Mathematical Programming Techniques Research Articles

Application of Data Envelopment Analysis (DEA) in Information and Communication Technologies

The consistent improvements and fast-growing trend of information and communication technology (ICT) have impacted all areas of society and the economy. In 2020, with the sudden pandemic of COVID-19, businesses worldwide faced great challenges and had to transform and become digital-native enterprises by using data analytics, digital business platforms and personalized customer approaches. In such a digital era, innovation, entrepreneurial dynamism and ICT are the key ingredients for business' success and sustainability. Furthermore, it has become very clear that the influence of the ICT industry on economic growth is immense. Therefore, it should not come as a surprise that the interest in research of the ICT industry is great. Data Envelopment Analysis (DEA) is the leading non-parametric mathematical technique for assessing performance and measuring efficiency of complex entities called Decision-Making-Units (DMUs), by conversion of multiple input variables to multiple output variables. DEA has experienced rapid growth in use in many areas ever since its introduction by Charnes, Cooper and Rhodes in 1978. The purpose of this paper is to present and describe Data Envelopment Analysis as the leading mathematical programming technique for data analysis and to provide an extensive literature review, to identify the studies implementing the DEA methodology in Information and Communication Technologies (ICT) and to present its findings. Furthermore, this study's goal is to inspire and encourage researchers to employ this methodology in the fields of ICT and to give guidance for future research in this area.

New Approach in Fixed Resource Allocation and Target Setting Using Data Envelopment Analysis with Common Set of Weights

One of the mathematical programming techniques is data envelopment analysis (DEA), which is used for evaluating the efficiency of a set of similar decision-making units (DMUs). Fixed resource allocation and target setting with the help of DEA is a subject that has gained much attention from researchers. A new model was proposed by determining a common set of weights (CSW). All DMUs were involved with the aim of achieving higher efficiency in every DMU after the procedure. The minimum resources and targets allocated to each DMU were commensurate to the efficiency of that DMU and the share of DMU in the input resources and the output productions. To examine the proposed method, other methods in the DEA literature were examined as well, and then, the efficiency of the method was demonstrated through a numerical example.

Analiza efikasnosti bankarskog sektora pomoću metode analize obavijenosti podataka - pre pandemijski period

During the last decade, the question of measuring efficiency became inevitable factor of successful management of banks. Therefore, the basic goal of this paper is to apply DEA - Data Envelopment Analysis in comparing unit efficiency of Serbian banking sector for three years period of time (2017, 2018 and 2019). DEA is a technique of mathematical programming which uses analysis and comparation of efficiency of different entities and it is suitable to solve problems of different number and nature of inputs and outputs. The presented paper employs an output-oriented data envelopment analysis with a constant return to scale assumption. The selected input variables are total assets and total capital, while net operating income and net profit were used as output variables. Results showed that the average efficiency of Serbian banking sector is about 50% in the observed years. Opportunity Bank achieved the maximal efficiency score in the entire time period while Mirabank had the lowest efficiency score.

Generalized Disjunctive Programming Model for Optimization of Reverse Electrodialysis Process

Reverse electrodialysis (RED), an emerging electrochemical technology that uses ion-selective membranes to directly draw electricity out from salinity differences between two solutions, i.e., salinity gradient energy (SGE), has the potential to be a clean and steady renewable source to reach a sustainable water and energy supply portfolio. Although RED has made notable advances, full-scale RED progress demands more techno-economic and environmental assessments that consider full process design and operational decision space from module- to system-level. This work presents an optimization model formulated as a Generalized Disjunctive Programming (GDP) problem to define the cost-optimal RED process design for different deployment scenarios. We use a predictive model of the RED stack developed and validated in our research group to fully capture the behavior of the system. The problem addressed is to determine the RED plant's topology and the working conditions for a given design of each RED stack which renders the cost-optimal design for the defined problem and scenario. Our results show that, compared with simulation-based approaches, mathematical programming techniques are an efficient and systematic approach to provide decision-making support in early-stage applied research and to obtain design and operation guidelines for full-scale RED implementation in real scenarios.

How to start a heuristic? Utilizing lower bounds for solving the quadratic assignment problem

The Quadratic Assignment Problem (QAP) is one of the classical combinatorial optimization problems and is known for its diverse applications. The QAP is an NP-hard optimization problem which attracts the use of heuristic or metaheuristic algorithms that can find quality solutions in an acceptable computation time. On the other hand, there is quite a broad spectrum of mathematical programming techniques that were developed for finding the lower bounds for the QAP. This paper presents a fusion of the two approaches whereby the solutions from the computations of the lower bounds are used as the starting points for a metaheuristic, called HC12, which is implemented on a GPU CUDA platform. We perform extensive computational experiments that demonstrate that the use of these lower bounding techniques for the construction of the starting points has a significant impact on the quality of the resulting solutions.

A new gradient free local search mechanism for constrained multi-objective optimization problems

Multi-objective evolutionary algorithms (MOEAs) are commonly applied to treat multi-objective optimization problems (MOPs) due to their global nature, robustness, and reliability. However, it is also well known that MOEAs need quite a few resources to compute a good approximation of the Pareto set/front. Even more, MOEAs may exhibit difficulties when dealing with highly constrained search spaces. A possible remedy is the hybridization of MOEAs with specialized local search operators; if the local search is based on mathematical programming techniques, gradient information is needed, resulting in relatively high computational cost in many problem instances.

Optimization Heavy Equipment Productivity Against Costs on Un-Top Soil and Spreading Work With Linear Programming Simplex Method

PT Bhumi Rantau Energi is a coal mining company in Indonesia located in South Kalimantan, Indonesia. As a mining company, one of the obligations that must be carried out is land reclamation so as not to cause environmental damage. Land reclamation is carried out by planting tree seeds on ex-mining land. The stages of the process for land reclamation are Top Soil excavation. Top soil is the top layer of soil that contains the most nutrients and has the most air content among other soil layers. The excavated top soil will be spread over the ex-mining land that has been provided for reclamation. The purpose of this study is to determine the productivity, number of heavy equipment and also the costs that will be incurred for the Top Soil and Spreading excavation activities. As for determining the minimum cost, it can be analyzed using mathematical programming techniques, one of which is linear programming using the simplex method. This technique is very useful in finding the best solution for a function with more than two variables under the given constraints. Linear programming is a mathematical method that allocates limited resources to achieve a goal such as maximizing profits and minimizing costs. The research method used is a quantitative method. From the results of the study, it was found that for Top Soil and Spreading work for 8 months, 2 Excavator Units with Productivity of 182.25 m³/hour, 2 Bulldozer Units with Productivity of 181.56 m³/hour, 9 Dump Truck Units with Productivity 39.94 m were needed. /hour and 1 Motor Grader Unit with Productivity of 16,128 m²/hour, then the cost incurred for the work is Rp. 18,017,984,600.

Flow modeling of high-viscosity fluids in pipeline infrastructure of oil and gas enterprises

Today, the issues related to solving the problem of finding an effective distribution of oil flows through the system of oil pipelines in order to reduce the total energy consumption are relevant. The solution to this problem is connected with selection of rational pumping modes for various technological sections of oil pipelines using modern methods of mathematical programming or new techniques for improving the energy and transport characteristics of oil.Reducing energy consumption during pumping of crude through oil trunk pipelines can be achieved by various methods. Numerous investigations in this direction are mainly carried out to save energy on separate single-line pipelines. However, due to the development of the network of trunk oil pipelines in the world over the past decades, the issues of energy efficient management of oil flows throughout the entire oil pipeline system of oil and gas enterprises become urgent.This paper analyses parameters for pipeline transport of high-viscosity and heavy oils. The article proposes a method for assessing the rheological properties of oil for further planning of pumping taking into account the preservation of oil quality and an increase in energy and transport characteristics. The proposed solutions and tasks for predicting changes in the viscosity-temperature characteristics of the flow for blends of different oil types are especially relevant in the current conditions of an increase in the share of oil production with complex rheological characteristics. Results of the presented investigations may be used for planning the measures of efficient transportation of high-viscosity and heavy oils.

Multiple Cross-docks Scheduling with Multiple Doors using Fuzzy Approach and Metaheuristic Algorithms

The issue of supply chain in today's world is a major competitive advantage in reducing costs. Supply chain includes procurement, logistics and transportation, marketing, organizational behavior, networking, strategic management, information systems management and operations management. One of the most important practices in logistics is cross-docking which sets its goals as inventory reduction and customer satisfaction increase. Customers receive goods through docks. Docks are responsible to provide a place for goods before being delivered to the customers. Then, these materials are directly loaded into outbound trucks with little or no storage in between to send to customers in the shortest possible time. This paper is mainly aimed at introducing a mixed integer linear programming model to solve scheduling several cross-docking problems. The proposed model is highly facilitated to allocate the optimal destinations to storage doors and truck scheduling in docks while selecting the collection and delivery routes. Using optimization approaches at uncertainty conditions is also of great importance. Mathematical programming techniques vividly fail to solve transportation problems that include fuzzy objective function coefficients. A fuzzy multi-objective linear programming model is proposed to solve the transportation decision-making with fuzzy objective function coefficients in this paper. On the other hand, the existences of computational complexities lead this model to be categorized as a NP-Hard one. Therefore, we applied metaheuristic algorithms such as genetic and ant colony in order to solve our proposed problem.

A linear physical programming model for assembly line balancing problem

This paper deals with the mixed-model assembly line balancing problem. This type of line is applied to more than one similar model of a product in an intermixed order. Despite their widespread use, these lines have received little attention in the literature. Metaheuristics, heuristics and mathematical programming techniques are developed to solve these types of assembly line balancing problems. However, linear physical programming method has never used. In this paper, a linear physical programming model is proposed for balancing a mixed-model assembly line. The performance of the proposed model is applied to a numerical example to analyze the usage of the methodology. Five objectives are considered in the model and the outperformance of the methodology is demonstrated by comparing it to a different approach. According to the results, it has been seen that the proposed linear physical programming model is practical and useful approach for mixed-model assembly line balancing problems.

A Hybrid Approach for Optimization of Distribution Networks with Photovoltaic Sources

This paper presents a hybrid approach, which associates a mathematical programming technique with a metaheuristic, to optimize the electricity distribution network with penetration of photovoltaic (PV) generation. This optimization considers the distribution network reconfiguration (DNR) and the adjustment of the power factor of photovoltaic (PV) inverters in relation to the reactive power, controlling the voltage profile and minimizing network losses. The methodology uses particle swarm optimization (PSO) for DNR and an optimal power flow (OPF) to adjust the value of the PV inverters and maintenance of network operating limits. The tests were performed using the AMPL Modeling Language in the 33-node system with the addition of PV generation. The approach considers the variations in the powers generated by the PV systems and the variations in the loads over a 24 h period. The results indicate that the combination of PV inverter control and DNR can reduce the active power losses by more than 37% in a 24-hour period.

Decision support algorithms for optimizing surgery start times considering the performance variation.

In this paper, we consider a stochastic optimization model for a surgical scheduling problem with a single operating room. The goal is to determine the optimal start times of multiple elective surgeries within a single day. The term "optimal" is defined as the largest surgically related utility value while achieving a given threshold defined by the performance variation of a reference solution. The optimization problem is analytically intractable because it involves quantities such as expectation and variance formulations. This implies that traditional mathematical programming techniques cannot be directly applied. We propose a decision support algorithm, which is a fully sequential procedure using variance screening in the first phase, and then employing multiple attribute utility theory to select the best solution in the second phase. The numerical experiments show that the proposed algorithm can find a promising solution in a reasonable amount of time.

Optimum Project Portfolio Selection for Developmental Plans Using Goal Programming

In vision-driven development plans, such as the Kuwait Mid-Range Development Plan 2015/2016–2019/2020, themes and pillars are derived from the plan's vision, and global indices are assigned by international organizations to accurately measure the performance against the vision's themes. This allows for comparison with other countries, and it also set targets for progression over time. One or more projects are assigned to the indicators of these global indices. A Multi-Criteria Mathematical Programming Technique (e.g., Goal Programming) is used with multiple goals and priorities where an Optimal Portfolio of Projects is found that satisfied the selection criteria.

Production efficiency of major crops among smallholder farmers in Central Ethiopia

Agricultural production of most smallholders in Ethiopia is dependent with recurrent rainfall resulted in production variations. Limited input availability and precarious environmental conditions determine smallholders’ decisions on their production and the production efficiencies vary from farmer to farmer. This study was carried out with the aim of analyzing the technical, allocative and economic efficiencies of smallholder farmers in the production of major crops and their determinants in central Ethiopia, Oromia special zone surrounding Addis Ababa. Multistage sampling technique was employed to randomly and proportionally select 386 smallholders from ten PAs. Primary data were collected from smallholders through a semi structured questionnaire using face to face interview. Cross sectional data collected from sampled households in the study area were analyzed using mathematical and econometric methods. Mathematical programming technique selected for this study was Data Envelopment Analysis (DEA) using linear programming technique assuming multi-input and multi-outputs were handled. Tobit regression model was regressed against the socioeconomic, demographic, and institutional variables that are expected to affect the technical, allocative and economic efficiencies of sampled households. The results of estimated efficiency scores show the mean technical, allocative and economic efficiencies were 0.75, 0.60 and 0.45 respectively. The mean scores of efficiencies show underutilization of resources and the possibilities of smallholders to increase their agricultural production by 25%, and reduce cost of production by 40% and total cost by 55%. Marital status, level of education, farming experience, access to credit, cooperative membership, access to farming information, and off/non-farm income has positive influence on the technical, allocative and economic efficiencies. While age of the household head, access to training and livestock size has negative relations to efficiencies. Delivery of agricultural inputs and trainings on time by the government is the key policy implication to improve the efficiencies of smallholders.

Optimum Project Portfolio Selection for Developmental Plans Using Goal Programming

In vision-driven development plans, such as the Kuwait Mid-Range Development Plan 2015/2016–2019/2020, themes and pillars are derived from the plan's vision, and global indices are assigned by international organizations to accurately measure the performance against the vision's themes. This allows for comparison with other countries, and it also set targets for progression over time. One or more projects are assigned to the indicators of these global indices. A Multi-Criteria Mathematical Programming Technique (e.g., Goal Programming) is used with multiple goals and priorities where an Optimal Portfolio of Projects is found that satisfied the selection criteria.

A multi-agent system for distribution network restoration in future smart grids

A main feature of future smart grids is their self-healing capability, which allows fault location, isolation and service restoration to be done automatically. Restoration is a combinatorial non-linear optimization problem for which conventional mathematical programming techniques and heuristic methods become computationally very costly. This paper proposes a decentralized restoration method that avoids the computational burden of fully centralized optimization techniques while still providing good solutions and avoiding single points of failure. By pre-calculating the amount of power that can be transferred from other feeders without violating their limits, restoration within the outage area is converted into a binary integer linear optimization problem which can be easily solved. To prove its effectiveness, different case scenarios were tested on 14-bus and 70-bus systems. The multi-agent system was implemented in JAVA Agent Development Framework (JADE) and MATLAB was employed for the main algorithms within each agent. The outcomes were compared to those of previously proposed centralized and decentralized approaches, proving that the method proposed shows better computational efficiency than the centralized approach and better results than the decentralized approach. Therefore, the proposed algorithm provides an overall improved solution.

Predictive Search for Capacitated Multi-Item Lot Sizing Problems

For capacitated multi-item lot sizing problems, we propose a predictive search method that integrates machine learning/advanced analytics, mathematical programming, and heuristic search into a single framework. Advanced analytics can predict the probability that an event will happen and has been applied to pressing industry issues, such as credit scoring, risk management, and default management. Although little research has applied such technique for lot sizing problems, we observe that advanced analytics can uncover optimal patterns of setup variables given properties associated with the problems, such as problem attributes, and solution values yielded by linear programming relaxation, column generation, and Lagrangian relaxation. We, therefore, build advanced analytics models that yield information about how likely a solution pattern is the same as the optimum, which is insightful information used to partition the solution space into incumbent, superincumbent, and nonincumbent regions where an analytics-driven heuristic search procedure is applied to build restricted subproblems. These subproblems are solved by a combined mathematical programming technique to improve solution quality iteratively. We prove that the predictive search method can converge to the global optimal solution point. The discussion is followed by computational tests, where comparisons with other methods indicate that our approach can obtain better results for the benchmark problems than other state-of-the-art methods. Summary of Contribution: In this study, we propose a predictive search method that integrates machine learning/advanced analytics, mathematical programming, and heuristic search into a single framework for capacitated multi-item lot sizing problems. The advanced analytics models are used to yield information about how likely a solution pattern is the same as the optimum, which is insightful information used to divide the solution space into incumbent, superincumbent, and nonincumbent regions where an analytics-driven heuristic search procedure is applied to build restricted subproblems. These subproblems are solved by a combined mathematical programming technique to improve solution quality iteratively. We prove that the predictive search method can converge to the global optimal solution point. Through computational tests based on benchmark problems, we observe that the proposed approach can obtain better results than other state-of-the-art methods.

Direct Restarted Pell Algorithm for Solving Calculus of Variation Problems

The Pell Polynomial series is employed to solve problems in calculus of variations. The solution can be considered as linear combinations of Pell polynomials with unknown coefficients. Then a calculus of variational problem transforms into an optimization problem and will be solved using mathematical programming techniques. The proposed method converges rapidly to the exact solution and gives accurate results using small number of Pell polynomials basis polynomials. Some illustrative examples are included and the approximate results obtained by restarted Pell series are compared with the exact solutions.

Efficiency and factors influencing it in forest districts in southern Poland: Application of Data Envelopment Analysis

The paper presents the efficiency evaluation of forest districts in Southern Poland carried out using the standard Data Envelopment Analysis (DEA) which is a nonparametric mathematical programming technique. The study aims to evaluate the efficiency and identify the external factors affecting the efficiency of forest districts by using the Tobit econometric model. The study was conducted for 113 forest districts in four Regional Directorates of State Forests (in Katowice, Kraków, Krosno and Wrocław) and covered the period from 2008 to 2012. The results show differences in the use of economic and financial resources by the analysed forest districts. Lowland forest districts were more efficient that highland ones, both in terms of financial efficiency and efficiency of economic resources. In addition, efficiency was significantly influenced by various exogenous factors, depending on the category of forest districts. The analysis showed that financial efficiency of lowland forest districts was significantly influenced by population density, with negative effects on economic performance. In turn, efficiency of economic resources in this group was significantly negatively influenced by the number of forest complexes and population density. In the case of the highland forest districts, their financial efficiency was positively influenced by the number of forest complexes and negatively influenced by the area of nature reserves. However, efficiency of economic resources of the highland forest districts was not affected by any of these factors. The combination of the DEA method with the Tobit econometric model appears to be a valuable and useful tool for identifying factors affecting the efficiency of forest districts.

A Hybrid Methodology to Minimize Freshwater Consumption during Shrimp Shell Waste Valorization Combining Multi-Contaminant Pinch Analysis and Superstructure Optimization

The conservation and proper management of natural resources constitute one of the main objectives of the 2030 Agenda for Sustainable Development designed by the Member States of the United Nations. In this work, a hybrid strategy based on process integration is proposed to minimize freshwater consumption while reusing wastewater. As a novelty, the strategy included a heuristic approach for identifying the minimum consumption of freshwater with a preliminary design of the water network, considering the concept of reuse and multiple pollutants. Then, mathematical programming techniques were applied to evaluate the possibilities of regeneration of the source streams through the inclusion of intercept units and establish the optimal design of the network. This strategy was used in the shrimp shell waste process to obtain chitosan, where a minimum freshwater consumption of 277 t/h was identified, with a reuse strategy and an optimal value of US $5.5 million for the design of the water network.