Production sequencing in a flow shop system using optimization and heuristic algorithms

abstract: The purpose of the research was to determine the sequencing of the production of n jobs in m operations in a small footwear company in an environment of flow shop machine characteristics, which optimizes the total time of completion of the job in the production system (Makespan). We used heuristic algorithms that were applied through Lekin and WinQSB softwares, and for the optimization algorithm we designed a mathematical model that was solved by Juliabox software. Results show that the integer linear programming and local search minimize the makespan with 3807 minutes, and different production sequences for each algorithm, which consider permutation, which improves the traditional way of programming the production in 97 minutes, however, the optimization presents better results in the performance measures of average waiting time, average time of flow, and average job in process. Application of heuristic algorithms proves to be simple and fast, but the mathematical model of optimization designed and encoded in the software is a flexible and valuable tool for decision making in production programming, which could be applied in other footwear companies, and in other productive sectors whose companies have the same characteristics of the case study, reducing costs and improving delivery times.

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The Art and Science of Modeling Decision-Making Under Severe Uncertainty

Decision Making in Manufacturing and Services ◽

10.7494/dmms.2007.1.2.111 ◽

2007 ◽

Vol 1 (2) ◽

pp. 111-136 ◽

Cited By ~ 20

Author(s):

Moshe Sniedovich

Keyword(s):

Mathematical Modeling ◽

Mathematical Model ◽

Decision Making ◽

Case Analysis ◽

Worst Case Analysis ◽

Art And Science ◽

Worst Case ◽

Severe Uncertainty ◽

The Mathematical Model

For obvious reasons, models for decision-making under severe uncertainty are austere. Simply put, there is precious little to work with under these conditions. This fact highlights the great importance of utilizing in such cases the ingredients of the mathematical model to the fullest extent, which in turn brings under the spotlight the art of mathematical modeling. In this discussion we examine some of the subtle considerations that are called for in the mathematical modeling of decision-making under severe uncertainty in general, and worst-case analysis in particular. As a case study we discuss the lessons learnt on this front from the Info-Gap experience.

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Modelling and Simulation of NO2 Dispersion Phenomenon in Atmosphere by Analytical-Experimental Methods

Revista de Chimie ◽

10.37358/rc.08.10.1979 ◽

2008 ◽

Vol 59 (10) ◽

Author(s):

Delia Perju ◽

Harieta Pirlea ◽

Gabriela-Alina Brusturean ◽

Dana Silaghi-Perju ◽

Sorin Marinescu

Keyword(s):

Mathematical Model ◽

Nitrogen Dioxide ◽

Modeling And Simulation ◽

Human Health ◽

Experimental Methods ◽

Negative Effects ◽

Real Situation ◽

Experimental Values ◽

The Mathematical Model

The European laws and recently the Romanian ones impose more and more strict norms to the large nitrogen dioxide polluters. They are obligated to continuously improve the installations and products so that they limit and reduce the nitrogen dioxide pollution, because it has negative effects on the human health and environment. In this paper are presented these researches made within a case study for the Timi�oara municipality, regarding the modeling and simulation of the nitrogen dioxide dispersion phenomenon coming from various sources in atmosphere with the help of analytical-experimental methods. The mathematical model resulting from these researches is accurately enough to describe the real situation. This was confirmed by comparing the results obtained based on the model with real experimental values.

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Developing an Analytical Model and Computing Tool for Optimizing Lapping Operations of Flat Objects Made of Alloyed Steels

Materials ◽

10.3390/ma13061343 ◽

2020 ◽

Vol 13 (6) ◽

pp. 1343 ◽

Cited By ~ 2

Author(s):

Tudor Deaconescu ◽

Andrea Deaconescu

Keyword(s):

Mathematical Model ◽

Surface Roughness ◽

Material Properties ◽

Depth Of Cut ◽

Operation Optimization ◽

Abrasive Grains ◽

Finishing Process ◽

Real World Applications ◽

The Mathematical Model

Lapping is a finishing process where loose abrasive grains contained in a slurry are pressed against a workpiece to reduce its surface roughness. To perform a lapping operation, the user needs to set the values of the respective lapping conditions (e.g., pressure, depth of cut, the rotational speed of the pressing lap plate, and alike) based on some material properties of the workpiece, abrasive grains, and slurry, as well as on the desired surface roughness. Therefore, a mathematical model is needed that establishes the relationships among the abovementioned parameters. The mathematical model can be used to develop a lapping operation optimization system, as well. To this date, such a model and system are not available mainly because the relationships among lapping conditions, material properties of abrasive grains and slurry, and surface roughness are difficult to establish. This study solves this problem. It presents a mathematical model establishing the required relationships. It also presents a system developed based on the mathematical model. In addition, the efficacy of the system is also shown using a case study. This study thus helps systematize lapping operations in regard to real-world applications.

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Applied Mathematical Approach for Decision-Making in Building Plan Design

Asian Journal of Behavioural Studies ◽

10.21834/ajbes.v3i9.59 ◽

2018 ◽

Vol 3 (9) ◽

pp. 39

Author(s):

Grit Ngowtanasuwan

Keyword(s):

Mathematical Model ◽

Mathematical Models ◽

Publishing House ◽

Unit Cost ◽

Construction Cost ◽

Model Unit ◽

International Publishing ◽

Plan Design ◽

The Mathematical Model

This article presents a method for solving decision in building plan design by using a mathematical model (nonlinear programming). First objective is to formulate mathematical models for analysis in dividing rooms and dimensions in a building plan. Secondly, to calculate the dimensions and room sizes which have minimum construction cost. A case study of a condominium building plan was analyzed in this research. The results found application of the mathematical model was applicable. The mathematical models were formulated, the minimum construction cost was ฿723,000 (US$24,100) and usable area in the condominium was 67.5 m2 and followed the assigned design constraints.Keywords: Building plan design; Mathematical model; Unit cost;eISSN 2398-4295 © 2018. The Authors. Published for AMER ABRA cE-Bs by e-International Publishing House, Ltd., UK. This is an open-access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer–review under responsibility of AMER (Association of Malaysian Environment-Behaviour Researchers), ABRA (Association of Behavioural Researchers on Asians) and cE-Bs (Centre for Environment-Behaviour Studies), Faculty of Architecture, Planning & Surveying, Universiti Teknologi MARA, Malaysia. DOI:

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A General Modeling Approach for Shock Absorbers: 2 DoF MR Damper Case Study

Frontiers in Materials ◽

10.3389/fmats.2020.590328 ◽

2021 ◽

Vol 7 ◽

Author(s):

Jorge de-J. Lozoya-Santos ◽

Juan C. Tudon-Martinez ◽

Ruben Morales-Menendez ◽

Olivier Sename ◽

Andrea Spaggiari ◽

...

Keyword(s):

Mathematical Model ◽

Degrees Of Freedom ◽

Linear Models ◽

Mr Damper ◽

Shock Absorbers ◽

Magneto Rheological ◽

The Mathematical Model ◽

Force Displacement ◽

Standard Tests

A methodology is proposed for designing a mathematical model for shock absorbers; the proposal is guided by characteristic diagrams of the shock absorbers. These characteristic diagrams (Force-Displacement, Velocity-Acceleration) are easily constructed from experimental data generated by standard tests. By analyzing the diagrams at different frequencies of interest, they can be classified into one of seven patterns, to guide the design of a model. Finally, the identification of the mathematical model can be obtained using conventional algorithms. This methodology has generated highly non-linear models for 2 degrees of freedom magneto-rheological dampers with high precision (2–10% errors).

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An Estimation of Dates Production Function in Karbala Governorate For The Agricultural Season 2020 (Al-jadual Al-gharby District A case Study)

IOP Conference Series Earth and Environmental Science ◽

10.1088/1755-1315/923/1/012070 ◽

2021 ◽

Vol 923 (1) ◽

pp. 012070

Author(s):

Sadeq H. Hussein ◽

Hayder Hamed Blaw

Keyword(s):

Mathematical Model ◽

Least Squares ◽

Production Function ◽

Returns To Scale ◽

Ordinary Least Squares ◽

Total Production ◽

Logarithmic Function ◽

The Mathematical Model

Abstract This study aimed to detect the most important factor that affects dates production. About 108 questionary forms collecttted palm orchard farmers in Karbala to estimate the dates production function in Karbala governorate for the agricultural season 2021 (the district of Al-jadual Al-Gharby). The study distributed those formmmsss for about 10% of the total palm orchards in Al-jadual Al-Gharby district of the holy governorate of Karbala. The study used the method of ordinary Least squares (OLS) to estimate the mathematical model of the function. The results showed that the double Logarithmic function in terms of its estimation of the estimated Coefficients by one unit leads to a corresponding change in the produced quality of dates and the same direction by 0.188 0.808) % respectively, and that the capital variable is more in fluently in production than the work variable. As for the total production elasticity (the sum of the partial elasticities of the resources used), which represents returns to scale, it amounted to about (0.996), which indicates a decrease in the return to scale.

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Estimating the Optimum Tilt Angles for South-Facing Surfaces in Palestine

Energies ◽

10.3390/en13030623 ◽

2020 ◽

Vol 13 (3) ◽

pp. 623 ◽

Cited By ~ 5

Author(s):

Ramez Abdallah ◽

Adel Juaidi ◽

Salameh Abdel-Fattah ◽

Francisco Manzano-Agugliaro

Keyword(s):

Mathematical Model ◽

Solar Radiation ◽

Tilt Angle ◽

Peak Power ◽

Horizontal Surface ◽

Geographical Information ◽

Solar Panels ◽

Energy Gains ◽

The Mathematical Model

The optimum tilt angle of solar panels or collectors is crucial when determining parameters that affect the performance of those panels. A mathematical model is used for determining the optimum tilt angle and for calculating the solar radiation on a south-facing surface on a daily, monthly, seasonal, semi-annual, and annual basis. Photovoltaic Geographical Information System (PVGIS) and Photovoltaic Software (PVWatts) is developed by the NREL (US National Renewable Energy Laboratory) are also used to calculate the optimum monthly, seasonal, semi-annual, and annual tilt angles and to compare these results with the results obtained from the mathematical model. The results are very similar. PVGIS and PVWatts are used to estimate the solar radiation on south-facing surfaces with different tilt angles. A case study of a mono-crystalline module with 5 kWP of peak power is used to find out the amount of increased energy (gains) obtained by adjusting the Photovoltaic (PV) tilt angles based on yearly, semi-annual, seasonal, and monthly tilt angles. The results show that monthly adjustments of the solar panels in the main Palestinian cities can generate about 17% more solar energy than the case of solar panels fixed on a horizontal surface. Seasonal and semi-annual adjustments can generate about 15% more energy (i.e., it is worth changing the solar panels 12 times a year (monthly) or at least 2 times a year (semi-annually). The yearly optimum tilt angle for most Palestinian cities is about 29°, which yields an increase of about 10% energy gain compared to a solar panel fixed on a horizontal surface.

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Cost Element Modelling, Prediction and Optimization in a Dual-Completion Well During a Coiled Tubing Unloading Operation

10.2118/207113-ms ◽

2021 ◽

Author(s):

Merit P. Ekeregbe

Keyword(s):

Mathematical Model ◽

Decision Making ◽

Cost Estimation ◽

Oil And Gas ◽

Oil And Gas Industry ◽

Correct Prediction ◽

Reservoir Pressure ◽

Gas Industry ◽

Coiled Tubing ◽

The Mathematical Model

Abstract In an era where cost is a significant component of decision making, every possibility of reducing operational cost in the Oil and Gas industry is a welcome development. The volatile nature of the Oil market creates uncertainty in the industry. One way to manage this uncertainty is by the ability to predict and optimize our operations to reduce all of our cost elements. When cost is planned and predicted as accurately as possible, the operation optimizations can be managed efficiently. Practically, all new drills require CT unloading of the completion or kill fluids to allow the natural flow of the wells. Hitherto, there is no mathematical model that combines information from one of the wells in an unloading dual completion project that can be used to aid decision-making in the other well for the same unloading project and thereby result in an effective cost-saving. Deploying the mathematical model of cost element prediction and optimization can minimize operational unloading costs. The two strings of the dual completion flow from different reservoirs. Still, the link between the two drainages post completion is the kill fluid density, and can aid in cost estimation for optimum benefit. The lesson learned or data acquired from the lifting of the slave reservoir string can be optimized to effectively and efficiently lift the master reservoir string. The decision of first unloading the slave reservoir string is critical for correct prediction and optimization of the ultimate cost. The mathematical model was able to predict the consumable cost elements such as the gallon of nitrogen and time that may be spent on the long string from the correlative analysis of the short string. The more energy is required for unloading the short string and it is the more critical well than the long string because it is the slave string since no consideration as such is given to it when beneficiating the kill fluid to target the long string reservoir pressure with a certain safety overbalance. The rule for the mud weight or the weight of the kill fluid is the highest depth with highest reservoir pressure which is the sand on the long string. With the data from the short string and upper sand reservoir, the lift depth and unloading operation can be optimized to save cost. The short string will incur the higher cost and as such should be lifted last and the optimization can be done with the factor of the LS.

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Cooperative Target Allocation for UCAV Team Air-to-Ground Attack Based on Decision Graph Bayesian Optimization Algorithm

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.457-458.655 ◽

2012 ◽

Vol 457-458 ◽

pp. 655-662

Author(s):

Lu Cao ◽

An Zhang ◽

Feng Juan Guo

Keyword(s):

Mathematical Model ◽

Decision Making ◽

Optimization Algorithm ◽

Optimal Solution ◽

Bayesian Optimization ◽

Bayesian Optimization Algorithm ◽

Decision Graph ◽

Target Allocation ◽

Cooperative Decision Making ◽

The Mathematical Model

In order to control and optimize cooperative air-to-ground attack decision-making of the unmanned combat aerial vehicle (UCAV) team, the principle of income maximum and loss minimum of UCAV team is built firstly. Accordingly, the mathematical model of cooperative target allocation is built based on the decision variables and constraints. Then Bayesian optimization algorithm (BOA) is introduced which is one kind of the evolution algorithm. For improving the ability of the BOA, decision graph is introduced to enhance the represent and learn of Bayesian network and compress the parameter saving. Finally decision graph Bayesian optimization algorithm (DBOA) is utilized to optimize and analyze the model. The simulation results verify that the mathematical model of cooperative target allocation can reflect the importance of cooperative decision-making, the DBOA can converge quickly to the global optimal solution and can effectively solve the cooperative target allocation problem of UCAV team air-to-ground attack.

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SOLVING RESOURCE-CONSTRAINED CONSTRUCTION SCHEDULING PROBLEMS WITH OVERLAPS BY METAHEURISTIC

Journal of Civil Engineering and Management ◽

10.3846/13923730.2014.906496 ◽

2014 ◽

Vol 20 (5) ◽

pp. 649-659 ◽

Cited By ~ 20

Author(s):

Wojciech Bożejko ◽

Zdzisław Hejducki ◽

Mariusz Uchroński ◽

Mieczysław Wodecki

Keyword(s):

Assembly Line ◽

Flow Shop ◽

Construction Process ◽

Scheduling Problems ◽

Construction Scheduling ◽

Efficient Construction ◽

Scheduling Method ◽

Hard Problems ◽

Reducing Costs

The paper concerns the problem of roadworks scheduling executed in the flow-shop system. Works may be performed parallelly with the acceleration (overlaps) of construction project, i.e. the following work on the assembly line can begin before the completion of the predecessor work. Taking into account the acceleration enables accurate modeling of complex real construction processes. The above fact can greatly shorten the time of realization of construction process which has a direct impact on reducing costs. The considered issue belongs to the class of NP-hard problems. We introduce the new: mathematical model, specific properties as an acceleration tools, as well as two new optimization algorithms for the problem considered: construction and tabu search. The execution of algorithms was illustrated on the example of a case study concerning the construction of roads. They were also verified on the examples taken from the literature and on already completed construction processes. The obtained results are fully satisfactory. The assigned execution times are close to optimal. The presented methods allow its practitioners (both the planners and the managers) to include in the model the acceleration of the works and the design of a much more efficient construction scheduling. The presented new scheduling method leads to a more competitive environment for contraction companies.

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