Weighted Goal Programming Approach Research Articles

Integrated supplier selection, scheduling, and routing problem for perishable product supply chain: A distributionally robust approach

Due to the global outbreak of COVID-19, the perishable product supply chains have been impacted in different ways, and consequently, the risks of food insecurity have been increased in many affected countries. The uncertainty in supply and demand of perishable products, are among the most influential factors impacting the supply chain networks. Accordingly, the provision and distribution of food and other perishable commodities have become much more important than in the past. In this study, a bi-objective optimization model is proposed for a three-echelon perishable food supply chain (PFSC) network with multiple products to formulate an integrated supplier selection, production scheduling, and vehicle routing problem. The proposed model aims to mitigate the risks of demand and supply uncertainties and reinforce the distribution-related decisions by simultaneously optimizing the total network costs and suppliers’ reliability. Using the distributionally robust modeling paradigm, the probability distribution of uncertain demand is assumed to belong to an ambiguity set with given moment information. Accordingly, distributionally robust chance-constrained approach is applied to ensure that the demands of retailers and capacity of vehicles are satisfied with high probability. Leveraging duality and linearization techniques, the proposed model is reformulated as a mixed-integer linear program. Then, the weighted goal programming approach is adopted to address the multi-objectiveness of the proposed optimization model. To certify the performance and applicability of the model, a real-world case study in the poultry industry is investigated. Finally, the sensitivity analysis is conducted to evaluate the impacts of influential parameters on the objective functions and optimal decisions, and then some managerial insights are provided based on the obtained results.

A simple method to find optimum efficient basic solutions to bi-objective transportation problems

This paper proposes a simple method to find an optimum and efficient basic solution to bi-objective transportation problem (BOTP) using weighted goal programming approach. Preferential weights for the goals (objectives) are derived from analytic hierarchy process (AHP). Solution obtained by the proposed approach has been found to be the nearest basic feasible solution to the ideal solution in terms of Euclidean distance measure. The method is illustrated with numerical examples taken from the literature and solutions compared in terms of the number of iterations, computational complexity and proximity to the ideal solution. The modified minimum supply and demand method is used to obtain initial basic feasible solutions that are found to be optimal, and hence this method is computationally simpler compared to other linear programming methods. It has been observed that weighted objective function optimization yields optimal efficient BOTP solutions using appropriate weights for the objective functions.

A knowledge system proposal with weighted goal programming approach for multi-criteria dea model and an application

In today's competitive environment, enterprises should use their resources correctly; they should continuously improve themselves and work efficiently. It is important to evaluate the performances of the units under the same conditions in enterprises according to each other, to see the current situations and to determine appropriate improvements in necessary points. One of the commonly used approaches to performance evaluation is Data Envelopment Analysis. Many approaches have been developed for the Data Envelopment Analysis model, and Goal programming using in multi-objective decision making solutions approaches is one of them. Goal Programming gives decision-makers the opportunity to evaluate many objectives together in the decision-making process. In this study, classical Data Envelopment Analysis and weighted goal programming approach for multi-criteria data envelopment analysis model was applied in the evaluation process of the projects worked in an automotive supplier industry. A knowledge system has also been proposed in order to evaluate the effectiveness of the projects periodically and to include new projects or conditions into the evaluation.

An integrated grey-based multi-criteria optimisation approach for sustainable supplier selection and procurement-distribution planning

Increasing pressure from government and stakeholders has led manufacturing companies to initiate sustainable practices into their supply chains (SCs). Integrating practices like sustainable supplier selection, performance-based order allocation and carbon efficient distribution planning can immensely improve companies' sustainable image and hence provide a competitive edge. The current study focuses on the development of an integrated two-stage multi-attribute optimisation model to discuss these issues. In first stage, Decision-Making Trial and Evaluation Laboratory (DEMATEL) technique based on grey numbers along with grey relational analysis (GRA) is utilised to evaluate suppliers' performance based on influential attributes. In the second stage, a multi-objective optimisation model was developed to optimise system's total cost, carbon emission and total value of purchasing (TVP) while contemplating delivery time windows. Weighted goal programming approach is utilised further for obtaining trade-off among multiple objectives. To validate the effectiveness of proposed methodology, a case study of an electronics company is considered.

An integrated grey-based multi-criteria optimisation approach for sustainable supplier selection and procurement-distribution planning

Increasing pressure from government and stakeholders has led manufacturing companies to initiate sustainable practices into their supply chains (SCs). Integrating practices like sustainable supplier selection, performance-based order allocation and carbon efficient distribution planning can immensely improve companies' sustainable image and hence provide a competitive edge. The current study focuses on the development of an integrated two-stage multi-attribute optimisation model to discuss these issues. In first stage, Decision-Making Trial and Evaluation Laboratory (DEMATEL) technique based on grey numbers along with grey relational analysis (GRA) is utilised to evaluate suppliers' performance based on influential attributes. In the second stage, a multi-objective optimisation model was developed to optimise system's total cost, carbon emission and total value of purchasing (TVP) while contemplating delivery time windows. Weighted goal programming approach is utilised further for obtaining trade-off among multiple objectives. To validate the effectiveness of proposed methodology, a case study of an electronics company is considered.

Evaluation and Selection of Software Vulnerabilities

Information systems are an integral part of every organization’s critical resource and are an important responsibility of all organizations in this digital world to defend them from attacks. Misuse of critical systems of data raises serious difficulties to organizations which involve loss of productivity, profits, company loss, credibility loss and often, legal issues. This paper develops a framework to analyze the optimal selection of vulnerabilities having maximum severity and can be resolved in minimum time. In this study, an integrated framework involving Analytical Hierarchy process (AHP) and Entropy method is used to calculate the subjective and objective weights of software vulnerabilities. Severity of vulnerabilities is then computed by taking into consideration the combined weights calculated from AHP and Entropy method. To select the most critical vulnerability, a bi-objective programming problem is used with the objective of weight maximization and time minimization. The weighted goal programming approach is used to achieve a compromise between conflicting objectives and to achieve a satisfactory solution to the bi-objective problem. The findings are tested in the Delhi-National Capital Region by a software firm.

A Fuzzy Goal Programming Approach for Solving Multi-Objective Supply Chain Network Problems with Pareto-Distributed Random Variables

Uncertainty is unavoidable and addressing the same is inevitable. That everything is available at our doorstep is due to a well-managed modern global supply chain, which takes place despite its efficiency and effectiveness being threatened by various sources of uncertainty originating from the demand side, supply side, manufacturing process, and planning and control systems. This paper addresses the demand- and supply-rooted uncertainty. In order to cope with uncertainty within the constrained multi-objective supply chain network, this paper develops a fuzzy goal programming methodology, with solution procedures. The probabilistic fuzzy goal multi-objective supply chain network (PFG-MOSCN) problem is thus formulated and then solved by three different approaches, namely, simple additive goal programming approach, weighted goal programming approach, and pre-emptive goal programming approach, to obtain the optimal solution. The proposed work links fuzziness in transportation cost and delivery time with randomness in demand and supply parameters. The results may prove to be important for operational managers in manufacturing units, interested in optimizing transportation costs and delivery time, and implicitly, in optimizing profits. A numerical example is provided to illustrate the proposed model.

A goal programming approach for multi-objective warranty optimization

Due to severe competition in the market, a manufacturer may need to redesign the product warranty so as to get an edge over the competitors. However, to be able to do that, a systematic approach is required that allows one to consider multiple objectives. In this paper, a multi-objective optimization approach is presented considering warranty type, warranty duration, component alternatives and support level as decision variables. The multiple-objectives are in the form of targets to be achieved for warranty attractiveness index, warranty cost, spare parts cost to the end user over the useful life of the product and mean time between failures. In this paper a weighted goal programming approach for solving this problem is presented, where the weights are derived for the different objectives using the criteria importance through intercriteria correlation method and the objective function is formulated using the loss function approach. The warranty optimization approach is illustrated using a real life example of an automobile engine manufacturer and is solved using a multi-objective genetic algorithm with elitism strategy.

A weighted goal programming approach to estimate the linear regression model in full quasi type-2 fuzzy environment

A weighted goal programming approach to estimate the linear regression model in full quasi type-2 fuzzy environment

Optimum Time-Censored Modified Ramp-Stress ALT for the Burr Type XII Distribution with Warranty: A Goal Programming Approach

Accelerated life tests (ALTs) are used to make timely assessments of the life time distribution of highly reliable materials and components. Much of the previous work on ALTs has focused on constant-stress, step-stress, ramp-stress schemes and their various combinations. In the literature ramp-stress ALTs that have been formulated can be conducted when more than one test chambers are available; installation of which may prove to be costly. Even when one test chamber is used the stress rate remains constant throughout the duration of the experiment. It is not only necessary but imperative to examine if the test specimen is able to withstand differing stress conditions with the passage of time. This paper therefore, presents an optimal design of multi-objective modified ramp-stress ALT model with weighted goal programming approach. The modified ramp-stress uses one test chamber in place of the various chambers used in simple ramp-stress ALT thus saving experimental cost. With the market being increasingly competitive the emphasis today is on goal attainment with minimum deviations. Goal programming is a method to solve multi-objective problems that has applications in varied fields of engineering and operational research. The optimal plan consists in finding out relevant experimental variables, namely, stress rate, stress rate change point and warranty period, by using goal programming on weighted sum of variance of reliability function and expected warranty cost with pre-specified mission time under normal operating conditions. The Burr type XII life distribution and time-censored data have been used for the purpose. Burr type XII life distribution has been found appropriate for accelerated life testing experiments. The method developed has been explained using a numerical example and sensitivity analysis carried out. Comparative study has also been done to highlight the merits of the proposed model.

Solving a multi-objective multi-echelon supply chain logistic design and planning problem by a goal programming approach

The performance of a supply chain should usually be measured by multiple criteria. In this paper, a logistic planning and design problem in a multi-echelon supply chain consisting of suppliers, manufacturers, and distribution centers is introduced. A multi-objective mixed integer mathematical programming model for both decreasing several logistics costs and increasing the service level in supply chain is proposed. Several constraints due to real-world conditions are also considered in the proposed model. Also, a weighted goal programming approach is proposed to solve the multi-objective optimization problem. The efficacy and applicability of the model are illustrated through a numerical example inspired from a real case study in the dairy industry. The results are promising and the proposed model is capable of handling the case study. The parameters of the proposed approach are also analysed using a sensitivity analysis procedure considering several scenarios.

A bi-objective model for the used oil location-routing problem

A staggering amount of used oils (e.g., 1.4 billion gallons in the U.S.) are generated annually as part of our industrial lifestyle. These are harmful to the population and environment in the vicinity of the transport routes as well as the storage, treatment and disposal facilities. In this paper, we provide an analytical framework to simultaneously answer the following questions: Where should the used oil storage, treatment and disposal facilities be located? What are the most appropriate capacity levels for these facilities? Which routes should be used among the different echelons of facilities in the used oil collection network? Focusing on the hazardous ingredients of used oils that are airborne on release, we propose an environmental risk measure by incorporating the Gaussian plume model in the box model. We present a bi-objective model for the location-routing problem so as to minimize the total environmental risk and the total cost. We use a modified weighted goal programming approach, which proved to be computationally efficient through a wide range of tests. The application of the proposed analytical framework in Chongqing of Southwest China provided interesting managerial insights.

A weighted goal programming approach to fuzzy linear regression with crisp inputs and type-2 fuzzy outputs

Many researches have been carried out in fuzzy linear regression the past three decades. However, almost all of them are limited to type-1 fuzzy data. A fuzzy linear regression model with type-2 fuzzy output data and type-2 fuzzy coefficients is studied in this paper. A linear programming model based on goal programming is proposed to calculate the regression coefficients. To evaluate the proposed model, we present some indices based on the standard deviation, the correlation coefficient, and the standard error of estimate. The proposed method is illustrated by some numerical examples.

A weighted goal programming approach for replenishment planning and space allocation in a supermarket

We propose a mixed integer non-linear goal programming model for replenishment planning and space allocation in a supermarket in which some constraints on budget, space, holding times of perishable items, and number of replenishments are considered and weighted deviations from two conflicting objectives, namely profitability and customer service level, are minimized. We apply a minimum–maximum approach to introduce demand where the maximum demand is a function of price change and allocated space. Each item is presented in the form of multiple brands, probably exposed to price changes, competing to obtain more space. In addition to inventory investment costs, replenishment costs, and inventory holding costs we also include costs related to non-productive use of space. The order quantity, the amount of allocated showroom and backroom spaces, and the cycle time of joint replenishments are key decision variables. We also propose an extended model in which price is a decision variable. Finally we solve the model using LINGO software and provide computational results.

Fertilizer price policy, the environment and farms behavior

The analysis of the effects of fertilizer pricing on intensive agriculture and farms behavior ought to be an important topic of research for agricultural and environmental economists in Bangladesh. Several possibilities for fertilizer policy have been debated, in particular for the pricing of fertilizer. Following this observation, this study, contributes to that discussion by simulating the impact that various policies based upon the price of fertilizer could have on agricultural production. Specifically, the study analyzes the economic, social and environmental implications of alternative fertilizer policies using a multi-criteria model. For this purpose the weighted goal programming approach is used to estimate a utility function considering three criteria, the maximization of the total gross margin, the minimization of the variance of the total gross margin and the minimization of the labor. The model is applied to an agricultural region of Bangladesh. The empirical results show that the most important criterion in farmers’ utility function is the minimization of labor and circumstantially the maximization of total gross margin and the minimization of risk. Moreover they show that a policy of increased fertilizer price would have a very important impact on farm income and employment.

TRADE‐OFF AND COMPROMISE IN SECONDARY SCHOOL REORGANISATION SCHEMES: A GOAL PROGRAMMING APPROACH

ABSTRACT The application of a weighted goal programming approach to the problem of generating and evaluating secondary school rcorganisation schemes is described and demonstrated. Emphasis is placed on highlighting the flexibility of the goal programming framework when it is employed to deal with the issue of admission area redefinition. An indication is given of how this flexibility can be exploited in applications relating to the secondary school system in Liverpool. Further measures are described that can be taken to increase the practical usefulness of the framework when used in exploring the likely consequences of the adoption of alternative reorganisation strategies.