Multi-objective Linear Programming Model Research Articles

Compromised supply chain planning under dominant systems with inventory policies and cost uncertainty

In practice, companies with dominant power influence partner operations for their benefits. This paper proposes the supply chain (SC) planning models that determine the optimal sale, pricing, production, and inventory plans of each SC member based on the dominant policy. The theoretical contributions of this paper include a development of linear mathematical functions and explicitly considering the inventory turnover as one of the business performance measures in addition to profit and revenue. The fuzzy multi-objective linear programming models (FMOLP) under dominant systems are developed. A case study in plastic fashion accessory industry in Thailand is performed. The performance measures are translated into satisfaction levels and plotted in a radar chart with an area of possibility, which clearly shows the sensitivity degree of uncertainty. Practical contribution is that this paper recommends suitable pricing and inventory plans based on the dominant policy. [Submitted: 15 August 2018; Accepted: 18 March 2019]

Compromised supply chain planning under dominant systems with inventory policies and cost uncertainty

In practice, companies with dominant power influence partner operations for their benefits. This paper proposes the supply chain (SC) planning models that determine the optimal sale, pricing, production, and inventory plans of each SC member based on the dominant policy. The theoretical contributions of this paper include a development of linear mathematical functions and explicitly considering the inventory turnover as one of the business performance measures in addition to profit and revenue. The fuzzy multi-objective linear programming models (FMOLP) under dominant systems are developed. A case study in plastic fashion accessory industry in Thailand is performed. The performance measures are translated into satisfaction levels and plotted in a radar chart with an area of possibility, which clearly shows the sensitivity degree of uncertainty. Practical contribution is that this paper recommends suitable pricing and inventory plans based on the dominant policy. [Submitted: 15 August 2018; Accepted: 18 March 2019]

External Virtual Water Contributes Greatly to Continual Development in Urumqi

Previous studies indicated that the population size would arrive at its “upper limits” under the intense water scarcity in Urumqi; yet the “upper limits” had been repeatedly exceeded. Two latest research paper put forward a new term “generalized water”, and estimated it under the framework of a noncompetitive input-output model. It was proved that generalized water made a main contribution to alleviate acute water scarcity in the past 40 years in the arid city, and answered the question why an urban population continues to grow under intensifying water scarcity. Another question is whether and how generalized water contributes to the continual development in the future in this city. This paper applied coefficients deduced from the noncompetitive input-output model, and set up a multi-objective linear programming model to investigate the question. Simulation results indicated that the upper limit of gross domestic products of Urumqi would be at most 1.3 times that in 2012; however, this “upper limit” was far more exceeded in 2018, about 1.7 times that in 2012. This phenomenon indicates that generalized water also made a main contribution to continual development, and this contribution mainly comes from external virtual water embodied in commodities. This contribution from generalized water results from the characteristic of dissipative structure in an urban economy, and it is suggested that polices should be designed to make the most use of generalized water.

Optimization of Land-Use Structure Based on the Trade-Off Between Carbon Emission Targets and Economic Development in Shenzhen, China

The approach of choosing an effective low-carbon land-use structure by multi-objective methods is commonly used in land-use planning. A common methodology is to calculate carbon emissions and conduct scenario simulations for the future. However, most Chinese cities have not implemented the methods for monitoring carbon emissions proposed by the Intergovernmental Panel on Climate Change (IPCC), especially Shenzhen, which is one of the fastest-growing cities in China. This study first calculated the carbon emissions for a typical year in Shenzhen under the guidance of the IPCC. Second, nighttime light data were used to spatialize the gross domestic product to obtain the economic benefit coefficients of the various land types. Finally, a multi-objective linear programming model was used to optimize the land-use structure under different scenarios for 2020 and 2025. The results show that (i) energy consumption contributed the most to local carbon emissions in 2016, at 94.75%; (ii) carbon emissions from paddy fields, animals, and humans were the second most dominant source; (iii) the intensity of carbon emissions from different land types in 2016 was variable; and (iv) compared with the natural scenario, an optimized land-use structure could reduce carbon emissions by 5.97% by 2020 and 12.61% by 2025. Under ideal simulation conditions, the simulated land-use pattern could not only meet the requirements of economic and social development, but also could effectively reduce carbon emissions, which is of great value to land managers and decision-makers.

Integrated model for renewable energy planning in Turkey

ABSTRACTAll economic sectors are associated with energy use; therefore, government organizations aim to supply sustainable energy for human needs and economic growth. In particular, increased environmental concerns of the public in Turkey have impacted policymaking for renewable energy (RE) management in Turkey. The primary objective for RE sources of the Turkish Ministry of Energy is to ensure that 30% of the share of electricity production is from RE resources in 2023. In this paper, the integrated multi-objective, multi-period linear programming model is presented to determine effective allocation of RE supply for seven different geographical regions in Turkey for the period of 2017 to 2024. The integrated model consists of two different stages. The first stage involves qualitative evaluations of RE sources for seven geographical regions. Analytical Hierarchy Process (AHP) is applied to determine criteria priorities and overall ratings of geographical regions across determined criteria for RE sources are computed. The second stage of the integrated model consists of a multi-objective, multi-period linear programming model. The proposed multi-objective linear programming model is coded in MPL (Mathematical Programming Language) and solved using the GUROBI 5.1.0 solver. The output of the integrated model presents the total supply amount of RE sources for geographical regions in planning period. The ε-constraints method is applied to compute the total supply amount of RE from geographical regions for the period of 2017 to 2024. In this study, a systematic decision-making model is generated to allocate renewable energy sources to the geographical regions. The presented model integrates qualitative evaluations and quantitative parameters of different geographical regions to determine the optimal supply amount of RE. The obtained results are consistent with the potential quantities of RE alternatives in geographical regions, regional specifications, and social requirements.

Designing a sustainable stochastic electricity generation network with hybrid production strategies

This paper aims to design a sustainable stochastic electricity production network where fossil fuels-based, biomass-based, and co-firing-based production strategies are simultaneously considered in order to take advantage of all the three production strategies. A multi-objective stochastic mixed integer linear programming model is proposed to achieve economic feasibility, as well as environmental and social benefits under multiple uncertainties. The model is solved by using the improved augmented epsilon constraint method. A case study is used to illustrate the effectiveness of the proposed model. Pareto optimal analysis is conducted to understand the trade-off between economic, environmental, and social aspects of sustainability.

ÇOK AMAÇLI ÜRETİM SÜREÇLERİNİN BULANIK KARAR ORTAMINDA İNCELENMESİ: BULANIK HEDEF PROGRAMLAMA VE BİR UYGULAMA

If the aspiration levels of the goals are set realistically by the decision maker in Goal Programming, the deviations from the goals could occur too high as a result of the solution. It leads the decision maker to make incorrect decisions. It is also the case for Fuzzy Goal Programming. When the fuzzy goals and their tolerance levels are not defined properly, there will be deviations from the goals. Additionally, if there are constraint functions besides the goals in the problems of either Goal Programming or Fuzzy Goal Programming, the solutions will deviate greatly from the incorrectly defined goal values as the solutions are realized based on the constraints. It is because the goals are limited by the constraints. This study firstly defines the positive and negative ideal solutions of objective functions in the problem organized in Multiobjective Linear Programming model for a business which manufactures hand crafted furniture. Afterwards, each objective is transformed into fuzzy goals using positive and negative ideal solutions.

ÇOK AMAÇLI ÜRETİM SÜREÇLERİNİN BULANIK KARAR ORTAMINDA İNCELENMESİ: BULANIK HEDEF PROGRAMLAMA VE BİR UYGULAMA

Hedef Programlamada karar verici tarafından belirlenen hedeflerin arzu edilen seviyeleri eğer gerçekçi değil ise, çözümün sonucunda hedeflerden sapmalar çok yüksek değerde gerçekleşebilir. Bu durum karar verici yanlış karar almasına yol açar. Benzer durum Bulanık Hedef programlama için de geçerlidir. Çünkü bulanık hedefler ve bu hedeflerin tolerans değerleri doğru belirlenmezse hedeflerden sapmalar artacaktır. Ayrıca ister Hedef Programlama problemi ister Bulanık Hedef programlama probleminde eğer hedeflerin yanı sıra kısıt fonksiyonları da olursa, kısıtlara bağlı çözüm gerçekleşeceği için doğru tanımlanmamış hedef değerlerden sapmalar çok fazla olacaktır. Çünkü hedefler kısıtlar tarafından sınırlandırılır. Bu çalışmada Çok Amaçlı Doğrusal Programlama modelinde kurulan el yapımı mobilya üretimi yapan bir işletme problemi Bulanık Hedef Programlama modelinde çözülebilmesi için ilk olarak amaç fonksiyonlarının pozitif ve negatif ideal çözümleri belirlenmiştir. Daha sonra her bir amaç fonksiyonu pozitif ve negatif ideal çözümler kullanılarak bulanık hedeflere dönüştürülmüştür.

Economic and environmental implications of incorporating distillers’ dried grains with solubles in feed rations of growing and finishing swine in Argentina

The Argentinean swine industry has quickly expanded over the past decade, hence increasing the demand for swine feedstuffs. The growing supply of distillers’ dried grains with solubles (DDGS) from the emerging Argentinean corn-based ethanol industry is a potential feedstuff for swine producers. Using a multi-objective linear programming model, this study examined the economic and environmental concerns (i.e. cost and phosphorus content) associated with introducing DDGS in swine feed rations. Results suggest that including DDGS in swine diets concurrently minimized cost and phosphorus content. The results were extrapolated to the entire Argentinean swine industry and show that the inclusion of DDGS in swine rations could potentially save the Argentinean swine industry about 19.21 million US dollars annually and reduce phosphorus content by up to 5%. In addition, sensitivity analysis of DDGS price was conducted and the potential demand for DDGS from swine by growth category was derived.

Green design of a cellulosic butanol supply chain network: A case study of sorghum stem bio-butanol in Missouri

Cellulosic butanol is a very promising renewable fuel to consider for the future transportation market. However, the seasonal availability of the raw materials, high maintenance cost, and high logistical cost of the biomass energy supply chain are the main factors impeding the commercialization and large-scale-production of this energy source. Furthermore, research focusing on an environmental or green supply chain network design of cellulosic butanol has been insufficient. This study focused on designing a green supply chain network for cellulosic butanol. A life cycle analysis was integrated into a multi-objective linear programming model to optimize the cellulosic butanol supply chain network. With the objectives of maximizing the economic profits and minimizing the greenhouse gas emissions, the proposed model can optimize the location and size of a bio-butanol production plant. The mathematical model was applied to a case study in the state of Missouri, and solved the tradeoff between the feedstock and market availabilities of sorghum stem bio-butanol.

Data envelopment analysis based fuzzy multi-objective portfolio selection model involving higher moments

We study the portfolio selection problem from the perspective of incorporating more information about the non-normality of asset returns by considering the mean-variance-skewness-kurtosis framework. Using additional criteria (namely asset turnover, earnings per share, earnings per share growth rate, leverage ratio, price/earnings ratio, and beta (β) value), we employ data envelopment analysis technique to construct a benefit criterion from the efficiency scores of the assets. To incorporate the uncertainty and vagueness of real financial markets, the input data (with respect of all criteria) are assumed as (λ, ρ) interval-valued fuzzy numbers constructed using the historical data. Marginal impacts of the assets on higher moments of the portfolio are used to formulate a fuzzy multi-objective linear programming model. The constraints of the proposed model include the bounds on investment in individual assets, full utilization of the investment capital, and no short selling of assets. The signed distance ranking method is used to obtain a numeric optimization model, which is solved through a weighted max-min approach (in order to incorporate the investor’s preferences regarding investment criteria). A case of real financial market portfolio selection is presented to demonstrate the efficiency of both the proposed model and the solution method.

Design of Green Cold Chain Networks for Imported Fresh Agri-Products in Belt and Road Development

The development of Belt and Road has seen a boom of imported fresh agri-products in China. This stimulates the growth of refrigerated transport, which accounts for much more carbon emissions than traditional transport. Designing a sustainable cold chain network is of vital importance from both financial and environmental perspectives. In this research, a multi-objective linear programming model is proposed for green cold chain design for multiple imported fresh agri-products in China to balance between the two competing goals—the total cost and carbon emissions. The effect of the outdoor air temperature on the carbon emissions of transportation and maintaining distribution centers is considered. By applying the ε-constraint method, the multi-objective model is solved. Numerical examples derived from the scenario of imported fresh-agri products in China are conducted to shed light on green cold chain design under Belt and Road development.

Identifying trade-offs between sustainability dimensions in the supply chain of biodiesel in Colombia

The study of the interactions among the economic, environmental and social dimensions of sustainability in supply chain management research has received increased attention in recent years. However, for the specific case of the biodiesel supply chain, little attention has been given to the inclusion of social aspects in an integrated analysis of sustainability performance. This paper in turn proposes and develops a deterministic multi-objective linear programming model to analyze the relationship among the economic, environmental, and food security dimensions of the biodiesel supply chain (BSC) in Colombia. Considering four echelons from the supply chain (palm cultivation, oil extraction, biorefineries, and mixers), the model seeks to minimize total cost, impact on food security, and emissions of greenhouse gases, including emissions from direct and indirect land use change. The Epsilon-constraint method is used to solve the multi-objective model for the BSC. A Pareto set of optimal solutions helped to assess the trade-offs involving the three objectives. The relationship between costs and emissions is contingent upon impact on food security; this is, the design of the supply chain network involving substitution of palm for agricultural crops exhibits lower total cost and lower CO2 emissions. The proposed generic mathematical model is applicable to any supply chain of agro-fuels and allows the calculation of production, inventory and distribution plans to better satisfy sustainability criteria.

Characterisations of the production possibility set in data envelopment analysis: an MOLP approach

The production possibility set in data envelopment analysis is a polyhedron and it is defined by the intersection of a finite number of half spaces which are constructed by their corresponding defining hyperplanes. Because of the importance of the characterisations of the production possibility sets in data envelopment analysis, we suggest two multi objective linear programming problems and then we identify some characterisations of the production possibility set by investigation of the relations among the suggested multi objective linear programming models and the input oriented envelopment and multiplier BCC models. In this paper, we use weighted sum and epsilon-constraint scalarisation methods to present some mathematical properties for finding some relations among the efficient solutions of the proposed multi objective linear programming models and the characteristics of the production possibility set and data envelopment analysis models.

Characterisations of the production possibility set in data envelopment analysis: an MOLP approach

The production possibility set in data envelopment analysis is a polyhedron and it is defined by the intersection of a finite number of half spaces which are constructed by their corresponding defining hyperplanes. Because of the importance of the characterisations of the production possibility sets in data envelopment analysis, we suggest two multi objective linear programming problems and then we identify some characterisations of the production possibility set by investigation of the relations among the suggested multi objective linear programming models and the input oriented envelopment and multiplier BCC models. In this paper, we use weighted sum and epsilon-constraint scalarisation methods to present some mathematical properties for finding some relations among the efficient solutions of the proposed multi objective linear programming models and the characteristics of the production possibility set and data envelopment analysis models.

A multi-objective programming model for selection third-party logistics companies and suppliers in a closed-loop supply chain

Due to globalisation and increasing competition in markets, the manufacturers and service organisations tend to outsource their logistics activities. On behalf of manufacturers and service organisations, an outer firm which called third party logistics (3PLs) company manages, controls and performs the logistics activities. In this paper, a general closed-loop supply chain network is designed that includes manufacturers, 3PLs, supplier, evaluation, disassembly, refurbishing and disposal sites. The proposed model of this paper has two phases. First phase determines 3PL and external supplier by using fuzzy sets theory. Namely, the preferences of decision makers for selecting 3PLs and suppliers are expressed by triangular fuzzy numbers and then, the weights of 3PLs and suppliers are determined. In the second phase, a multi-objective mixed integer linear programming model is proposed to determine the product optimum quantity assigned to the 3PL and parts purchased from supplier. The proposed model considers 3PL and supplier selection, simultaneously. To illustrate the capability of the suggested model, a numerical example is solved and the results are analysed.

Modelling sustainable supply chain management problem with fuzzy demand based on multi-criteria decision making methods

Nowadays, environmental issues are playing a significant role in our real lives and need to be taken into account in many decision-making problems. In order to incorporate environmental concerns into supply chain management problem as one of the most important decision-making problems, a new sustainable supply chain model is developed in this paper in which collection/inspection, recycling and returning unsatisfying and end-of-life products are examined in an uncertain environment. In this regard, a multi-objective mixed integer linear programming model with fuzzy demand parameter is proposed in which the flows through the sustainable supply chain network and facilities locations are determined in such a way that four objective functions are optimised including minimising total cost, minimising energy consumption, maximising number of jobs, and minimising delivery time. Using modified fuzzy parametric programming (MFPP) and weighted metrics method as the solution procedure to solve the developed model, it is implemented on a real case study to demonstrate its capabilities in a practical context.

Application of interactive fuzzy goal programming for multi-objective integrated production and distribution planning

Integrating two interconnected processes and controlling conflicting goals of a production and distribution problem is necessary for better planning. The aim of this integration is to allocate the limited available resources to produce the products over the time periods and ensure economical dispatching to distribution centres. In a responsive and competitive market, production and distribution planning modules is considered here within the framework of satisfaction level of decision maker. Triangular fuzzy numbers and the concept of minimum accepted level are employed to formulate the problem. Minimum operator and weighted average operator method is used to aggregate all fuzzy set and solved by three algorithms and goal programming method. The proposed approach aims to formulate a fuzzy multi-objective linear programming model to simultaneously minimise the total production cost, distribution cost and delivery time for multi-product and multi-time period under multiple uncertainty. AHP is used to rank multiple objectives and solved with MATLAB.

A unified method of defuzzification for type-2 fuzzy numbers with its application to multiobjective decision making

This paper introduces a process of defuzzification for ranking of type-2 trapezoidal fuzzy numbers. A two-phase defuzzification method has been developed using probability density function of the random variables associated with the fuzzy numbers. This method finds an equivalent defuzzified value of type-2 fuzzy numbers through phasewise reduction. The process reduces the computational complexities for using type-2 fuzzy numbers significantly and it is applicable to not only type-2 fuzzy numbers but also to any types of fuzzy numbers for ranking them properly. To illustrate the proposed defuzzification process, the method is applied on a set of type-2 trapezoidal fuzzy numbers and ranked them according to their defuzzified values. The achieved results are compared with other existing ranking methods. Furthermore, a multiobjective linear programming model having type-2 fuzzy numbers as parameters is solved using the proposed defuzzification process. Fuzzy goal programming technique is used for achieving the highest degree of each of the defined membership goals to the extent possible in the decision-making context. A numerical example is provided to demonstrate the efficiency of the proposed methodology.

Trade-Offs between Economic and Environmental Optimization of the Forest Biomass Generation Supply Chain in Inner Mongolia, China

The utilization of forest residue to produce forest biomass energy can mitigate CO2 emissions and generate additional revenue for related eco-enterprises and farmers. In China, however, the benefit of this utilization is still in question because of high costs and CO2 emissions in the entire supply chain. In this paper, a multi-objective linear programming model (MLP) is employed to analyze the trade-offs between the economic and environmental benefits of all nodes within the forest biomass power generation supply chain. The MLP model is tested in the Mao Wu Su biomass Thermoelectric Company. The optimization results show that (1) the total cost and CO2 emissions are decreased by US$98.4 thousand and 60.6 thousand kg, respectively; 3750 thousand kg of waste-wood products is reduced and 3750 thousand kg of sandy shrub stubble residue is increased; (2) 64% of chipped sandy shrub residue is transported directly from the forestland to the power plant, 36% of non-chipped sandy shrub residue is transported from the forestland to the power plant via the chipping plant; (3) transportation and chipping play a significant role in the supply chain; and (4) the results of a sensitivity analysis show that the farmer’s average transportation distance should be 84.13 km and unit chipping cost should be $0.01022 thousand for the optimization supply cost and CO2 emissions. Finally, we suggest the following: (1) develop long-term cooperation with farmers; (2) buy chain-saws for regularly used farmers; (3) build several chipping plants in areas that are rich in sandy shrub.