Multi-choice mixed integer goal programming optimization for real problems in a sugar and ethanol milling company

Blood Supply Chain (BSC) concerns with flow of blood products from blood collection by donors to transfusion of blood components to patients. BSC comprises of collection, testing, processing, storage, distribution and transfusion activities, which are normally responsibility of Blood Centre and hospitals. In Malaysia, National Blood Centre (PDN) is responsible to organize blood donation, collection and processing. Current procedure practised by PDN is to have vehicles sending staffs and equipment while one vehicle is assigned to collect donated blood from donation sites and transport the blood to PDN within six hours. As consequence, vehicles shortages are encountered and resources optimization unachieved especially when many blood donation sites involved per day. This paper presents the results of a preliminary study which aims at proposing blood collection optimal routes for blood collecting vehicles that adhere to all pre-determined time windows for blood collection at blood donation sites. A Mixed Integer Goal Programming (MIGP) model based on Vehicle Routing Problem with Time Windows (VRPTW) has been formulated. The MIGP model pursues four goals, namely, to minimize total distance travelled, to minimize total travel time, to minimize total waiting time of vehicles and to minimize number of vehicles (routes). The model was solved using preemptive goal programming approach and existing heuristics for the VRPTW. Based on the results, it can be concluded that the donated blood can be collected and transported using reduced number of vehicles as proposed by the MIGP model’s optimal compared to the total number of vehicles used by current practice, Thus, the proposed VRPTW based MIGP model has promising significant impact for donated blood transportation in terms of resources optimization and costs savings. The model and approach could be easily extended to solve larger problem involving large number of donation sites with variants of time windows for the sites.

On the mixed binary goal programming problems

Polynomial goal programming: A procedure for modeling preference trade-offs

This paper presents the development of a goal programming (GP) model as an aid to strategic planning and allocation for limited human resources in a health-care organization. The purpose of this study is to assign the personnel to the proper shift hours that enable management to meet the objective of minimizing the total payroll costs while patients are satisfied. A GP model is illustrated using the data provided by a health-care organization in the midwest area. The goals are identified and prioritized. The model result is examined and a sensitivity analysis is performed to improve the model applicability. The GP model application adds insight to the planning functions of resource allocation in the health-care organizations. The proposed model is easily applicable to other human resource planning process.

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.

ABSTRACTThe Goal Programming (GP) model is one of the first models that have been developed to deal with managerial decision‐making problems where several incommensurable and conflicting objectives are involved. The GP variants integrate the decision maker's preferences differently. This model has also been applied to group decision‐making situations. The aim of this paper is to propose a new typology based on preferences articulation of decision makers through the GP model. This typology is based on the articulation and the elucidation process of the group decision makers' preferences. Copyright © 2012 John Wiley & Sons, Ltd.

Goal programming approach to solving network design problem with multiple objectives and demand uncertainty

The strategic planning is important in bank financial management. The banks and financial institutions have to achieve multiple goals in optimizing asset, liability, equity, earnings, profit and optimum management item. The subjective judgment in assigning weight of the goals is a drawback in financial management of the banks since it may cause inconsistent judgment. In addition, there are no comprehensive studies done on comparison among the banks for benchmarking based on the past studies in optimizing the financial management. Hence, this paper aims to improve the bank financial management by proposing a two-stage goal programming (GP) model to compare and optimize the bank financial management. The proposed model is developed based on entropy method in determining the weight of the goal at the first stage before optimizing the financial management with GP model at the second stage. Four listed banks in Malaysia are investigated in this study. The results indicate that the goal for asset, equity and optimum management item have been achieved by all banks. Furthermore, the target value of asset, equity, earning and profit can be increased according to the optimal solution of the proposed model. The significance of this paper is to provide insights to the banks for further improvement based on the optimal solution of the proposed model.KeywordsEntropyGoal programmingOptimizationFinancial managementPotential improvement

Financial management is important for the construction sector, as construction companies contribute to the development of countries. Malaysia encourages the construction sector to develop advanced infrastructure related to transport and housing. Financial management is a multi-criteria decision making (MCDM) problem, since companies have to consider multiple goals in order to make the optimal decision. Therefore, goal programming is proposed in financial management to solve optimization in MCDM problems. According to previous studies, there has been no comprehensive study conducted on optimization and comparison among the construction companies with a goal programming model. Thus, this study aims to propose a goal programming model to optimize and compare the financial management of listed construction companies in Malaysia for benchmarking purposes. Six goals of financial management, namely the total assets, total liabilities, equity, profit, earnings, and optimum management of construction companies are examined in this study. The results of this study show that the goal programming model is able to determine the optimal solution and goal achievement for each construction company. In addition, the model value can be further enhanced according to the optimal solution of the goal programming model. This study provides insights to the listed construction companies in Malaysia to identify the potential improvement based on the benchmarking and optimal solution of the goal programming model.

Dynamic multiple criteria decision making (DMCDM) represents an extension of classical multiple criteria decision making to a context in which all variables are depending on time. This complex decision making problem requires the development of methodologies able to incorporate different and conflicting goals in a satisfying design of policies. We formulate two different goal programming models, namely a weighted goal programming model and a goal programming model with satisfaction functions, for solving DMCDM models. We present an application of this methodology to analyze the trade-off between consumption and investment in a traditional Ramsey-type macroeconomic model with heterogeneous agents. For a specific realistic parameterization, such a model is solved by means of the proposed goal programming formulations.

A very useful multi-objective technique is goal programming. There are many methodologies of goal programming such as weighted goal programming, min-max goal programming, and lexicographic goal programming. In this paper, weighted goal programming is reformulated as goal programming with logarithmic deviation variables. Here, a comparison of the proposed method and goal programming with weighted sum method is presented. A numerical example and applications on two industrial problems have also enriched this paper.

Multiple-criteria decision-making in two-sided assembly line balancing: A goal programming and a fuzzy goal programming models

A Fuzzy Goal Programming model for solving aggregate production-planning problems under uncertainty: A case study in a Brazilian sugar mill

We use data from the Ethiopia Rural Household Survey and the Ethiopian Central Statistics Agency to demonstrate a set of techniques for estimating optimal investment allocation in smallholder farming. The approaches treat farming tasks, constraints, and investments as a portfolio problem, characterized by multiple competing objectives. We formulate several versions of the multi-objective problem and solve them in three alternative ways; 1) using a scalarized Markowitz portfolio optimization, 2) using a weighted goal programming model, and 3) a multi-horizon goal programming model, estimating all model parameters using real data. The main benefit of the goal programming formulation is the possibility to simplify in a single criterion problem complex situations in which the Decision Maker (DM) faces a trade-off between two or more objectives. We discuss the importance of portfolio allocations for smallholder farmers in minimizing risk and increasing return, and discuss how these approaches provide a framework that can be extended to practical applications in smallholder farming.

In complex real-world environments characterized by conflicting objectives and dynamic constraints, conventional Goal Programming (GP) approaches often struggle to deliver flexible and adaptive solutions. This paper presents an AI-augmented Goal Programming framework that integrates artificial intelligence techniques—such as neural networks for demand prediction and evolutionary algorithms for multi-objective optimization—to enhance traditional GP models. The proposed approach allows real-time adjustment of priorities, constraints, and aspiration levels based on contextual data and system feedback. Case studies in healthcare logistics, renewable energy planning, and supply chain optimization demonstrate the framework’s efficacy in producing robust and high-quality solutions. Comparative numerical simulations show that the AI-enhanced GP model significantly outperforms classical GP in adaptability, accuracy, and computational efficiency. This research contributes to the fusion of intelligent systems and mathematical programming, providing a scalable decision-support methodology for addressing multifaceted challenges in applied mathematics.