Modified Goal Programming Research Articles

Modified goal programming approach for solving multi-objective environmental management problem

Modified goal programming approach for solving multi-objective environmental management problem

Modified Goal Programming Model for Limited Available Budget Allocation for Equipment Procurement under Inflation Condition

Equipment procurement budget is of a great challenge in manufacturing industries by reasons of its multi-objectives, insufficient funds, and inflation problems. Solutions were proffered to these problems by identifying the strategic decisions required in equipment procurement (machine, accessories, spare parts and miscellaneous costs). Procurement changes from year to year based on equipment industrial needs. Hence eleven (11) scenarios for procurement but this study focused on a scenario where all the decisions are needed for procurement. This problem is multi-objective decision problem where there is need for multi-objective decision tool for its solution, therefore a goal programming tool was adopted and improved by integrating inflation model into it to be able to solve inflation problems. International Brewery Ilesha, Nigeria was used as case study for the model’s application to evaluate its performance. The strategic decisions deviated above or positively by 0.4604, 4.1311 and 2.3760 for machines, spare-parts and miscellaneous costs respectively while accessories cost was not deviated. Therefore, the procurement cost for Machines, Accessories, Spare-parts and Miscellaneous costs would be (N 166,015,000; $ 461,152.77), (N 127,968,000; $ 355,466.67), (N 548,075,000; $ 1,522,430.56), (N 271,091,500; $ 753,031.94). US Dollar exchange rate was at N 360 to a Dollar as at the time of this research. This multi-criteria decision tool will find its application useful in small, medium and large scale industries that equipment procurement budget affects their production.v

Study on Structure Optimization of the Allocation of Water Resources of Minqin Based on Goal Programming

Using the theory of goal programming, this paper studies the optimal allocation schemes for water resource in 2015 of Minqin, by establishing a model of optimized allocation of water resources which aims at the maximization of ecological, economic and social benefits. The results show that:1) In the scheme of the utilization of water resource in Minqin based on the modified goal programming model (Ecological scheme A2), the total water consumption reduces by 35.25%, of which: the consumption for planting reduces by 43.3%, but the consumption for industry increases by 61.78%, and the consumption for the third industry increases by 124.68%. Meanwhile the total planning output value increases by 88.35%, of which: the planting output value reduces by 5.42%, but the industrial output value increases by 159.16%, the third industrial output value increases by 57.06%. Therefore it realizes the minimization of the water resource consumption and achieves the goal of maximizing ecological benefit, economic benefit and social benefit at the same time.2) Reducing the water consumption of planting is the basic approach to achieve the goal of ecosystem comprehensive harness in Minqin basin. Actively promoting and developing the modern animal husbandry, industry and the third industry is the sustainable development direction to achieve maximum economic benefits and social benefits on the premise of ecological protection.

Daily scheduling of nurses in operating suites

This article provides a new multi-objective integer programming model for the daily scheduling of nurses in operating suites. The model is designed to assign nurses to different surgery cases based on their specialties and competency levels, subject to a series of hard and soft constraints related to nurse satisfaction, idle time, overtime, and job changes during a shift. To find solutions, two methodologies were developed. The first is based on the idea of a solution pool and the second is a variant of modified goal programming. The model and the solution procedures were validated using real data provided by the University of Texas MD Anderson Cancer Center in Houston, Texas. The results show that the two methodologies can produce schedules that satisfy all demand with 50% less overtime and 50% less idle time when benchmarked against current practice.

Formulating the mixed integer fractional posynomial programming

The mixed integer fractional posynomial programming (MIFPP) problem arises from the summation minimization of several quotient terms appearing in the objective function subject to given constraints. All decision variables of the problem could be binary, integer, and/or continuous with (without) absolute value functions. This paper addresses the problem of providing an optimization approach, which could certainly obtain a solution as close as possible to a global optimum. In order to solve the complex MIFPP problem, several strategies are used including linear programming relaxation, modified goal programming, logarithmic piecewise function (LPF) and so on. In addition, the proposed model solves the undefined problem of the logarithm of zero or negative in the LPF. This significantly improved the utility of LPF in real applications. Finally, an illustrative example is included to demonstrate the solution procedure of the proposed model.

Reformulation of the modified goal programming for logarithmic piecewise linear function

The purpose of this paper is to present a reformulation of the model presented by Chang [A modified goal programming model for piecewise linear function, European Journal of Operational Research 139 (2002) 62–67]. The modified goal programming (MGP) model of Chang has been accepted as an efficient method published for solving polynomial/posynomial (P/P) programming problems. However, it still cannot be used to fully practical applications because the problem with negative variable is undefined in logarithmic piecewise linear function (LPLF). This paper presents some appropriate strategies to overcome this undefined problem. The reformulation MGP model can be used to solve P/P programming problems with negative/positive variables. In addition, an illustrative example is included for demonstrating the correctness of the proposed method.

A modified goal programming approach for the mean-absolute deviation portfolio optimization model

The purpose of this paper is to present a reformulation of the model presented by Feinstein and Thapa [C.D. Feinstein, M.N. Thapa, Notes: a reformulation of a mean-absolute deviation portfolio optimization model, Management Science 39 (12) (1993) 1552-1553]. The approach of Feinstein and Thapa has been accepted as the most efficient technique published, requiring the least number of auxiliary constraints and additional continuous variables. To solve a portfolio optimization problem with T periods, in their method would introduce T+2 auxiliary constraints, 2T auxiliary sign constraints, and 2T additional continuous variables. This note indicates that it is still possible to reduce the number of auxiliary constraints and additional continuous variables in the model of Feinstein and Thapa. The equivalent concise model is proposed in this note, which has T+2 auxiliary constraints, T auxiliary sign constraints, and T additional continuous variables.

A modified goal programming model for piecewise linear functions

Piecewise linear function (PLF) is an important technique for solving polynomial and/or posynomial programming problems since the problems can be approximately represented by the PLF. The PLF can also be solved using the goal programming (GP) technique by adding appropriate linearization constraints. This paper proposes a modified GP technique to solve PLF with n terms. The proposed method requires only one additional constraint, which is more efficient than some well-known methods such as those proposed by Charnes and Cooper's, and Li. Furthermore, the proposed model (PM) can easily be applied to general polynomial and/or posynomial programming problems.

Water supply planning under interdependence of actions: Theory and application

An ongoing water supply planning problem in the Regional Municipality of Waterloo, Ontario, Canada, is studied to select the best water supply combination, within a multiple‐objective framework, when actions are interdependent. The interdependencies in the problem are described and shown to be essential features. The problem is formulated as a multiple‐criteria integer program with interdependent actions. Because of the large number of potential actions and the nonconvexity of the decision space, it is quite difficult to find nondominated subsets of actions. Instead, a modified goal programming technique is suggested to identify promising subsets. The appropriateness of this technique is explained, and the lessons learned in applying it to the Waterloo water supply planning problem are described.

A piecewise regression analysis with automatic change-point detection

Most of the conventional regression methods can only estimate a piecewise polynomial function in which the exact positions or the probabilistic distribution of the change-points is prespecified. This paper proposes an optimization method to estimate a piecewise polynomial function with unknown change-points. We first express a piecewise function by the addition of some absolute terms. Utilizing the properties of this function, a piecewise regression model is then formulated to minimize the estimation errors subjected to an amount of change-points. The model is then solved by a modified goal programming technique, which is more computationally efficient than conventional goal programs. Numerical examples demonstrate that the proposed method is very promising in estimating the piecewise regression with automatic change-point detection.

Solve least absolute value regression problems using modified goal programming techniques

Least absolute value (LAV) regression methods have been widely applied in estimating regression equations. However, most of the current LAV methods are based on the original goal program developed over four decades. On the basis of a modified goal program, this study reformulates the LAV problem using a markedly lower number of deviational variables than used in the current LAV methods. Numerical results indicate that for the regression problems with hundreds of observations, this novel method can save more than 1/3 of the CPU time compared to current LAV methods.

Optimal balance between recycling and waste‐to‐energy programs by grey fuzzy nonlinear goal programming (I) theory

This paper specifically describes the disparity between several fuzzy goals in a decision making process and solves the potential conflicts by a new approach: the grey fuzzy goal programming (GFGP) model. In particular, it demonstrates how the grey uncertainties embedded in parameter values and fuzzy messages existing in goals can be quantified within a modified goal programming analytical framework to fully interpret the complexity from both system nature and human aspiration. Such a theoretical development indicates that the grey fuzzy optimal solutions constitute an important step toward the identification of more flexible management policy of many real world systems.