Unit iii-2-sp
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The document discusses sequencing problems in operations research. It defines key terminology used in sequencing problems, such as processing time and total elapsed time. It also presents Johnson's algorithm for sequencing jobs on two machines, which sequences jobs by starting with the job having the smallest processing time on the first machine. Examples are given of applying the algorithm to problems with different numbers of jobs and machines.
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The document discusses sequencing models for production processes involving multiple jobs and machines. It defines sequencing as finding the optimal order of jobs to minimize total processing time. The objective is to determine the best sequence of jobs across machines. It provides assumptions of the models and describes different types of sequencing problems involving various numbers of jobs and machines. Solution methods discussed include Gantt charts and converting problems with more than two machines into equivalent two-machine problems.
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This document discusses line balancing, which involves arranging machine capacity and workstation tasks to ensure uniform workflow and minimize idle time. It aims to balance workloads, identify bottlenecks, determine the optimal number of workstations, and reduce costs. The key aspects of line balancing are precedence constraints, which require some tasks to be completed before others, and cycle time restrictions, which set a maximum time for each workstation. Balanced lines promote efficient one-piece flow and minimize waste, while unbalanced lines cause excessive workload, variation and idle time. The line balancing process involves drawing precedence diagrams, determining cycle times, assigning tasks to workstations, and calculating line efficiency.
Chapter 2 line_balancing no pics
This document discusses techniques for line balancing to meet production goals efficiently. It defines an assembly line as composed of work stations where specific operations are performed. The line must be balanced so work flows evenly between stations. Common approaches to balancing include estimating operator needs and work element sharing between stations. An example problem applies techniques like determining standard times, calculating cycle times, and identifying the slowest station. The goal is to balance workloads across stations while meeting production rate targets.
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Ranked Positional Weight Method | Management
The Ranked Positional Weight Method is a technique used for assembly line balancing that takes into account precedence relationships and task processing times. It involves calculating a Ranked Positional Weight for each work element based on duration and precedence, arranging them in descending order, and then assigning them to workstations to optimize time, machinery, labor and output. The example shows the steps of constructing a precedence diagram, calculating RPW values, ordering by RPW, and assigning elements to six workstations with the goal of minimizing idle time.
Recommended
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Line balancing ppt By Wakil Kumar
The document summarizes key concepts related to line balancing problems in manufacturing. It defines terms like minimum work element, total work content, workstation process time, cycle time, and precedence constraints that are important to consider when balancing a production line. It also describes the largest candidate rule method for assigning work elements to stations in a way that aims to balance station times and meet production rate requirements while respecting precedence constraints.
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This document discusses line balancing, which involves arranging machine capacity and workstation tasks to ensure uniform workflow and minimize idle time. It aims to balance workloads, identify bottlenecks, determine the optimal number of workstations, and reduce costs. The key aspects of line balancing are precedence constraints, which require some tasks to be completed before others, and cycle time restrictions, which set a maximum time for each workstation. Balanced lines promote efficient one-piece flow and minimize waste, while unbalanced lines cause excessive workload, variation and idle time. The line balancing process involves drawing precedence diagrams, determining cycle times, assigning tasks to workstations, and calculating line efficiency.
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This document discusses techniques for line balancing to meet production goals efficiently. It defines an assembly line as composed of work stations where specific operations are performed. The line must be balanced so work flows evenly between stations. Common approaches to balancing include estimating operator needs and work element sharing between stations. An example problem applies techniques like determining standard times, calculating cycle times, and identifying the slowest station. The goal is to balance workloads across stations while meeting production rate targets.
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Ranked Positional Weight Method | Management
The Ranked Positional Weight Method is a technique used for assembly line balancing that takes into account precedence relationships and task processing times. It involves calculating a Ranked Positional Weight for each work element based on duration and precedence, arranging them in descending order, and then assigning them to workstations to optimize time, machinery, labor and output. The example shows the steps of constructing a precedence diagram, calculating RPW values, ordering by RPW, and assigning elements to six workstations with the goal of minimizing idle time.
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This document provides an overview of industrial engineering topics including line balancing, assembly lines, and progress control. It discusses types of assembly lines like single model, mixed model, and multi model lines. Line balancing aims to distribute work evenly across stations to minimize idle time. Methods like heuristic assignment are used. Progress control monitors production schedules and addresses delays to ensure schedules are met.
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The document describes a study conducted to improve productivity at Champion Brewery in Nigeria through line balancing. Researchers used a heuristic method called Longest Operation Time to balance the production line for Champion lager beer. Currently the line has 9 workstations and takes 12856 seconds to produce one pallet, with a cycle time of 108 seconds per crate. Researchers analyzed task times, calculated station times, and identified bottlenecks. They determined the theoretical minimum number of workstations is 3 based on total work content and desired daily output. Balancing the line to have 3 workstations instead of 9 will improve efficiency by reducing idle time.
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This document discusses line balancing in manufacturing, which aims to evenly divide work among workstations in a production process. The goal is to determine the optimal number of workstations, tasks assigned to each, and minimum resources needed. Key terms defined include tasks, task times, cycle time, workstations, and more. Common line balancing procedures involve determining tasks, precedence, times, cycle time, and minimum workstations. Computer programs now help balance large production lines using heuristics like incremental utilization and longest task time.
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This document introduces the force equilibrium method for analyzing various metal forming processes. It discusses types of forming processes like rolling, forging, drawing, bending, and extrusion. The force equilibrium method is used to determine important parameters like the roll separating force in rolling, the forging force, drawing force, and bending moment. It provides the key assumptions made in analyzing each process, such as constant yield stress and coefficient of friction. Formulas are presented for calculating forces, stresses, and dimensions in each process. The objective is to correlate initial and final workpiece dimensions and accurately estimate the required forming forces.
Balancing the line by using heuristic method based on cpm in salbp –a case study
Abstract
In mass production systems, line balancing plays a great role, but this is not easy even if it is a simple straight line. So, in order to
solve these problems Heuristic methods are very much desirable. It is also found that Heuristic methods play a great role in the
formation of metaheuristic methods.Therefore it is very much important to use more efficient heuristic methods. In this research
paper we presents a heuristic method that is based on critical path method for simple assembly line balancing. This research is
mainly concerned with objectives of minimizing the number of workstations, improvement of smoothness index, mean absolute
deviation (MAD) and increasing line efficiency.
Keywords-Heuristic methods,Assembly line balancing problem, Critical path method, Simple assembly line balancing.
Assembly line balancing
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This presentation provided an overview of Ishikawa's seven basic quality tools: histograms, Pareto charts, cause-and-effect diagrams, run charts, scatter diagrams, flow charts, and control charts. For each tool, the presentation defined the tool, explained how to construct it, and provided an example of how the tool can be used. The tools are designed to be simple visual aids to help analyze data, identify relationships and causes, improve processes, and monitor quality.
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The document discusses assembly line balancing. It provides examples of unbalanced toy train and chocolate assembly lines that have bottlenecks or low utilization. The key points of line balancing are to understand when a line is balanced or unbalanced, calculate takt time which is the maximum time a workpiece can spend at each station, and identify methods to balance lines such as adding workers, combining stations, or automating processes. The goal of line balancing is to eliminate waiting times and have a smooth flow of work from one station to the next.
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Assembly Line Balancing to Improve Productivity using Work Sharing Method in ...
The garment factories are always trying to improve production and the quality of the garments to sustain in the enormous competitive market. This paper is about the productivity improvement by reducing cycle time with work sharing in garment factories. A garment factory manufactures different types of garments. In many types of garment productions, this paper is to improve productivity of lady pencil skirts production process. Overall efficiency of single model assembly line by reducing the non value added activities, cycle time and distribution of work load at each work station by line balancing. For that, the productivity improvement is shown by two ways. The first way is proper training and supervision for activities and the second is work sharing with same type of jobs and skills. Keywords Cycle Time, Line Balancing, Productivity, Training, Work Sharing. Khin Nann Yu Aung | Yin Yin Tun "Assembly Line Balancing to Improve Productivity using Work-Sharing Method in Garment Factories" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-5 , August 2019, URL: https://www.ijtsrd.com/papers/ijtsrd26656.pdfPaper URL: https://www.ijtsrd.com/engineering/mechanical-engineering/26656/assembly-line-balancing-to-improve-productivity-using-work-sharing-method-in-garment-factories/khin-nann-yu-aung
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This document discusses line balancing in garment manufacturing. Line balancing aims to design a smooth production flow by evenly allotting processes to workers so that each can complete their workload within the same amount of time. This keeps inventory costs low and production balanced. Tools for line balancing include production sheets and reports tracking inventory levels and output. Balancing starts by determining required operators and work-in-process inventory levels. It aims to keep all operators working at maximum capacity while solving problems before they become large. Key aspects of balancing include pitch time, bottleneck processes, and setting control limits.
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This document summarizes line balancing techniques for optimizing production line efficiency. It discusses calculating standard minute values using time studies and setting production targets. Pitch time and control limits are explained to balance the workload across workstations. Bottleneck processes are identified and methods to reduce them are provided, such as work improvement, equipment upgrades, and job reassignment. The overall goal of line balancing is to design a smooth production flow that allows each worker to complete their allotted work within an even time frame.
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This document contains the resume of Gobi S, who has 3 years of experience in manufacturing operations such as CAM programming, process planning, and fixture design verification. Some of his responsibilities include conducting meetings to design new processes, introducing new products, and improving existing ones. He has expertise in cutting tools, turning and milling machines. He has achieved several accomplishments like completing complex machining projects within tight tolerances, optimizing manufacturing processes to significantly reduce times, and being recognized as top performer. He is proficient in various CAM and CAD software and holds a Bachelor's degree in Mechanical Engineering.
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This document provides information about line balancing processes in a textile factory. It begins with an introduction to line balancing and its importance for improving production throughput and reducing costs. It then discusses various line balancing methods like time study analysis, bottleneck identification, and work allotment. Specific steps for balancing a production line are outlined, including determining operator requirements, work-in-process inventory levels, and establishing rules to ensure maximum operator capacity. Formulas for calculating standard minute values and organization efficiency are also presented.
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Line balancing and its formulation
Line balancing and how the productivity can be optimized through the help of formula and by working of 4Ms
assembly line balancing
This document discusses line balancing, which involves assigning tasks along an assembly line to workstations in order to achieve minimum idle time and meet production rates. It defines key terms like cycle time, station time, line efficiency, and smoothness index. It also covers precedence constraints, which restrict the order that work elements can be completed in. Finally, it outlines several common line balancing methods, including Helgeson and Birnie's Ranked Positional Weight method, Kilbridge and Wester's region approach, and the Largest Candidate Rule.
Industrial engineeering pli
This document provides an overview of industrial engineering topics including line balancing, assembly lines, and progress control. It discusses types of assembly lines like single model, mixed model, and multi model lines. Line balancing aims to distribute work evenly across stations to minimize idle time. Methods like heuristic assignment are used. Progress control monitors production schedules and addresses delays to ensure schedules are met.
Line balance
Line balancing is a manufacturing process that evenly divides work tasks along an assembly line among workstations. It aims to minimize idle time and improve productivity. The key aspects of line balancing include identifying each task, determining the cycle time of processes, and assigning tasks to workstations in a way that balances the workload. Tools used for line balancing include calculators, stopwatches, and time study sheets to analyze process times and balance the workflow. Metrics like cycle time, takt time, and utilization are calculated to evaluate balancing and identify areas for improvement.
Line balancing example
The document describes a study conducted to improve productivity at Champion Brewery in Nigeria through line balancing. Researchers used a heuristic method called Longest Operation Time to balance the production line for Champion lager beer. Currently the line has 9 workstations and takes 12856 seconds to produce one pallet, with a cycle time of 108 seconds per crate. Researchers analyzed task times, calculated station times, and identified bottlenecks. They determined the theoretical minimum number of workstations is 3 based on total work content and desired daily output. Balancing the line to have 3 workstations instead of 9 will improve efficiency by reducing idle time.
Line balancing and heuristics
This document discusses line balancing in manufacturing, which aims to evenly divide work among workstations in a production process. The goal is to determine the optimal number of workstations, tasks assigned to each, and minimum resources needed. Key terms defined include tasks, task times, cycle time, workstations, and more. Common line balancing procedures involve determining tasks, precedence, times, cycle time, and minimum workstations. Computer programs now help balance large production lines using heuristics like incremental utilization and longest task time.
Product layout in Food Industry and Line Balancing
The product or line layout is the basic type of layout commonly used by the food industry. Line balancing is done to analyze the net output of our production line and processing time at various steps.
Introduction to force equilibrium method
This document introduces the force equilibrium method for analyzing various metal forming processes. It discusses types of forming processes like rolling, forging, drawing, bending, and extrusion. The force equilibrium method is used to determine important parameters like the roll separating force in rolling, the forging force, drawing force, and bending moment. It provides the key assumptions made in analyzing each process, such as constant yield stress and coefficient of friction. Formulas are presented for calculating forces, stresses, and dimensions in each process. The objective is to correlate initial and final workpiece dimensions and accurately estimate the required forming forces.
Balancing the line by using heuristic method based on cpm in salbp –a case study
Abstract
In mass production systems, line balancing plays a great role, but this is not easy even if it is a simple straight line. So, in order to
solve these problems Heuristic methods are very much desirable. It is also found that Heuristic methods play a great role in the
formation of metaheuristic methods.Therefore it is very much important to use more efficient heuristic methods. In this research
paper we presents a heuristic method that is based on critical path method for simple assembly line balancing. This research is
mainly concerned with objectives of minimizing the number of workstations, improvement of smoothness index, mean absolute
deviation (MAD) and increasing line efficiency.
Keywords-Heuristic methods,Assembly line balancing problem, Critical path method, Simple assembly line balancing.
Assembly line balancing
Line balancing aims at grouping the facilities or workers in an efficient pattern in order to obtain an optimum or most efficient balance of the capacities and flows of the production or assembly processes.
Seven quality tools
This presentation provided an overview of Ishikawa's seven basic quality tools: histograms, Pareto charts, cause-and-effect diagrams, run charts, scatter diagrams, flow charts, and control charts. For each tool, the presentation defined the tool, explained how to construct it, and provided an example of how the tool can be used. The tools are designed to be simple visual aids to help analyze data, identify relationships and causes, improve processes, and monitor quality.
Assembly Line Balancing
The document discusses assembly line balancing. It provides examples of unbalanced toy train and chocolate assembly lines that have bottlenecks or low utilization. The key points of line balancing are to understand when a line is balanced or unbalanced, calculate takt time which is the maximum time a workpiece can spend at each station, and identify methods to balance lines such as adding workers, combining stations, or automating processes. The goal of line balancing is to eliminate waiting times and have a smooth flow of work from one station to the next.
Assembly Line Balancing | Case Study
This presentation is on the based on case study done by using line balancing technique which a prime concern for an industrial engineer. This shows an efficient line balancing for a better production line performed at Runner Automobiles Ltd, Bangladesh.
Work Center Scheduling
This document discusses workcenter scheduling and related topics. It introduces workcenter scheduling and its objectives like meeting due dates, minimizing lead times and setup times. It also discusses job sequencing rules like first come first serve, shortest processing time and earliest due date. Methods for scheduling jobs on 1, 2 and multiple machines are presented, including Johnson's rule and assignment method. Finally, it briefly covers personnel scheduling in services, like deriving staffing plans and applying the first hour principle.
Assembly Line Balancing to Improve Productivity using Work Sharing Method in ...
The garment factories are always trying to improve production and the quality of the garments to sustain in the enormous competitive market. This paper is about the productivity improvement by reducing cycle time with work sharing in garment factories. A garment factory manufactures different types of garments. In many types of garment productions, this paper is to improve productivity of lady pencil skirts production process. Overall efficiency of single model assembly line by reducing the non value added activities, cycle time and distribution of work load at each work station by line balancing. For that, the productivity improvement is shown by two ways. The first way is proper training and supervision for activities and the second is work sharing with same type of jobs and skills. Keywords Cycle Time, Line Balancing, Productivity, Training, Work Sharing. Khin Nann Yu Aung | Yin Yin Tun "Assembly Line Balancing to Improve Productivity using Work-Sharing Method in Garment Factories" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-5 , August 2019, URL: https://www.ijtsrd.com/papers/ijtsrd26656.pdfPaper URL: https://www.ijtsrd.com/engineering/mechanical-engineering/26656/assembly-line-balancing-to-improve-productivity-using-work-sharing-method-in-garment-factories/khin-nann-yu-aung
Line balancing
This document discusses line balancing in garment manufacturing. Line balancing aims to design a smooth production flow by evenly allotting processes to workers so that each can complete their workload within the same amount of time. This keeps inventory costs low and production balanced. Tools for line balancing include production sheets and reports tracking inventory levels and output. Balancing starts by determining required operators and work-in-process inventory levels. It aims to keep all operators working at maximum capacity while solving problems before they become large. Key aspects of balancing include pitch time, bottleneck processes, and setting control limits.
Determininstic rounding of linear programs
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Line balancing
This document summarizes line balancing techniques for optimizing production line efficiency. It discusses calculating standard minute values using time studies and setting production targets. Pitch time and control limits are explained to balance the workload across workstations. Bottleneck processes are identified and methods to reduce them are provided, such as work improvement, equipment upgrades, and job reassignment. The overall goal of line balancing is to design a smooth production flow that allows each worker to complete their allotted work within an even time frame.
RESUME FINAL
This document contains the resume of Gobi S, who has 3 years of experience in manufacturing operations such as CAM programming, process planning, and fixture design verification. Some of his responsibilities include conducting meetings to design new processes, introducing new products, and improving existing ones. He has expertise in cutting tools, turning and milling machines. He has achieved several accomplishments like completing complex machining projects within tight tolerances, optimizing manufacturing processes to significantly reduce times, and being recognized as top performer. He is proficient in various CAM and CAD software and holds a Bachelor's degree in Mechanical Engineering.
A line in apparel
This document provides information about line balancing processes in a textile factory. It begins with an introduction to line balancing and its importance for improving production throughput and reducing costs. It then discusses various line balancing methods like time study analysis, bottleneck identification, and work allotment. Specific steps for balancing a production line are outlined, including determining operator requirements, work-in-process inventory levels, and establishing rules to ensure maximum operator capacity. Formulas for calculating standard minute values and organization efficiency are also presented.
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Product layout in Food Industry and Line Balancing
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Balancing the line by using heuristic method based on cpm in salbp –a case study
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Assembly Line Balancing to Improve Productivity using Work Sharing Method in ...
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The document discusses sequencing problems and various sequencing rules used to optimize outputs when assigning jobs to machines. It describes Johnson's rule for minimizing completion time when scheduling jobs on two workstations. Johnson's rule involves scheduling the job with the shortest processing time first at the workstation where it finishes earliest. It provides an example of applying Johnson's rule to schedule five motor repair jobs at the Morris Machine Company across two workstations. Finally, it discusses Johnson's three machine rule for sequencing jobs across three machines.
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Modern manufacturing systems are constantly increasing in complexity and become more agile in nature such
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Modern manufacturing systems are constantly increasing in complexity and become more agile in nature such
system has become more crucial to check feasibility of machine scheduling and sequencing because effective
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but when number of machine increases traditional scheduling methods e.g. Johnson‟s ,rule is becomes in
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This document discusses job shop scheduling, which involves scheduling jobs at general purpose work stations. It describes factors like arrival patterns, number of machines, work sequences, and performance criteria. For arrival patterns, it notes static and dynamic types. For work sequences, it discusses fixed and random types. It provides examples of performance criteria like makespan and machine utilization. It also introduces Gantt charts for scheduling displays and discusses scenarios like scheduling n jobs on 1 machine, n jobs on a flow shop with 2 machines, and n jobs on m machines in general. Heuristics for the n jobs on m machines case include shortest processing time, earliest due date, and critical ratio rules.
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Scheduling
A bill of materials (BOM) lists all raw materials, components, and parts needed to manufacture a product along with their quantities. It defines the product structure by breaking the final product down into subassemblies and components in a hierarchical manner. There are two main types of scheduling: forward scheduling which plans tasks from the start date, and backward scheduling which plans tasks from the due date backwards. Production, planning and control (PPC) aims to efficiently utilize resources through planning and coordinating production activities to transform raw materials into finished goods optimally.
Scheduling
A bill of materials (BOM) lists all raw materials, components, and parts needed to manufacture a product along with their quantities. It defines the product structure by breaking the final product down into subassemblies and components in a hierarchical manner. There are two main types of scheduling: forward scheduling which plans tasks from the start date, and backward scheduling which plans tasks from the due date backwards. Production, planning and control (PPC) aims to efficiently utilize resources through planning and coordinating production activities to transform raw materials into finished goods optimally.
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These are my slides from the third year Advanced Algorithms course I used to give at the University of Bristol, UK.
Operations Research -Sequencing Problems
The document discusses sequencing problems and provides an example problem. A sequencing problem aims to determine the optimal order of jobs to minimize costs. The example problem involves 6 jobs that must pass through 2 machines (A then B) with processing times provided. The optimal sequence was determined to be jobs 2, 3, 4, 5, 6, 1 with a total elapsed time of 85 hours and idle times of 8 hours for machine A and 17 hours for machine B.
Lotstreaming
Lot-streaming scheduling with consistent size sublots including defectives goods for makespan minimization in flow shop including sublot-attached setups
Production & Operation Management Chapter33[1]
This document provides information about scheduling techniques and concepts. It discusses shop loading vs scheduling, uses of Gantt charts, limitations of the assignment problem and Johnson's rule, how line of balance can help management identify production problems, differences between line production and job shops, and sequencing rules. It also provides sample scheduling problems and solutions using techniques like Johnson's rule, minimum slack per operation, and the assignment problem.
Sequential Models - Meaning, assumptions, Types and Problems
Sequencing problems involve determining the optimal order of a series of jobs or tasks. They are common in manufacturing where the order of production processes can impact the overall efficiency. The document provides an example of a sequencing problem with 2 jobs and 2 machines, calculating the processing times and idle times for each of the 4 possible sequences. The optimal sequences are identified as those with the minimum total elapsed time and lowest machine idle times.
LINE PACING ETC...ppt
Manual assembly lines are used to assemble consumer products where demand is high or medium. The assembly process involves dividing the total work into small tasks performed at sequential workstations by one or more workers. Products are assembled on these lines if they are identical or similar, and the work can be broken down into elements that may be too difficult to automate. Key considerations for manual assembly lines include line pacing to maintain production rates, balancing work assignments across stations, and designing products and components for ease of assembly.
LINE PACING ETC..-2.ppt
Manual assembly lines are used to assemble consumer products where demand is high or medium, products are identical or similar, and total work can be divided into small elements. They consist of sequential workstations where one or more workers complete tasks. Line pacing is important to maintain production rates, assigning tasks to be completed within each cycle time. Proper line balancing algorithms are used to evenly distribute work among stations, such as the Largest Candidate Rule. Factors like precedence constraints and minimum rational work elements are considered.
Similar to Unit iii-2-sp (20)
Parallel Line and Machine Job Scheduling Using Genetic Algorithm
Parallel Line and Machine Job Scheduling Using Genetic Algorithm
A case study on Machine scheduling and sequencing using Meta heuristics
A case study on Machine scheduling and sequencing using Meta heuristics
A case study on Machine scheduling and sequencing using Meta heuristics
A case study on Machine scheduling and sequencing using Meta heuristics
Job Shop Scheduling Using Mixed Integer Programming
Job Shop Scheduling Using Mixed Integer Programming
Approximation Algorithms Part Two: More Constant factor approximations
Approximation Algorithms Part Two: More Constant factor approximations
Sequential Models - Meaning, assumptions, Types and Problems
Sequential Models - Meaning, assumptions, Types and Problems
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Simplex method maximisation
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Project networks
A publisher has contracted an author to produce a textbook. The production process involves the author submitting a manuscript and files, editing, sample page and cover design, artwork, formatting, and printing. The critical path through the network is the author submitting the manuscript, editing, formatting, artwork approval, plate production, and binding, taking 17 weeks total to complete the project.
Or flowchart
This flowchart outlines an optimization process to find an optimal solution. It starts with finding an initial basic solution, then checks if that solution is optimal. If it is optimal, that solution is the final answer. If not, the process seeks a better solution to try and find the optimal one.
Strategic management model
The document outlines a strategic management model that includes four main stages: strategic intent, formulation, implementation, and evaluation. It involves analyzing internal and external environments to determine a vision, mission, goals and objectives. Strategies are then formulated, implemented through resource allocation and structure, and evaluated for effectiveness with feedback into reformulation.
Maximisation problem
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Lpp numerical
an LPP problem asked in aktu mba exam in 2008 (operations research) formulated, and solved using simplex method
Lpp numerical solved
a linear programming problem asked in aktu mba exam of operations research in 2008, formulated, and solved using graphical method
Lpp formulation
This document presents a linear programming problem involving assigning quality inspectors to minimize total inspection costs. There are two types of inspectors (Grade I and Grade II) with different inspection rates and accuracy. The objective is to minimize total costs based on wages, inspection pieces, and error costs with constraints on minimum inspection pieces and available inspectors.
Lp formulation
This document formulates a linear programming problem to determine the optimal production quantities of Products P1 and P2 given machine time and contribution margin constraints. Product P1 takes 4 hours on machine M1 and 2 hours on M2, while Product P2 takes 2 hours on M1 and 4 hours on M2. The objective is to maximize total contribution by choosing the quantities x1 and x2 subject to the 60 hours available on M1, 48 hours on M2, and non-negativity constraints.
Graphical method
The document describes a production problem involving two products (P1 and P2) that are manufactured using two machines (M1 and M2). P1 requires 4 hours on M1 and 2 hours on M2, while P2 requires 2 hours on M1 and 4 hours on M2. The goal is to determine the optimal quantities of P1 and P2 to maximize total contribution, given 60 hours available on M1 and 48 hours on M2. This problem is modeled as a linear programming problem and graphically solved by plotting the constraint lines and finding their intersection point.
Games
The document contains information about game theory including pure strategies, mixed strategies, and solving games. It provides examples of games represented as payoff matrices and discusses applying the principles of dominance, algebraic methods for 2x2 games, graphical methods for 2xn and mx2 games, and linear programming for mxn games. It also includes an example analyzing a 6x6 game modeling the Allied invasion of Normandy in WWII.
Game theory
Four teams will participate in a game involving selecting strategies of A or B. The aim is to score the maximum dividends. Scoring is based on the number of As and Bs selected. The document then explains the Prisoner's Dilemma game theory concept where two prisoners can either cooperate or betray each other, and discusses why rational individuals may not cooperate even if it is in their best interest to do so.
Dual formulation example
The document discusses how to formulate the dual of a primal linear programming problem. It provides 10 steps for converting a primal maximization problem into a dual minimization problem. As an example, it formulates the dual of the primal problem: Maximize z = -5x1 + 2x2 subject to x1 - x2 ≥ 2 and 2x1 + 3x2 ≤ 5, with non-negativity constraints. The dual is formulated as: Minimize z = -2y1 + 5y2 subject to -y1 + 2y2 ≥ -5 and y1 + 3y2 ≥ 2, with non-negativity constraints on the dual variables y1 and y2.
Decision tree solved
A finance manager is considering drilling a well on their property. Based on past data, there is a 70% chance of finding water at 20 meters depth, and a 20% chance of finding water between 20-25 meters if no water is found at 20 meters. The costs to drill are Rs.500 per meter plus Rs.15,000 to buy water externally if the well is not drilled. The optimal decision tree strategy is to first drill to 20 meters, and if no water, then drill further to 25 meters, resulting in an expected cost of Rs. 11,350.
Decision theory numerical
The grocer must decide how many cases of milk to stock for tomorrow's demand. Each case sold yields a profit of Rs.3, but unsold cases at the end of the day lose Rs.5. Historical demand data shows the number of cases demanded and the probability of each quantity. The optimal decision can be determined by calculating the expected monetary value (EMV) of stocking different quantities of milk based on the probabilities and outcomes. The expected profit for the grocer if they stock the quantity with the highest EMV is Rs.47.7.
Crashing
project management. crashing a network. finding optimum duration and optimum cost of project. operations research (OR)
Assignment model problems
A fast food chain wants to build four new stores and received bids from six construction companies. The document shows the bid amounts in a table and describes using the Hungarian method to determine the optimal assignment of companies to stores that minimizes the total cost. The method involves reducing the table through successive steps to reveal a unique solution with no remaining zeros. The result assigns each store to a single construction company to minimize the total cost for building all four stores.
Minimisation problem
a minimisation linear programming problem (LPP), solved using simplex method (operations research: OR)
Operations research
Operations research (OR) is a tool used to increase the effectiveness of managerial decisions. It can help with profit maximization, production management like determining optimal product mix and scheduling, financial management, marketing management, and personnel management. Some common OR models include linear programming, transportation, assignment, and sequencing problems. OR uses mathematical techniques like linear programming, decision theory, game theory, queuing theory, simulation, network analysis, and inventory models.
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Unit iii-2-sp
- 3. Basic Terminology 1. Number of machines means the service facilities through which a job must pass before it is assumed to be completed. 2. Processing time means the time each job requires at each machine. 3. Processing order refers to the order in which various machines are required for completing the job.
- 4. Basic Terminology 4. Total elapsed time is the time interval between starting the first job and completing the last job including the idle time (if any) in a particular order by the given set of machines. 5. Idle time on a machine is the time a machine remains idle during the total elapsed time. 6. No passing rule implies that passing is not allowed, that is the same order of jobs is maintained over each machine.
- 5. Notation
- 6. Johnson’s Algorithm • Select the smallest processing time. • If this is on M1, place the corresponding job at the beginning of the sequence. • If this is on M2, place the corresponding job at the end of the sequence. • Repeat the process until all the jobs are sequenced.
- 7. n Jobs 2 Machine Problem Batch J1 J2 J3 J4 J5 J6 M1 4 7 3 12 11 9 M2 11 7 10 8 10 13
- 8. n Jobs 3 Machine Problem Job 1 2 3 4 5 6 M1 8 3 7 2 5 1 M2 3 4 5 2 1 6 M3 8 7 6 9 10 9
- 9. n Jobs m Machine Problem Job 1 2 3 4 M1 7 6 5 8 M2 5 6 4 3 M3 2 4 5 3 M4 3 5 6 2 M5 9 10 8 6
- 10. n Jobs m Machine Problem Job 1 2 3 4 M1 7 6 5 8 M2 5 6 4 3 M3 2 4 5 3 M4 3 5 6 2 M5 9 10 8 6