Goal Programming Solution Research Articles

A Stochastic Goal-Based Economic Order Quantity Model for Dairy Products

Resilient efforts are still sought to optimize the inventory of dairy products under demand uncertainty. Several industries operate under uncertainties that severely affect company performance. In this paper, a multi-objective goal programming model is proposed to optimize the economic order quantity of dairy products under stochastic demand. Adopting a Markov chain approach, the model initially defines the demand transition matrix, inventory cost matrix, objective function, priorities, and goal constraints of dairy products. The model seeks to minimize the deviation variables from the targeted economic order quantity and total inventory costs of dairy products over a finite period planning horizon. The sum of deviations is minimized so that the actual economic order quantity and inventory costs meet the targeted levels of dairy products. Using the simplex method, an analytical solution is obtained and a numerical example is presented for illustration; demonstrating the overachievement or underachievement of the targeted economic order quantity and inventory costs of dairy products. Results indicate how priority-based goal programming solution is sensitive to the highest priority to be achieved. The proposed model can be effective where the relevant economic order quantity and inventory costs can be prioritized if necessary.

The Optimization of Production and Inventory Management Processes in Tissue Paper Production: The Goal Programming Approach

This paper aimed to apply the Goal Programming approach to optimize important parameters in the production and inventory management processes of tissue papers and paper towel manufacturing. A real-life scenario problem was formulated and solved, and a sensitivity analysis was conducted to examine the effects of changes in goal priorities and target values. The goal programming solution optimized the company’s profit while meeting the demand and also minimizing raw material and labor usage. The results show the optimal inventory levels for the four products as determined by market demand in the target month to be: I1* = 215 tons (SSTP), I2* = 380 tons (MSTP), I3* = 550 tons (JSTP), and I4* = 275 tons (PT). The sensitivity analysis reveals that changes in goal priorities and target values have significant effects on optimal production and inventory levels, thereby highlighting the importance of careful goal setting and prioritization. The findings from the research revealed that a 50-tonne increase in production will increase the profit margin by ten percent for jumbo-size toilet paper. The proper understanding of the production implications will enable the mill to optimize its production, manage resources, and also maximize profit.

Stochastic Chebyshev Goal Programming Mixed Integer Linear Model for Sustainable Global Production Planning

Production planning is a necessary process that directly affects the efficiency of production systems in most industries. The complexity of the current production planning problem depends on increased options in production, uncertainties in demand and production resources. In this study, a stochastic multi-objective mixed-integer optimization model is developed to ensure production efficiency in uncertainty conditions and satisfy the requirements of sustainable development. The efficiency of the production system is ensured through objective functions that optimize backorder quantity, machine uptime and customer satisfaction. The other three objective functions of the proposed model are related to optimization of profits, emissions, and employment changing. The objective functions respectively represent the three elements of sustainable development: economy, environment, and sociality. The proposed model also assures the production manager’s discretion over whether or not to adopt production options such as backorder, overtime, and employment of temporary workers. At the same time, the resource limits of the above options can also be adjusted according to the situation of each production facility via the model’s parameters. The solutions that compromise the above objective functions are determined with the Chebyshev goal programming approach together with the weights of the goals. The model is applied to the multinational production system of a Southeast Asian supplier in the textile industry. The goal programming solution of the model shows an improvement in many aspects compared to this supplier’s manufacturing practices under the same production conditions. Last but not least, the study develops different scenarios based on different random distributions of uncertainty demand and different weights between the objective functions. The analysis and evaluation of these scenarios provide a reference basis for managers to adjust the production system in different situations. Analysis of uncertain demand with more complex random distributions as well as making predictions about the effectiveness of scenarios through the advantages of machine learning can be considered in future studies.

Multi-choice multi-objective capacitated transportation problem — A case study of uncertain demand and supply

In this paper, we study a special class of transportation problem with capacitated restrictions. The formulated multi-objective capacitated transportation problem (MOCTP) has some of the objective functions are linear and fractional; these objectives are conflicting in nature. This problem defined in an uncertain environment where the uncertainty in input information presented by the multi-choices and trapezoidal fuzzy numbers. The multi-choice in input information dealt with the binary numbers and transformed it into the equivalent deterministic form by the suitable method. While the other pattern of uncertainty in input information defined by the trapezoidal fuzzy numbers and handled by ranking function approach to get the crisp value. Due to the presence of the uncertainties, and the conflicting objective functions, we cannot directly solve the formulated multi-choice MOCTP. So, therefore, we solve the formulated MOCTP in two phases. In the first stage, we transform the uncertain MOCTP into the deterministic form by using the suitable solution procedure of multi-choice and fuzzy numbers respectively. In the second stage, we have suggested a goal programming solution procedure to linearise the fractional objective function and then solve the resultant MOCTP for the compromise solution. A case study has also done to illustrate the stepwise solution procedure.

Multi-objective Nurse Scheduling Models with Patient Workload and Nurse Preferences

The purpose of this paper is to develop a nurse scheduling model that simultaneously addresses a set of mu ltip le and oftentimes conflict ing objectives in determin ing an optimal nurse schedule. The ob jectives we consider are minimizing nurse labor costs, min imizing patient d issatisfaction, minimizing nurse idle time, and maximizing job satisfaction. We formulate a series of mu lti-objective b inary integer programming models for the nurse scheduling problem where both nurse shift preferences as a pro xy fo r job satisfaction and patient workload as a pro xy for patient dissatisfaction are considered in our models. A two-stage non-weighted goal programming solution method is provided to find an efficient solution that addresses the multip le objectives. Nu merical results show that considering patient workload in the optimization models can make positive impacts in nurse scheduling by (1) imp roving nurse utilization while keeping higher nurse job satisfaction and (2) min imizing unsatisfied patient workloads.

A new approach for generating efficient solutions within the goal programming model

This paper deals with the issue of efficiency in the Goal Programming (GP) model. A general approach for the determination of an efficient solution of GP is presented. An efficiency test for the GP solution is developed; moreover, when this solution is not efficient, an efficient solution that dominates it is determined.

Information resource planning for a health-care system using an AHP-based goal programming method

This paper presents a goal programming (GP) model which aids in allocating a health-care system's information resources pertinent to strategic planning. The model is developed based on the data obtained from a major health-care system in the United States. The overall objective is to design and evaluate a model for effective information resource planning in a health-care system. The proposed model: (1) utilizes a GP approach to reflect the multiple, conflicting goals of the health-care system; (2) employs a GP solution process to reflect multi-dimensional aspects of the resource allocation planning; and (3) allows for some degree of flexibility of decision-making with respect to resource allocation. The goals are decomposed and prioritized with respect to the corresponding criteria using the analytic hierarchy process (AHP). The model result is derived and discussed. This GP model facilitates decision-making planning process and managerial policy in health-care information resources planning and similar planning settings.

Intelligent solution and analysis of goal programmes: the GPSYS system

An overview of GPSYS, an intelligent linear and integer goal programming system is presented in this paper. The intelligent goal programming system is one which is designed to allow a non-specialist access to, and clear understanding of, goal programming solution and analysis techniques. GPSYS is equipped with GP speed up techniques and analysis tools such as Pareto detection and restoration, normalisation, automated lexicographic redundancy checking and an interactive facility.

Optimizing lot size and setup time in a JIT environment: a multiple objective application

Abstract The just-in-time (JIT) system has been studied extensively and implemented by a number of US firms as an ell'ective production system. The core of JIT involves determination of lot size and setup time reduction so as to increase manufacturing flexibility while minimizing the inventory level. This decision problem usually involves multiple conflicting objectives and mixed-model production. In this paper, goal programming (GP) is applied to a real-world JIT problem involving fabrication of different automotive and industrial rubber composite belts. The model results provide new insights concerning the conflicting nature of several goals, especially between meeting demand and reducing setup or idle time. Also, the GP solution is superior to the current JIT practice of the company.

The linear multi-objective R&D project selection problem

A multi-objective model of the project-selection problem is described. The model departs from an earlier goal-programming formulation of the problem, which suggested Delphic methods for selection of priorities and aspiration levels. It is shown that the multiobjective formulation yields multiple nondominated solutions for the same problem solved by goal programming, whereas the goal-programming formulation revealed only one solution, and that the goal-programming solution is sensitive to choice of aspiration levels. The multiobjective model is recommended as a more general approach to the research and development project-selection problem, since it will develop a set of all nondominated solution. Subjective methods (such as the Delphic technique) can then be called for at a later point in the analysis to choose among alternative nondominated solutions.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Nonlinear structural optimization using goal programming

This paper presents a method for solving nonlinear structural optimization problems using goal programming techniques. The method can be used as a conceptual design tool since goal programming removes the difficulty of having to define one equation as the objective function and the rest as constraints. The developed algorithm uses the linear goal programming techniques with successive linearization for the nonlinear equations to obtain the solution for the nonlinear goal optimization problems. The linear goal programming method with the steps required to obtain the goal programming solution are discussed. The linearization of the general nonlinear optimization problem along with the flow chart of the algorithm are presented. In order to demonstrate the formulation of the nonlinear goal optimization problem and the use of the method, as a design tool, an illustrative example of a three-bar truss structure is included.

Application of the Bootstrap to Assess the Precision of Industry Risk Measures

ABSTRACT A recent contribution In the finance literature presents a goal programming solution to the problem of estimating the systematic risk (beta) of an operating division. The estimation problem is difficult, but the necessity of a reliable risk estimate is undeniable for sound capital budgeting decisions. This paper describes a method Introduced recently In the statistics literature for assessing the precision of the estimator.

An alternative solution method for goal programming problems: The lexicographic goal programming case

This article provides an example of the use of an alternative goal programming solution procedure. The solution procedure is applied to solve a lexicographic goal programming problem. In the process of illustrating the problem, a number of unique technical problems and their solution procedures are discussed. This study provides a flowchart as a procedural guide to aid in its use. This article also provides a comparative analysis of GP algorithms. The results demonstrate the tableau element reduction capabilities of the proposed alternative goal programming solution procedure.

Nondominance In Goal Programming

AbstractThis paper investigates the notion of nondominance in goal programming (GP). Nondominance in the standard sense of a vector maximum (VM) problem is not always desirable. A definition of “GP-nondominance” and a test for determining whether an optimal GP solution is GP-nondominated are provided. It is demonstrated that one or more GP-nondominated solutions can be found by exploring the alternative optima of the GP solution. A formulation for determining the set of GP-nondominated solutions is provided and examples are used to illustrate the concept of GP nondominance.

Profit Maximization with the Aid of Goal Programming for Speculative Housing Estate Developers

This article discusses the applicability of goal programming as a prescriptive tool for the new town planner. A model is presented which illustrates how the planning objectives for the new community can be transformed into a land allocation problem which is amenable to a goal programming solution. The results of an application of this approach indicate that the model is useful if given an accurate ordering of the planner's objectives. However, the goal programming model requires significantly more computations than an analogous linear programming model with the sole objective of profit maximization.

QUADRATIC PREFERENCES AND GOAL PROGRAMMING

One of the shortcomings of goal programming lies in its linearity, assumption, specifically in the objective function. This assumption compels one to work with constant marginal utilities and rates of substitution. In this paper a quadratic preference function, which is more consistent with economic theory and reality, is formulated and introduced into goal programming. In an effort to facilitate the understanding of the proposed procedure, two illustrative examples—one with symmetric preferences and the other with asymmetric preferences, both applied to the objective function—are solved and compared with a goal programming solution.

Mathematical methods of optimization for multi-objective transportation systems

Transportation systems have multi-objective functions and there are multi-factor decision situations. A general mathematical optimization model for such systems is developed which has broad applications for the planning, system design and evaluation of many transportation systems. Three types of solution techniques are discussed. For multi-objective linear programs, a solution is obtained which satisfies the decision maker's preferences and optimization from the decision maker's point of view is considered. A goal programming solution technique is given when goals for the system can be defined. If this is not possible, an overall utility function is defined on the various objective functions and a concept of additive utilities is explored and a parametric programming solution is given.