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In this work, we simulate a pre-sampled demand of blood units for the blood bank of a tertiary care super specialty hospital specializing in cardiac care and neuro care to mimic the present system based on last year's data. Simulation is a useful tool to address various problems related to healthcare as it is timesaving and can behave close to the actual system. In this study, we simulate the blood bank for 2000 days. This work also considers separate inventory systems for fresh and normal demand types of blood units based upon the age of blood units demanded for different patients. We consider three inventory policies (s, S) policy, (s, Q) policy and (s, S, q, Q) policy for the blood bank. To find the respective best re-order level (s), order-up-to level (S) and fixed-order quantity (q and/or Q) of blood units, we initially develop an Integer Linear Programming (ILP) model for the (s, S), (s, Q) and (s, S, q, Q) policies without considering the compatibility across blood groups. To overcome scaling issues encountered with the ILP model, we have proposed an approach based on the Genetic Algorithm (GA) to find high-quality solutions for large problem instances within a reasonable time duration, thereby reducing the total wastage or amount of outdated blood units while satisfying the random demand. We have compared the random and tournament selection techniques used for GA and found the latter to perform better. After comparing the three policies, we find that both the (s, Q) and the (s, S, q, Q) policies are competitive, and they outperform the (s, S) policy. The need for fewer parameters and the relative ease of implementation makes the (s, Q) policy preferable to the (s, S, q, Q) policy. [ABSTRACT FROM AUTHOR]

This research paper was designed to use a Linear programming technique, by the data collected from Rufaidah Yoghurt Processing Company. The company produces different sizes of yogurt milk ranging from 2 liters to 330ml per day. To maximize the profit, the Mathematical Tools (Simplex and Dual Simplex methods) were employed to find the optimal solution. The result shows that, the Simplex method performed better than the Dual Simple method in terms of number of iterations with aim to maximize the profit of the company. [ABSTRACT FROM AUTHOR]

This paper aims to identify the Lipschitz continuity for the objective and constraint functions in the linear optimization model with uncertainty through the convexity properties of these functions. Robust optimization is one of the optimization models for dealing with data uncertainty. This data uncertainty is in an uncertainty set. In Robust Optimization, the objective and constraint functions' convexity guarantee a globally optimal solution. Based on local and global Lipschitz continuity criteria for a proper lower semicontinuous convex function in Banach space, this research observed Lipschitz continuity of objective and constrain functions in a linear Robust Optimization model. The uncertainty in the optimization model is assumed to be in the box uncertainty set, which is formulated into Robust Counterpart. Based on our research, we discovered that the objective and constraint functions in ordinary linear programming problems are global Lipschitz continuous functions. We also obtained that the robust linear optimization problem's Robust Counterpart form with the box uncertainty set has an objective function and a global Lipschitz continuous constraint function. In addition, we provide an example for a simple linear optimization model with uncertainty. [ABSTRACT FROM AUTHOR]

The Transportation Problem (TP) is a special case of linear programming that aims to allocate a number of goods from source to destination. There are many methods to solve TP, either to find an initial feasible solution or an optimal solution to the TP. This study aims to find out how to use the BCE (Bilqis Chastine Erma) method which is the latest method at its time to get an initial feasible solution to the TP. The algorithm itself starts by allocating a number of goods according to the number of goods demanded from each column to the cell that has the lowest value in each column, then focuses on changing the allocation of a number of goods in the row with excess goods from the lowest cost cell to the second lowest cost cell or on the other hand, after checking several conditions that must be satisfied before changing the allocation, and if there is only 1 row that has not satisfied, the total minimum transportation can be calculated. The application of this method in the case of balanced data minimization with a size 3 × 4 obtained an allocation from source 1 to destination 2 as many as 5 units of goods and to destination 4 as many as 10 units of goods, from source 2 to destination 2 as many as 10 units of goods and to destination 3 as many as 15 units of goods, from source 3 to destination 1 as many as 5 units of goods and to destination 4 as many as 5 units of goods. And the minimum total transportation cost obtained is 435 units of cost. [ABSTRACT FROM AUTHOR]

It is imperative for university undergraduate programs to possess effective allocation and optimal utilization of its resources. Evaluating undergraduate programs' relative efficiency enables the university to rank the programs and identify the strengths and weaknesses of the programs. This is crucial for the programs' continuous quality improvement plans and measures. In order to achieve this, Data Envelopment Analysis (DEA) can be used to determine and rank relative efficiency for each decision-making unit (DMU) or in this case the undergraduate program based on its inputs and outputs. This method can also identify the factors that possess a significant effect on a DMU through its relative efficiency score and slacks. In this study, DEA is utilized to evaluate and rank the efficiency of nine DMUs which are the programs under the Faculty of Science and Natural Resources, Universiti Malaysia Sabah in order to determine whether the allocation and utilization of educational purposes is effective or otherwise. The inputs (Xm) and outputs (Yn) for this study are identified as the number of academic staff (X1), number of taught course students (X2), average students' qualifications in CGPA (X3), number of graduates from program (Y1) and graduation rate (Y2). The outcome of this research is expected to be aligned with previous studies where the inputs and outputs for each DMU into a linear programming form can be transformed and from there, the virtual weights for each input and output can be determined. It is anticipated that this study will aid faculty administrators in determining which programs are relatively efficient or otherwise. It is hoped that the faculty administrators can formulate appropriate measures to maintain the programs with a higher relative efficiency score as well as aiding the programs with a relatively low efficiency score. [ABSTRACT FROM AUTHOR]

Hot Mixtures Asphaltic plants are one of the most prominent engines of the construction wheel in the country, as they are the only source for supplying Road construction and maintenance projects with asphaltic concrete. Since the country is now going through a reconstruction stage, so, Asphalt waste is generated in Iraq in gigantic proportions due to a large part of its roads undergoing reconstruction. Therefore, selecting the optimal site for these plants, depending on the criterion for recycling this waste in addition to other criteria, has significant impacts on the long-running economical, environmental, social, and institutional aspects. This paper aims to select the most suitable site out of the four sites for the construction of the HMA plant for paving projects and maintenance of roads in the Al-Hur district / Karbala Province in particular and an explanation of the role of sustainability in this selection. These sites are: Industrial Zone of Razzaza, Industrial Zone of Al-Sharia, Industrial Zone of Khan Al-Rubue, and Industrial Zone of Husseiniya. To achieve this aim, a set of quantitative and qualitative sustainability criteria were employed with their relative importance and used to build a mathematical model according to the basics of linear programming. The mathematical model was solved using the POM-QM program. Where, when applying this model to the four industrial areas, it was found that the best site in terms of cost would be in the Industrial Zone of Razzaza This work guides decision-makers in the asphalt industry to assess the optimal and sustainable selection for the sites of Hot Mix Asphaltic plants in Iraq in light of current necessity for road projects and maintenance. [ABSTRACT FROM AUTHOR]

Optimizing harvest costs inherently influences the efficiency and profitability of the sugar processing industry. Therefore, planning the schedule by considering various variables is necessary to achieve maximum efficiency in harvest and load activities at the sugar factory. This research conducted a case study at X Factory in Jatiroto, Lumajang Regency, Indonesia, focusing on optimizing sugarcane harvesting and loading schedules with a Linear Programming model. The objective of this research is to design a Linear Programming mathematical model that minimizes sugarcane harvesting and loading costs at X Sugar Factory, with the objective function being the minimization of total costs. The constraints include land area, milling capacity, transportation capacity, and harvesting cost. Scheduling was performed over five milling months, aligned with X Sugar Factory's actual milling period (150 days). The Linear Programming optimal result reveals a significant 6.653% total cost saving, approximately Rp 7.5 billion, compared to the actual costs at X Sugar Factory. Conversely, the optimal model result also reduces land area usage by 550.474 hectares, representing 4.612% of the current areas. Moreover, the harvested sugarcane meets the daily minimum milling target criteria of 6,400 tons/day. The model result additionally provides a sophisticated schedule table for each harvest period and land area, offering valuable insights into land use and sugarcane production estimates. [ABSTRACT FROM AUTHOR]

The capacity of Generative Artificial Intelligence (AI) models in formulating optimization problems is an interesting area of exploration in this rapidly evolving field. This study explores the capability of AI to interpret and formulate mathematical modeling problems from English descriptions. Five Large Language Models (LLMs) were selected, including OpenAI's ChatGPT-4, Google's Gemini, Microsoft's Copilot, Anthropic’s Claude, and an open-sourced model by Meta Llama-2. The research is conducted through a systematic comparison between human-expert generated formulations and those produced by the LLMs to better understand the strengths and shortcomings of the five LLMs. A diverse set of 26 linear programming problems was used for this evaluation. The effectiveness of these AI tools is measured based on the correctness of the formulations. ChatGPT-4 outperformed its competitors with a mean score of 88.55, followed by Copilot at 84.93, Gemini at 83.57, Claude at 81.21, and Llama-2 at 46.26. The test problems were example in Linear programming from typical junior level course in industrial engineering and were graded using a rubric. Overall, ChatGPT-4 was the best earning a "B+" grade compared to others Copilot ("B"), Gemini ("B-"), Claude ("B-"), and Llama-2 ("F"). These findings indicate considerable variation in current Generative AI technologies in their ability to automatically formulate mathematical optimization problems. There are interesting opportunities to harness these technologies as they continue to rapidly evolve in research, education, and practice. [ABSTRACT FROM AUTHOR]

In this study will be presented in extenso two methods to avoid collision between two or more space objects and a definite answer is formulated to prevent the actual collision. Collision detection and avoidance is a fundamental issue for many areas which consists in knowing whether for any two objects of study there is a non-zero probability as when they are in the immediate vicinity, their trajectories to intersect. Regarding in-flight collision detection methods, the literature records two categories of methods in the discrete domain and the continuous domain. An extensive bibliography on this subject has been studied, which shows that many software products have been developed, and also multiple interactive applications. Some of them implement the Gilbert Johnson Keerthi algorithms in GJK or LinCanny in the I-COLLIDE product, which include the first library for the problem of in-flight collisions. There are also applications that aim to implement dynamics and constraints, so that obstacles must be avoided and there are different objective functions, such as minimum fuel consumption, the minimum time required to reach the destination or the time required to cover the area subject to observation (in the case of UAS). These applications formulate linear programming problems (YALMIP - with Gurobi solver, Mixed Integer Linear Programming - MILP); the objects are characterized by the specified mathematical models. [ABSTRACT FROM AUTHOR]

A simple limit analysis modeling for masonry arches with innovative strengthening is proposed in this paper, where the arch ring is discretized by rigid blocks according to the real bond pattern and the reinforcement effect is modeled through updating the failure surface of the contact joints. Considering all the extra force resultants provided by the reinforcement layer, we have first derived the constraints for the new yield condition and flow rule, defining the failure surface after applying the strengthening, and the new limit analysis formulation with consideration of reinforcement effect is then given. Such modeling is also very convenient to incorporate with sequential linear programming to solve non-associated problems. Applying the proposed theory, collapse analysis of an FRP-reinforced arch in 2D is presented and the results predicted from associated and non-associated formulations are compared. The results show that when analyzing the arch with reinforcement, the associated limit analysis may overestimate the ultimate load, as well as produce an incorrect collapse mechanism. Therefore, it is necessary to employ the non-associated flow rule for an accurate prediction of the collapse performance of reinforced arches. [ABSTRACT FROM AUTHOR]

The work is a case study in a wooden pallet factory that experienced issues with standardizing the cutting of its logs. Since logs serve as the base material for assembling the product, the lack of standardization in this process led to wasted materials and increased stock levels. Consequently, the research was conducted within the company's sawmill sector to enhance the efficiency of the process, standardize it, minimize waste, and align production with customer demand. To achieve this goal, data were collected from the factory floor, and concepts such as cutting problems, production planning and control, operational research, and linear programming were utilized, alongside tools such as solver software and Microsoft Excel. Following data collection, analysis, and tool implementation, control and standardization were successfully achieved. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to propose a linear programming model that satisfies hypothetical nutritional requirements that the U.S. Army canine unit might have. The study established specific amounts of protein, carbohydrates, and fat necessary for canines that partake in military activity. It was determined that each daily portion would consist of a base amount of protein, carbohydrates, and fat. However, in order not to compromise the dogs' health and maintain their peak performance, there had to be a limit set on the daily intakes of macronutrients. Through linear programming optimization sensitivity and dual analysis, our research highlights the economic and sustainable feasibility of producing a plant-based diet for military dogs without compromising the canine's health or military performance. The scope of this research is purely based on a theoretical proposed diet using public data to provide a methodological approach for balancing nutritional quality while maintaining cost efficiency. [ABSTRACT FROM AUTHOR]

One of the robust uses of linear programming is known as assignment problem. This is a special case of the transportation problem. Assignment problem manages the inquiry about how to dole out n items to m different articles in an injective style in the most ideal way. Mostly, researchers found numerous applications of Assignment problems in real world which are: Production planning, Telecommunication, VLSI design, Economics, etc. In this paper, we made an effort to solve assignment problems solved by new proposed method by Maximization Assignment Problem (MAP) by A.N. Jasim [17], Method of Solving Extension Interval (MSEI), Average Total Opportunity Cost Method (ATOC), New Approach to Zero Suffix Method (NAZs), Method by E. R. Wulan et al. [22] and compare it with the existing method. Some real-life examples are carried out which are related to profit maximization of assignment model to check validity of Assignment model and compared it graphically. [ABSTRACT FROM AUTHOR]

One of the most crucial requirements for any power system is optimal power flow (OPF). The relevant optimisation problem thus attempts to create new distributions of active and reactive power while respecting the necessarytechnological and financial limitations. Considering this as an optimisation problem that entails minimising a target function while considering practical and budgetary constraints, an attempt is made in this work to redistribute both active and theoretical power, an approach that necessitates modification and the use of several control variables in the system. The purpose of this research is thus to discuss the OPF problem based on four target functions: real power losses, fuel value, voltage enhancement, and imaginary power losses, recruiting the assistance of a particle swarm optimisation)PSO(technique. After resolving the OPF issues, the PSO outputs were thus compared to those for various other techniques, including genetic algorithms and linear programming. The proposed PSO was demonstrated to achieve lower costs and losses and an improved voltage profile in case studies involving IEEE-30 buses when implemented in MATLAB environment R2018a. PSO also reduces the target function voltage profile or voltage deviation from the initial state of 0.48378 p.u to the optimal state of 0.199181 p.u. while reducing the target function's fuel cost from a starting condition of 901.9 $/hr to an ideal state of 800.636 $/hr. [ABSTRACT FROM AUTHOR]

Linear programming is one of the basic concepts to further study in applied mathematics and optimization. If the constraints of the linear programming problem form a convex region, then the problem must have an optimal solution. Cube is convex and, in terms of geometry, cube is very special. Cube has some special properties that all edges are congruent and also the all sides are congruent. Other special properties of the cube are related to orthogonality and parallelism. This paper discus linear programming problems with cube constraints. This research is study literature research to describe linear programming problems with cube constraints on geometrical angle. Considering the peculiarities of a cube, this linear programming problem must have an optimal solution. The results show the following points: 1) A cube is a convex polyhedron; 2) The steps for solving linear programming with cube constraints are analogous to the steps for solving linear programming in two dimensions using the graphical method, finding all the vertices of the cube and calculating the value of the objective function at all of the vertices, and then determining the vertex point that produces the optimal value; 3) The problem can have a unique solution (vertex) or have infinitely many solutions (the points along the edges or on the side planes of the cube). [ABSTRACT FROM AUTHOR]

This paper aims at an improvement in the frame of a passenger car for its higher efficiency. A special feature of this improvement is the closed configuration of the center sill that can be formed with sheets. The mass of the center sill can be minimized through its optimization with linear programming. The results of the calculation demonstrated that the mass of the frame in terms of the solutions proposed was 1.7% lower than that of the standard structure. The paper presents the results of the strength calculation of the frame of a passenger car at main loading modes. It was established that the strength of the frame at the schemes of loading studied was ensured. The motion of the improved frame of a car was estimated with the vertical accelerations on the frame. The motion was estimated as excellent. The research also included the modal analysis of the frame of a passenger car. The research can be used by those who are involved in the design of the bearing structure of a passenger car with better technical and operational characteristics that can increase the operational efficiency of passenger cars. [ABSTRACT FROM AUTHOR]

In this paper use model vehicle sharing system. Formulate modified model passive regulation lower Bound. This research focused on One-Way Vehicle Sharing System. It is the system that user can rent and return vehicle at any station. The modified model passive regulation lower bound aims to minimize total of excess time for all user so there is vehicle in initial station and there is parking space in destination station. So the user did not need to wait to long until vehicle available in initial station or parking space available in destination station. In real life often there is no vehicle to rent and there is no parking space to park vehicle that had been rented. So in this paper will analyze total excess time for all users. Model formulated as Mix Integer Linear Programming. To formulate and solve model used Lingo. 17. The result show minimum total excess time for all users is 10,25 minutes. [ABSTRACT FROM AUTHOR]

Due to the general inherent volatility of the data, it is difficult to draw firm conclusions about it in real time. Like in decision-making situations, an optimization problem known as a vector-maximum problem includes several objective functions. It is explained here how to deal with the fuzzy multi-objective optimization linear programming problem (FMOLPP) by utilizing several fuzzy and non-fuzzy ways. Reducing the gap between ideal and feasible goals is at the heart of the suggested technique. Using ranking functions, problems that are ambiguous can be made to be more precise and precise. The employment of precise optimization techniques has become standard. The very first model handles MOLPP by solving a sequence of single-goal sub-problems where the objectives are turned into constraints. Using an ambiguous strategy, the fuzzy version of the perpendicular divergence (between the parallel hyperplanes at the ideal locations of the desired function) is possible. Supreme perpendicular separation has developed a suitable degree of membership. To better understand these hypotheses, numerical experiments had to be looked at. [ABSTRACT FROM AUTHOR]

Due to the obvious inherent confusion of the information, actual analysis of it tends to be a bit fuzzy. Fuzzy arithmetic operations are used rather than more complicated basic mathematics and reasoning for intervals. In this article, a solution to the fuzzified linear fractional technique (FLFP) problem is presented. It is here that FLFP's issue gets turned into MOLFP's equivalent issue. In this article, you will learn how to solve multi-objective linear fractional programming problems. An LP dilemma with a singular goal is created using Fuzzy Arithmetic Programming from the MOLFP problem. Using the proposed method, numerical problems are also resolved. [ABSTRACT FROM AUTHOR]

The primary aim of this study is to design an optimal production unit within the constrain of the existing workforce, aimed at maximizing profitability in the songket industry, which had been significantly impacted by pandemic. The industry faced a sharp decline in orders, leading to a substantial reduction in income and increased costs. To address these challenges, the industry reduced its workforce. With the gradual recovery of industry conditions, customer orders have resumed. However, effective strategies are needed to manage customer demand while optimizing the existing workforce. Focuses on pinpointing the optimal resources required to meet customer demands and enhance industry profitability. By producing 25 units songket, allocating 125 mandays (60.09%) to routine workforce tasks, 50 mandays (48.08%) to professional workforce activities, and utilizing 75 unitdays (48.08%) of equipment, the study remarkably demonstrates a substantial IDR 23,750,000 improve in overall industry profits. This stands as a practical solution to the challenges previously outlined. [ABSTRACT FROM AUTHOR]

This paper deals with Fuzzy Integer Linear Programming problems (FILPP) in which all the constraints and variables are PFN. In this research, a technique created on the combined construction of m-LPPs for solving FILP Problems is presented. Also, an attempt is made to compare the present result with previous methods proposed by different authors. This study helps out to choose the better procedure for solving FILP Problems. [ABSTRACT FROM AUTHOR]

The global shift towards sustainable transportation is centered around the growth of electric vehicles (EVs) primarily due to their zero tailpipe emissions. To facilitate the seamless transition from non-EVs to EVs and to alleviate the range anxiety experienced by EV users, substantial improvements in charging infrastructure is required. This involves the development of new fast charging stations and battery-swapping facilities. This research focuses on a step ahead and proposes an innovative solution by providing recharging and battery swapping services to EV users at their preferred time and location with mobile EV recharging and mobile battery swapping vans. The problem is formulated as a Multi-Depot Capacitated Vehicle Routing Problem (VRP) considering Hard Time Windows and Simultaneous Pickup and Delivery, using integer linear programming. The objective is to minimize the total cost of routing the recharging and battery swapping vans from charging stations to customer locations by satisfying the customer’s requirements effectively. The proposed mathematical formulation was tested on a small set of 8 customers and solved using Gurobi solver. Furthermore, this NP-hard problem is tackled by developing heuristics known as large neighborhood search aimed at scalability for larger instances of the problem. The heuristics was successfully implemented and tested for the same small set of 8 customers and a larger instance with two sets (100,200) customers and different depots generated randomly. Therefore, this study introduces an innovative approach to tackle challenges related to EV adoption thereby contributing to a more sustainable and accessible future for electric mobility. [ABSTRACT FROM AUTHOR]

The Fleet Assignment Problem (FAP) deals with assigning aircraft types to the scheduled flights based on fleet capabilities, aircraft availabilities, flight requirements, and operational costs. Due to high operating costs, the large number of flights scheduled each day, and the dependency of the following processes in the airline scheduling processes on FAP output, solving the FAP has always been a challenging task for the airlines. In this work, a revised integer linear programming model is proposed for solving the daily FAP. The model has an objective function of minimizing the operating cost of assigning a fleet type to a specific flight. In addition, the proposed model of the daily FAP aims to satisfy the following constraints: flight cover, aircraft type balance, fleet size, flight traffic (demand), flight flying altitude, and runway length requirements. The proposed model was successfully applied on a real-world dataset related to a national airline and solved using Gurobi software. Furthermore, sensitivity analysis has been performed to show the effect of changing different FAP parameters on the obtained results. [ABSTRACT FROM AUTHOR]

Optimizing supply chain costs is essential for maintaining a cost-effective yet efficient operation that can adapt to market changes. This research focuses on optimizing apparel supply chain costs by maximizing overall efficiency through the application of Data Envelopment Analysis (DEA), a linear programming (LP) approach. Yarn suppliers in the complex fabric supply chain are categorized into effective and average frontiers using DEA, providing a comprehensive evaluation of their performance. To assess independent efficiencies for each DMU, we formulated goal functions and constraints using MATLAB software allowing for a nuanced understanding of supplier performance within the selected subset. The collected data reveals crucial insights into yarn supply chain dynamics, emphasizing factors such as lead time, purchase profit, availability, and purchase quantities. The identification of role models within effective frontiers, depicted as convex curves, establishes benchmarks for suppliers seeking to improve efficiency. Ineffective Decision-Making Units (DMUs) within the curve gain insights into their shortcomings and strategies for improvement. Suppliers can identify role models by determining the shortest distance from effective frontiers, promoting the adoption of best practices. These insights serve as a foundation for strategic decision-making, empowering businesses to optimize supplier relationships and cost-effectively enhance overall supply chain efficiency. Furthermore, this study highlights the importance of advanced computational tools in analyzing complex supply chain networks. [ABSTRACT FROM AUTHOR]

The awareness of the Indonesian people to invest using stock instruments is still low. Therefore, this research is expected to provide an understanding of the risks arising from investment. In this study, we form a model that minimizes the risks and constraints as an investment fund, a particular return from the investor, and stocks purchased in lots units. The risk is measured using the mean semi-absolute deviation of the portfolio return. So, the model is a type of mixed-integer linear programming and will be solved using the branch and bound method. We will use the library Gekko from Python to find the solution to this problem. After we form the portfolio from the model's solution, principal component analysis (PCA) will be used to identify the correlated stocks. We used the stocks in the LQ45 index to form the portfolio and analyzed them using PCA as described before. From the model, we get the portfolio that consists of nine stocks that meet the constraints. However, using data during the financial crisis 2020 (due to the Covid-19 pandemic) in the PCA shows that the difference in proportions between the first up to sixth principal components is not too significant. [ABSTRACT FROM AUTHOR]

Machine learning is the process of discovering patterns in data and using those patterns to forecast or predict future occurrences of those patterns. The machine learning process consists of three steps: input data management, model construction, and model evaluation. Combining machine learning and quantum computing allows for the design and operation of quantum circuits with behavior resembling that of classical machine learning. Variable quantum circuits are frequently used in quantum machine learning. Parameterized variables, a crucial part of variable quantum circuits, must be adjusted in order to achieve good performance of these circuits. It is possible to modify parameterized variables in a variety of ways, such as by using gradient methods or linear programming to determine the circuit's optimal point. This study proposes a method for automatically designing a variational quantum circuit to classify the different datasets, including the well-known 1-dimensional and 2-dimensional datasets, iris and MNIST, using a genetic algorithm to find the best values for the parameterized variables. The Qiskit quantum simulation tools are employed in these experiments. The results show that genetic algorithms can find solutions with greater accuracy than linear-based optimizers by 94 percent and 37.5 percent, respectively, for the iris dataset and the MNIST dataset. [ABSTRACT FROM AUTHOR]

Absolute value detectors implement a widely used spike-detection algorism called absolute value detection. 4-bit absolute value detectors are extensively used in computer storage and acquiring neural signals. As a basic logic component, there's a rising demand for low energy cost and high working frequency. This paper performed a series of optimizations to the conventional design. A traditional absolute value finder is composed of an absolute value finder using ripple-carry adder and multiplexer, and a comparator. In this paper, both parts are redesigned with static-CMOS logic and transmission gate logic (TGL) to shorten critical path. After the circuit topology is determined, two methods are used to control delay and power consumption: sizing logic gates and adjusting supply voltage. A technique called logic effort is used to derive the delay of critical path. By using a linear programming solver, three sets of parameters are found, in which 38.59-unit delay, 52.75-unit energy cost is a balanced design, with the lowest EDP (Energy delay product). [ABSTRACT FROM AUTHOR]

XYZ is a distribution company engaged in food distribution, especially in the rice sector, located in Cimahi City, West Java. The activity carried out by XYZ company are transporting and distributing goods from their distribution center (DC) to end customers daily. The delivery plan for each day is generated based on first-order-first-plan. While transporting products to customers, several delays reduce the customer service level. This problem is mainly caused by the mechanism to plan their daily delivery plan. In this study, the problem is to design a set of routes for vehicle fleets servicing delivery nodes with defined demands and time windows to reduce lateness and total delivery costs. This study implements a mixed-integer linear programming (MILP) model to create a delivery plan to reduce lateness and total delivery costs. In addition, this study also generates a transportation plan using tabu search algorithm to enhance the computational speed. According to the numerical experiment based on the real delivery data, the proposed delivery plan reduces delivery lateness and costs. The proposed delivery plan generated mechanism can reduce the delivery lateness to zero. Furthermore, it also reduces 16,75% of overall travel time in average and transportation cost by about 4,14% in overall. [ABSTRACT FROM AUTHOR]

Building structures are very diverse in their purpose and application. The reliability and safety of their work depends on many factors: geometric dimensions, materials used, acting external loads and their combinations, etc. The more optimal the design scheme is, the less labor-intensive the stages of calculation and design of the corresponding structure will be. If the efficiency criterion is a linear function, and the variables in the constraint system are also linear, then such a problem is a linear programming problem. Of the listed methods of mathematical programming, the most common and developed is linear programming. Solver is a Microsoft Excel add-in that can be used in structural analysis tasks. With its help, you can find the optimal value (maximum or minimum) of the formula contained in one cell, called the target, taking into account the restrictions on variable values in other cells. Simply put, with the help of the Search for a solution add-in, you can determine the maximum or minimum value of one cell by changing other cells. Most often, the Search for a solution add-in is used to solve optimization problems of the economy (simplex method, transport problem, etc.). There are practically no results of using this approach in the calculations of building structures. [ABSTRACT FROM AUTHOR]

Industries use multi-head weigher machines for the automatic packing process of products with heterogeneous characteristics. In this process, the products are supplied to several weighing hoppers, and an optimization program will choose some of them so that the total weight is as close as possible to the package's label weight. This optimization process plays an important role in determining the weight consistency of the final products; thus, any improvement in the optimization strategy will also improve the quality of the overall production process. Furthermore, an improved optimization algorithm is also needed to deal with the more sophisticated design and complex configuration and packaging scenario of recent types of these packing machines. Ant Colony Optimization (ACO) is an optimization algorithm that has already been applied successfully to numerous classical combinatorial optimization problems. This work is an initial study on how ACO should be implemented and how it performs in the context of packing process optimization in multi-head weigher machines. We developed and tested an ACO program for a single-layer multi-head weigher machine in this work. The optimization program was tested on many problem instances consisting of several groups with different difficulty levels. The quality of the solutions produced by the ACO program was evaluated against the results obtained by IBM's Integer Linear Programming (ILP) solver CPLEX. ACO produces optimal results like the ones produced by the ILP solver CPLEX in 97.3 % of all problem instances. Moreover, all results are obtained well under the time of 1 second allocated for the execution. This initial study shows that the ACO algorithm is a potential candidate that can be used as an optimization algorithm in multi-head weigher machines. [ABSTRACT FROM AUTHOR]

The product mix problem is one of the salient issues faced by SMMEs. The study aims to establish a product mix optimisation model to address the problem. To achieve this goal, QM for Windows software is deployed to ascertain an optimal production level to maximise profit for NAYO Aluminum Company fabricators of aluminium products in Enugu (Eastern Nigeria). This software uses raw material and production requirements data to perform optimisation calculations. The analysis includes (1) the number of windows and doors to be produced using the available resources to maximise total income, (2) total costs of production, and (3) gross income. The findings indicate unused resource levels, which helps to manage input resource procurement and minimise waste. The analysis result using QM for Windows, after linear and integer programming, shows an optimal production: 28 aluminium doors and 2 casements (P1 =0; P2 =2; P3 =28, P4 =0) to make the highest income of 119720.00 Naira (Max Z = 1720P1 + 4000P2 + 3990P3 + 2970P4). This application can improve productivity, inventory management and company profitability. [ABSTRACT FROM AUTHOR]

The study aims to obtain information regarding students' representation ability in linear programming courses in the mathematics education department. The method used is a quantitative description with the instrument in the form of a description test and analyzed using the logit size on the Winsteps software. The participants were second-year students who took linear programming courses and had already completed integral calculus subjects. Mathematical representation ability test as an instrument to collect data, then analyzed using Rasch Model. The results showed that students were divided into three levels of representational ability, namely high, medium, and low. Fifty-two students were at the intermediate level, and their verbal representation skills contributed to low scores. Many indicators with a high level of difficulty for students cause the low representation ability. Some answers are related to each other so that there are answers that are affected. This research impacts the need to improve the ability of students, one of which can be through changes in learning methods because the chosen representations-oriented teaching may influence students' representations. [ABSTRACT FROM AUTHOR]

Additive manufacturing (AM) or 3D printing (3DP) has been considered as revolutionary in terms of manufacturing and its impact on supply chain configurations This paper attempts to investigate the economic and environmental benefits of using 3D Printing (3DP) technology through constructing two scenarios for the location of 3DPs, namely a centralized and a discrete decentralized 3DP locations, taking into consideration different number of printers at different number of warehouses and/or different number of stores. The paper studies these scenarios from the perspective of a spare parts retailer, using the hazard button with relevant empirical data, as a real-life case study. A linear programming model has been developed, with an objective function setup to minimize total costs, that is broken down into transportation, inventory, overhead, labour and production costs, as well as the quantity of 3DPs deployed across different locations. The model thus, functions as a decision-making tool for stakeholders in determining the optimal placement of 3DP resources within the supply chain. The study concludes by demonstrating tipping points where 3DP deployment decisions shift between different configurations. Notably, labour costs significantly influence decision-making, particularly in high-wage countries like Germany. [ABSTRACT FROM AUTHOR]

This study aims to address the One-Dimensional Cutting Stock Problem (1D-CSP) by developing an optimized approach for designing cutting plans for one-dimensional construction materials with the primary goal of minimizing material waste during the cutting process. The methodology involves the implementation of a Matlab algorithm based on linear programming principles and uses data derived from previous studies to formulate efficient cut-off plans. The investigation entails an analysis of the collected data from relevant studies, focusing on total material consumption and loss within the cutting plans. The study begins by considering foundational variables, which encompass the length of the standard linear inventory, the required lengths for each type, and the overall quantity of required lengths. These parameters are then processed using Matlab software to establish a solution through linear programming. The comparative analysis involves evaluating the collected data to demonstrate the advantages of the proposed model. This comparison encompasses the assessment of standard linear inventory utilization, material utilization effectiveness, and the residual waste generated during the cutting process. In comparison to the first relevant research, the developed method yields a material cutting plan with a loss rate of 1.21%, requiring less than one standard linear material inventory—improving upon the original result of 1.24%. Similarly, when compared to the second relevant study involving ten cases, the developed method generates a material cutting plan with a loss rate of 6.45%, utilizing fewer than three standard linear materials. [ABSTRACT FROM AUTHOR]

This research article proposed three distinct Average Methods with various mean technique is used to determine a solution of the Multi-Objective Linear Programming Problem (MOLPP) in Neutrosophic environment. A Numerical illustration is given to explain the effectiveness of the methods. [ABSTRACT FROM AUTHOR]

This paper provides healthy lifestyle of diabetic patients by using mathematical modeling. In this paper we construct a mathematical model of diet planning for diabetes. The formulated mathematical model is the application of linear programming and integer programming. All the requirements and restrictions were fulfilled in the mathematical model which was developed in this paper. An optimal and feasible solution was produced by using linear and integer programming. This optimal solution gives the diet problem of diabetic patients. All the constraints and objective functions are defined in the diet problem. To provide daily needs of supplement for the particular age of diabetic patients. [ABSTRACT FROM AUTHOR]

A kinematic limit analysis approach for three-dimensional curved rigid blocks is presented. To maintain the exact geometry of curved structures in a three-dimensional context, NURBS solids are used. Under the hypotheses of rigid elements and frictional behavior at interfaces, a kinematic limit analysis problem is defined and solved through a linear programming formulation. The Gothic arches in the Carmo convent, Lisbon (Portugal), are studied to prove the efficiency of the method. [ABSTRACT FROM AUTHOR]

The global trend to combat climate change by maintaining the balance of climate-active gases has a significant impact on the economic, social, and environmental spheres around the world. One of the important aspects of its solution is the construction of economic models that encourage businesses to "green up". The publication considers an economic model for making calculations on obligations related to compensation of greenhouse gas emissions by companies, financial support for environmental services, sale of rights to additional emissions. Data on mutual obligations can be presented in a matrix, where indexes determine the enterprises between which obligations have arisen, and the element of the matrix is the value of the obligation. The information on mutual obligations of enterprises presented in the matrix allows you to calculate the values of the balance of the settlement participants. The problem of minimizing mutual obligations is a linear programming problem with a special structure of the constraint matrix. In the matrix of coefficients, we can distinguish a matrix with a structure characteristic of the transport problem of linear programming. To solve it, we have developed an algorithm. It allows you to find the optimal distribution of mutual debts in a finite number of steps and has the following main advantages: firstly, step-by-step compliance with the rules for conducting financial transactions; secondly, taking into account the features of filling with non-zero elements of the matrix containing information about obligations. [ABSTRACT FROM AUTHOR]

This article used MATLAB to resolve the fuzzy assignment, fuzzy transportation, and fuzzy linear programming problems. Cell arrays in MATLAB are used to hold fuzzy numbers that are later converted to crisp numbers in the Fuzzy Assignment Problem, Fuzzy Transportation Problem, and Fuzzy Linear Programming Problem. The obtained Crisp Linear Programming Problem, Transportation Problem and Assignment Problem are solved using the built-in function linprog and other MATLAB codes. The techniques are well elucidated in detail. [ABSTRACT FROM AUTHOR]

In this manuscript, we solve Interval linear programming problem (ILP) with help of new interval arithmetic operation. This work gives the feasible and maximal solution space (Close to the optimal solution (OS)) for all type of ILP. Main thought of this work is to reduced solution space of ILP and also analyzing this study with some previous methods such as, ILP, TSM, BWC, ISOM—2, ITSM and SOM—2. The solution space (SS) of this work is unquestionably compromised with some other methods. Finally, several methods are presented in order to enlighten the proposed method by comparing it to other methods and the best solution. [ABSTRACT FROM AUTHOR]

Scheduling is the process of allocating resources or machines to carry out a set of tasks for a certain period. Scheduling based on process flow can be divided into flow shop and job shop. Flow shop scheduling is sequencing several jobs that each job has the same operation, and the second job cannot be done before the first job is completed. Flow shop scheduling becomes the main topic related to fulfilling orders on time. This paper presents the design of the flow shop scheduling system in sausage production. The proposed formulations are to design the buffer stock prediction model to determine the quantity of sausage production and design the flow shop scheduling model to minimize makespan. Recognizing business processes that occur in the system is the first step before the system is modeled. Business processes are presented in BPMN. Then, system modeling is documented in the Unified Modelling Language (UML). Buffer stock prediction model is solved using Ordinary Least Square (OLS) or multiple linear regression, and flow shop scheduling model is solved using Mixed-integer Linear Programming (MILP). In the buffer stock model, the predictors can explain the expected target linearly, and the model provides the predictive value of production level with a small error and accuracy of more than 90%. Then, the flow shop scheduling model can give the sequence of sausage production jobs that results in the shortest makespan. [ABSTRACT FROM AUTHOR]

The implementation of Demand Side Management (DSM) for an industrial plant by solving a Unit Commitment Problem (UCP) is hoped to solve imbalances between electricity supply limitations and demand requirements which many times lead to partial or total shutdown of production plants because of trips due to under voltage or high frequency, when the supply is overloaded or a unit is suddenly stopped. While there is a need to maintain production. For the purpose of this study, a cement industry was divided into operating units and simulated under two scenarios and solved using Mix Integer Linear Programming (MILP) in an Excel solver. The result shows that there is a reduction in cost by 30 percent from $1,203 to $880 for same production requirement. [ABSTRACT FROM AUTHOR]

Computational analysis of fracture in materials with inclusions is considered as a multi-domain problem. Cracks may appear inside the materials or along material interfaces. The computational model introduces two independent damage parameters which enable to represent fracture by mechanical damage. One of the parameters is defined at the interface, considering it as a thin adhesive layer. The interface damage supposes general stress-strain relationships to behave like in cohesive zone models. The other damage parameter defined for the structural domains is based on the theory of phase-field fracture which causes elastic properties degradation only in a narrow material strip that forms a smeared crack. Both these damaging schemes are expressed in a unique quasi-static energy evolution process, the proposed computational approach is thus introduced in a variational form. The solution is approximated by a staggered time stepping procedure related to a separation of deformation variables from damage ones. Both the deformation solution and damage solution at each instant are obtained by non-linear programming algorithms implemented together within a MATLAB finite element code. The numerical simulation with the model includes a simplified material element with inclusions. [ABSTRACT FROM AUTHOR]

A stochastic programming problem is an optimization model in the presence of uncertainty over time. Essentially, this model is proposed to replace the deterministic model, in which the unknown coefficient or parameter is random and the probability distribution is assumed to be independent of the decision variable. The key to solve the stochastic programming problem is to transform the model to be the model of the linear programming problem. It is possible because of the improbability and time which can be modeled as kinds of scenarios. In other words, the observator does not wear the probability function distribution to present the improbability because of function distribution can cause discontinuity and non-convexs. In this paper a heuristic method is proposed to find the scenario of the stochastic programming problems. [ABSTRACT FROM AUTHOR]

Robust optimization (RO) assumes that uncertain data has a convex set and a bounded set called uncertainty and seeks a solution that is feasible for all possible data parameters. This paper discusses a decomposition method for solving a robust optimization problem. Benders' decomposition, which is typically used to solve large scale integer programming problems, is investigated in order to crack down on the model's uncertainty. [ABSTRACT FROM AUTHOR]

Productivity is the relationship between the amount of output produced and the number of inputs required to produce that output. Data Envelopment Analysis (DEA) is a linear programming-based mathematical programming technique used to measure and evaluate the productivity of a decision-making unit that is responsible for using a number of inputs to obtain a targeted output. In many cases, the input and output values can only be integers. Rounding real numbers will produce inaccurate results in this case. This paper discusses the Data Envelopment Analysis (DEA) problem of determining the size of the productive scale with real and integer value data. [ABSTRACT FROM AUTHOR]

This paper investigates a multimodal system that integrates the general dial-a-ride problem with a set of fixed-line vehicles having a flexible schedule. The passenger trips are made in a three-stage journey using a dial-a-ride vehicle and a fixed-line bus. Passengers are picked up from an origin point and transferred to a collecting point via a dial-a-ride vehicle. Then, fixed-route buses transfer passengers to a second collecting point where another dial-a-ride vehicle will pick up and transfer them to their requested destination. The main objective of this integration is to reduce the total trip cost by carrying part of it through cheaper fixed-route service while maximizing the utilization of seats in the fixed-route vehicle. The model provides each fixed line with a suggested start time. A mixed-integer linear programming model was developed for the problem, and computational testing on small-size instances has been carried out to demonstrate the viability of the proposed system. [ABSTRACT FROM AUTHOR]

Batujai and Pengga Reservoirs are water infrastructure with a cascade operation system. The water source comes from the Penujak River of the Dodokan River Basin in Central Lombok District, West Nusa Tenggara Province. Batujai Reservoir began its operation since 1982 with a storage capacity of 15.59 million m3, and a storage area of 5.89 km2. This reservoir was built to meet the water demands of the Batujai Irrigation Area, which covers 3,390 ha, and domestic water of 130 l/sec. Pengga Reservoir is located about 13 km at the downstream of Batujai Reservoir with a storage capacity of 27.00 million m3, and its operation started in 1995. Pengga Reservoir serves the irrigation water in West Lombok District with an area of 3,189 ha. The two reservoirs have been operating for quite a long time, therefore, there is a decrease in effective storage capacity due to sedimentation. This problem has impact on the operational performance of the two reservoirs in serving the irrigation and the domestic water. Therefore, it is necessary to conduct research to improve the performance of water utilization in the cascade reservoir system by considering the current condition of reservoir and water demands. This study aims to maximize the annual cropping intensity by optimizing release of water in both reservoir simultaneously. The optimization model was formulated using linear programming method by considering water availability, priorities for water supply, storage characteristics, cropping pattern, and cropping schedule. The model formulation used k factor, the ratio between actual release and target release discharges according to the water demand with a minimum value of 0.7 for irrigation water, and 0.85 for domestic water. Evaluation of optimization results uses several indicators of water utilization, namely planted area, crop intensity, and reliability of water supply, which was calculated for a dry year, normal year, and wet year inflow condition. [ABSTRACT FROM AUTHOR]

Bener Reservoir was built in Guntur Village, Purworejo Regency, Central Java Province. It was designed to serve various purposes, such as domestic water supply, irrigation water supply, and micro-hydro-electric power generation. Reservoir operating rules are essential to maximizing supply capacity to cater to these water demands. This study aims to determine the optimal water release by considering the water needs hierarchy and five alternative cropping schedules applied in the study area. For this purpose, an optimization model was developed using the linear programming method to obtain optimal water release for all water demands. Inputs for the optimization include water availability, irrigation water demand, domestic water demand, and reservoir characteristics. Water availability was calculated based on the daily discharge observed at the Penungkulan Weir, located approximately 5 km downstream of the Bener Dam. The irrigation areas served by Bener Dam include Guntur, Penungkulan, Kedungputri, Boro, and development irrigation areas with a total area of 12,314 Ha. The irrigation water demand was calculated according to Irrigation Standards Planning Criteria-01. The domestic water demand used was 1.5 m3s−1. Several criteria were used to assess the application of the optimization model, consisting of the cropping intensity, factors to fulfil water needs: k, and reliability of water supply for domestic water and irrigation water. The determination of the optimal variable values was carried out using the Solver Tool of Microsoft Excel. The alternative selected in the optimization was to vary the cropping schedule. Each alternative starts two weeks later than the previous one, beginning from the third week of September. Optimization was carried out for wet, normal, and dry year inflow scenarios. The results indicated that applying the linear programming optimization model may significantly optimize domestic water and irrigation water services. In conclusion, the first alternative of cropping schedule produced a higher crop intensity and k factor value. Optimization with wet, normal, and dry year inflow scenarios resulted in cropping intensity reaching 300% and all water services performing 100% reliability. In addition, the minimum value of the k factor for domestic and irrigation water was 0.85 and 0.80, respectively. These assessment results may be utilized to develop an appropriate rule curve of Bener Reservoir operations. [ABSTRACT FROM AUTHOR]

Bottleneck transportation problems have significant importance not only in military operations and disaster situations but also in higher education field, wherein in those cases time is a very important factor when supplying to the destination. In linear programming problems, there are the minimum and maximum problems, allocating products from source to destination which is known as the Transportation Problems. This bottleneck problem in the Islamic Higher Education Enrollment is formulated mathematically with transportation barriers that are commonly found in everyday life. In this research, an algorithm is shown to find the optimal solution by determining Z from the transportation table from the calculation of the initial feasible solution, then form a pseudo-cost matrix as a cell reference that must be minimized, rearrange the matrix and check on, if=0 then the solution already optimal if not then repeat from step to form pseudo cost matrix. From the case of unbalanced data in the Islamic Higher Education Enrollment with a data size of 4x6, the optimal solution is 2775 units of time with 2 iterations, the optimal solution from the Mallia-Das algorithm, when compared to the NWC method, is 2885 and VAM is 2725, still the minimum optimal solution for the VAM method. Although it produces an optimal solution that is slightly larger than the VAM method, the Mallia-Das algorithm for the bottleneck case is superior because it pays attention to the bottlenecks. [ABSTRACT FROM AUTHOR]