decision-making methodology is then developed to take into account both qualitative and quantitative factors in supplier selection. While the AHP process matches product characteristics with supplier characteristics (using supplier ratings derived from pairwise comparisons) to qualitatively determine supply chain strategy, PGP mathematically determines the optimal order quantity from the chosen suppliers. Since PGP uses AHP ratings as input, the variations of pairwise comparisons in AHP will influence the final order quantity. Therefore, users of this methodology should put greater emphasis on the AHP progress to ensure the accuracy of supplier ratings.

A methodology for selection problems with multiple, conflicting objectives and both qualitative and quantitative criteria

This paper presents a methodology to assist decision-makers in selecting from a finite number of alternatives when there is more than one objective and both qualitative and quantitative factors must be considered. The methodology uses fuzzy QFD to convert qualitative information into quantitative parameters and then combines this data with other quantitative data to parameterize a multiobjective mathematical programming model. A slightly modified version of preemptive goal programming is used to resolve the model in such a way that the decision-maker is provided a number of near optimal solutions from which a final decision can be made. An example is presented to illustrate the methodology.

Multi-objective, decision-based assessment of a water quality monitoring network in a river system.

Water quality monitoring network design has historically tended to use experience, intuition and subjective judgement in locating monitoring stations. Better design procedures to optimize monitoring systems need to simultaneously identify significant planning objectives and consider a number of social, economic and environmental constraints. The consideration of multiple objectives may require further decision analysis to determine the preference weights associated with the objectives to aid in the decision-making process. This may require the application of an optimization study to extract such information from decision makers or experts and to evaluate the overall effectiveness of locating strategies. This paper assesses the optimal expansion and relocation strategies of a water quality monitoring network using a two-stage analysis. The first stage focuses on the information retrieval of preference weights with respect to the designated planning objectives. With the aid of a pre-emptive goal programming model, data analysis is applied to obtain the essential information from the questionnaire outputs. The second stage then utilizes a weighted multi-objective optimization approach to search for the optimal locating strategies of the monitoring stations in the river basin. Practical implementation is illustrated by a case study in the Kao-Ping River Basin, south Taiwan.

Product life cycle analysis: a goal programming approach

This paper considers the role of Life-Cycle Costing (LCC), Time-Based Competition (TBC), and other relevant goals at the three planning-horizon levels of strategic, intermediate, and tactical with respect to time and cost of products to market in a concurrent engineering environment. A conceptual framework has been developed in which the general areas of LCC and TBC are delineated. Based on the conceptual framework, the specific components of LCC and TBC at each level of planning are developed and presented. Subsequently, a Preemptive Goal Programming (PGP) model is developed. This model uses the components of LCC, TBC, and other relevant goals as the decision variables. Then, a case study of a company that has developed LCC and TBC is considered. The PGP model is then applied to the company's operations by using the actual data obtained from the company in order to capture the essence of the conceptual framework. This example explains and validates the PGP model in practice and provides managerial implications of the solution. Finally, a set of conclusions and an assessment of the results are presented.

An improved solution methodology for the arsenal exchange model (AEM)

We develop an iterative approach for solving a linear programming problem with prioritized goals. We tailor our approach to preemptive goal programming problems and take advantage of the fact that at optimality, most constraints are not binding. To overcome the problems posed by redundant constraints, our procedure ensures redundant constraints are not present in the problems we solve. We apply our approach to the arsenal exchange model (AEM). AEM allocates weapons to targets using linear programs (LPs) formulated by the model. Our methodology solves a subproblem using a specific subset of the constraints generated by AEM. Violated constraints are added to the original subproblem and redundant constraints are not included in any of the subproblems. Our methodology was used to solve five test cases. In four of the five test cases, our methodology produced an optimal integer solution. In all five test cases, solution quality was maintained or improved.

An Algorithm to Solve Linear Fractional Bilevel Programming Problem Via Goal Programming

In this paper an algorithm to solve a Bilevel Programming Problem in which the leader’s and the follower’s both objective functions are linear fractional is developed. The algorithm is based on Preemptive Goal Programming. The Bilevel Programming problem is solved by converting it into a goal programming problem. An example to illustrate it is also presented.

MOCACEF 1.0: Multiple objective capability based approach to form part-machine groups for cellular manufacturing applications

A pre-emptive goal programming formulation is developed for concurrently forming independent part/machine cells. Machine independent capability units, which are known as Resource Elements (RE), are used to define processing requirements of parts and processing capabilities of machine tools. Representation of unique and shared capability boundaries of machine tools is possible via RE, which increases the opportunity to form independent manufacturing cells and efficient utilization of them. RE-based operation sequences, processing times, capacities, demand, cell sizes, cell flexibility, load balance between cells, cell interaction, copies of each machine type in the job shop are all considered in the problem formulation. The model is solved by a specially developed tabu search algorithm.

Solution of goal programming models using a basic taboo search algorithm

Goal programming is a very powerful technique for solving multiple objective optimisation problems. It has been successfully applied to numerous diverse real life problems. In this paper a Taboo search based method is developed to solve preemptive goal programming problems. The method can easily be applied to any kind of preemptive goal programming problems.

Energy resource allocation using multi-objective goal programming: the case of Lebanon

The traditional energy-resources allocation problem is concerned with the allocation of limited resources among the end-uses such that the overall return is maximized. In the past, several techniques have been used to deal with such a problem. In this paper, the energy allocation process is looked at from two points of view: economy and environment. The economic objectives include costs, efficiency, energy conservation, and employment generation. The environmental objectives consider environmental friendliness factors. The objective functions are first quantified and then transformed into mathematical language to obtain a multi-objective allocation model based upon pre-emptive goal programming techniques. The proposed method allows decision-makers to encourage or discourage specific energy resources for the various household end-uses. The case of Lebanon is examined to illustrate the usefulness of the proposed technique.

An approachto the machine layout problem in a cellular manufacturing environment

The model of the machine layout problem MLP in a cellular manufacturing environment attains additional dimensions as it should satisfy the qualitative interconnections between the machines and the location restrictions of an existing factory environment. A new MLP model based on merging pre-emptive goal programming and simulated annealing has been developed for machine layout in cells. This model seeks to find feasible solutions by addressing practical issues of implementation as well as reducing the total travel distances for parts between machines. The new model can also be applied to facility layout problems FLP . The computational work is demonstrated by applying the model to problems of both quantitative and qualitative types, and has produced encouraging results. This model is particularly attractive for layout problems with realistic goals and constraints. To show the performance of the model in handling real-world problems, a practical example has been introduced and solved using the proposed model.

Resource-constrained project scheduling with renewable and non-renewable resources and time-resource tradeoffs

The resource-constraint project scheduling problem is modeled as a zero-one integer programming model. The model considers many important characteristics of project scheduling including activity preemption, renewable and non-renewable resources, time-resource tradeoffs, and multiple objectives. Solution algorithms are developed for three single objective problems (time minimization, cost minimization, and resource leveling) and for the preemptive goal programming model that includes time, cost and resource leveling objectives.

Improving the dispersion of surplus labor in personnel scheduling solutions

Linear programming-based heuristics for personnel tour scheduling have focused primarily upon the minimization of the workforce size (or cost) necessary to satisfy forecast demand. There are often a myriad of alternative optimal LP solutions and these solutions may differ substantially in terms of secondary criteria. An even dispersion of surplus labor, which is associated with consistent customer service and employee workload, is one of the most important of these secondary criteria. This paper presents a two-stage preemptive goal programming (PGP) approach that enables service operations managers to provide a more even dispersion of surplus labor while maintaining low-cost solutions. The cost incurred for improved surplus dispersion is the time required to run a second mathematical programming model (in this study 1–4 min on a 386 PC). If management has already invested the resources to use LP-based scheduling methods, implementing this alternative model would result in greater consistency of employee workload and customer service.

An Integer Goal Programming Model to Allocate Offices to Staff in an Academic Institution

This paper investigates the problem of allocating office space to members of staff in an academic institution. We identify several conflicting objectives and formulate an integer pre-emptive goal programming model to address them. Using data from a pilot site of the University of Westminster, UK, we then experiment with alternative rankings of the objectives. Finally, given the plans to consolidate the activities of this university into fewer sites and the resulting need to relocate some staff members, we discuss how this model can be used to ensure that this process is carried out with the least possible inconvenience.

Optimal allocation of time in a hospital pharmacy using goal programming

This paper presents a preemptive goal programming model for optimal allocation of personnel time among various tasks in a hospital pharmacy. The model assigns priorities based on daily time intervals, and ensures that the incomplete tasks belonging to the time interval under consideration are fully satisfied in the next interval. We apply the goal programming model to a situation involving a large hospital pharmacy and make a recommendation regarding its staffing requirements.