Manufacturing systems Design presentation.

Manufacturing system design

1. GROUP A MEMBERS SN NAME REGISTRATION NUMBER 1 SSESANGA EDGAR 2020/A/KME/0069/G/F 2 KALAGALA ABDULBAST 2020/A/KME/0071/G/F 3 IGIRANEZA JACKIN 2020/A/KME/0097/G/F 4 BULONDO RODNEY 2020/A/KME/0730/F 5 KATWESIGYE WILFRED 2020/A/KME/1160/F MANUFACTURING SYSTEM DESIGN PRESENTATION

2. INTEGER AND LINEAR PROGRAMMING In the manufacturing industry, optimization challenges often arise that can be solved using linear programming or integer programming techniques. These techniques involve maximizing or minimizing a linear objective function, subject to a set of constraints, to achieve efficient and effective solutions. Linear programming models comprise an objective function and constraints, while IP focuses on integer solutions. The goal is to optimize a linear objective function subject to constraints, ensuring efficient decision-making in manufacturing processes.

3. QUEUING MODELS FOR MANUFACTURING SYSTEMS Manufacturing processes often involve queuing systems, similar to those found in service industries like banking, healthcare, and retail. In fact, queuing models are frequently used to analyze and optimize various manufacturing systems, recognizing that production processes often involve wait times, bottlenecks, and flow management. Example: When mechanics queue up in a two-room space to await assignment to a job. Allocating machines to multiple tasks, optimizing their usage and timelines.

4. In various scenarios, entities wait in line for a processing system to provide service, followed by a departure process. When building queuing models, arrivals (inputs) are governed by probabilistic processes, as are the processing times. The order in which customers are served is determined by the Queue Discipline or Service Discipline, which defines the servicing rules.“ Queuing Queuing theory simplifies complex service systems into a manageable model, consisting of a service counter, multiple parallel machines, and a waiting area. Arrivals occur at random intervals, and service commences when a machine becomes available. The A/B/c/m notation captures the system's essential characteristics, enabling performance evaluation. In manufacturing, Little's Law reveals that throughput time is directly proportional to work in progress and inversely proportional to average throughput, providing a crucial insight for system optimization.

5. SINGLE WORK STATION MODEL A workstation is unique to one group, defining production capacity. It performs one operation at a time, and is grouped with similar resources. Input (arrival rate) 𝜏 → waiting line → workstation → output(service rate) 𝜇 Queue Displine FCFS Where FCFS= First come first serve 𝜏 = Arrival rate 𝜇 =𝑠𝑒𝑟𝑣𝑖𝑐𝑒 𝑟𝑎𝑡𝑒

6. IMPORTANT NOTATION P𝑛 = 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑡ℎ𝑎𝑡 𝑛 𝑗𝑜𝑏𝑠 𝑎𝑟𝑒 𝑤𝑎𝑖𝑡𝑖𝑛𝑔 𝑡𝑜 𝑏𝑒 𝑠𝑒𝑟𝑣𝑒𝑑 Po = 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑡ℎ𝑎𝑡 𝑡ℎ𝑒 𝑠𝑦𝑠𝑡𝑒𝑚 𝑖𝑠 𝑒𝑚𝑝𝑡𝑦 𝑖𝑒 𝑧𝑒𝑟𝑜 𝑢𝑛𝑖𝑡𝑠 𝑖𝑛𝑡ℎ𝑒 𝑞𝑢𝑒𝑢𝑒 𝑎𝑛𝑑 𝑧𝑒𝑟𝑜 𝑢𝑛𝑖𝑡𝑠 𝑖𝑛 𝑡ℎ𝑒𝑠𝑒𝑟𝑣𝑖𝑐𝑒 L𝑞 = 𝑀𝑒𝑎𝑛 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑢𝑛𝑖𝑡𝑠 𝑖𝑛 𝑡ℎ𝑒 𝑞𝑢𝑒𝑢𝑒 FORMULAE X= mean rate of arrival in the system W= mean time unit spends in the system W𝑝=mean time unit spends in the queue ∝= utilization factor

7. EXAMPLE: Jobs arrive at work station for packaging an exponential function at a mean rate of 120 per hr. processing time is exponentially distributed with mean rate of 140 jobs per hour. Determine the following: (a) The mean ideal time per hour for the workstation (b) The mean number of jobs waiting for processing (c) The mean waiting per job SOLUTION:

8. CONSTANT SERVICE TIME AND UNLIMITED QUEUE LENGTH In this type of model, a single server services incoming units, and the service time is consistent for all customers or jobs. The queue size is allowed to grow indefinitely, without any maximum limit.“ FORMULAE:

9. EXAMPLE: A conveyor feeds units of product to work station for packaging. Each unit is packaged separately and in order of its arrival at the workstation. Products are packaged at constant rate of 500 units per hour. The random nature of spacing between units on the conveyor has been found that the time between successive arrivals is exponentially distrusted with mean arrival rate of 400 units per hour. Determine the following 𝑃o 𝑙 𝑙𝑝 𝑤 𝑤𝑝

10. OPEN NETWORK MODELS An open network models customers pass through the system once. E.g.1. A work station processing a bundle of packets 2. A supermarket cashier handling a line of customers The number of customers in the system is calculated from arrival rate and characteristic of the service centers. The derivation of L, 𝑙𝑝, 𝑤𝑝, 𝑤 and 𝑃o is basically the same as for the case of single workstation model for the 2 cases discussed i.e. exponential service with unlimited queue length and constant time with unlimited queue length .

11. CLOSED NETWORK MODELS In a closed network model, the customer population is fixed, and no new arrivals are allowed once the maximum capacity (M) is reached. Classic examples include time-sharing computer systems with a fixed number of user terminals and parking lots with limited parking spaces. Since the number of customers is fixed, the queue length is also limited, and any additional arrivals are rejected if the system is already at full capacity (M).

12. SIMULATION MODELS FOR MANUFACTURING SYSTEMS Simulation mimics the behavior of real-world manufacturing systems, allowing for analysis and experimentation through modeling. Simple models can be analyzed using mathematical techniques like calculus, probability, and linear programming to gain insights. However, realistic manufacturing systems are often too complex for analytical solutions, making simulation the necessary tool for studying and understanding their behavior. "Simulation is a computer-based approach to experimentation, utilizing mathematical and logical relationships to model and analyze complex real-world systems over extended periods. This technique is applied in various industries to solve practical problems, such as: Optimizing chemical process design - Streamlining distribution systems - Scheduling maintenance operations - Designing efficient queuing systems - Managing inventory control "

13. SIMULATION OF OPERATIONS AND PROCESSES Industrial operations rely on timely and relevant information to coordinate activities, guide organizational units, and instruct individuals on the execution of tasks. In production, this information defines products (bill of materials) and processes (bill of operations), enabling the engineering and automation of production processes and data processing. Electronic Data Processing (EDP) plays a crucial role in driving manufacturing and process innovations. As a result, engineering focuses on formal design, analysis, and representation of enterprise structures and processes, integrating products into a comprehensive information flow that spans supply, design, manufacturing, assembly, distribution, and sales. Enterprise modeling methods support these complex tasks, facilitating efficient operations and process management .

14. Continued.. Simulation is employed when real-world problems are too intricate or complex to be mathematically modeled or solved. Often, simulation is mistakenly interchangeably used with optimization, necessitating clarification. While both methods rely on reality-based models, created by users based on their knowledge and assumptions, the key difference lies in their objectives. Simulation aims to replicate real-world behavior, providing insights into complex systems, whereas optimization focuses on finding the optimal solution among various possibilities. Both methods utilize problem descriptions and procedures to generate solutions from these models.

15. A set of decisive differences between optimization and simulation are listed in the following Table below: OPTIMISATION SIMULATION - Predominantly works with mathematical models or matrices. - Uses mathematical rules and procedures. An algorithm is only used once for problem. - It can be fully repeated. - If an optimum solution exists, it will surely be deter mined - Works with graphical models or formal languages Simulation models are based on mathematical theories / probability theory Users not build a mathematical model, but works in between mathematical and real system - Simulation produces the dynamic behavior of the systems by modelling different states There is no evaluation, Only quantitative statements are made - Interpretations and evaluations of states are to be carried out by the user The user may modify or improve the existing model - The work results in a multiple repeating experimentation on the model

16. The decisive advantage of simulation experiments is given by the possibility to analyses: Real, but non-existent or not yet existing systems 2. Real existing systems without direct dimensions 3. Several variants of a system with low effort 4. The system’s behavior over a long period in short time 5. Ramp up phases, starting phases and transitions between defined states . Simulation experts can translate the fundamental principles of technical systems, processes, organizations, and control strategies into software, creating tailored models that provide problem-solving tools. These tools are designed to be flexible and adaptable, allowing users to efficiently execute tasks of varying complexity, leveraging their expertise and experience, and seamlessly integrating into their workflow

17. SIMULATION OF MANUFACTURING PROCESS AND SYSTEMS Mathematical modeling excels when applied to small organizational subsystems or components. However, as system complexity increases, mathematical modeling becomes increasingly challenging. In such cases, simulation modeling emerges as a viable alternative. While simulation models require significant computational resources and produce outputs with inherent randomness, they offer valuable insights into system performance. The simulation of entire manufacturing systems, involving multiple processes and equipment, is particularly crucial. It enables plant engineers to optimize machinery organization, identify critical elements, and assist manufacturing and industrial engineers with scheduling and production routing. Fortunately, commercial software packages are available to support such simulations.

18. SIMULATION MODELS DEVELOPMENT Creating a credible simulation model relies on two essential factors: a comprehensive understanding of the system's operations and the ability to generate accurate values for the random variables that impact the system's behavior.“ STEPS 1. Define a problem by identifying the parameters and variables 2. Design the model. This phase includes critical examination of any decision rules, data distribution, time patterns and initial conditions 3. Development of computer program. The analytical use of the flow charts, coding and data generation is important of this stage. 4. Simulate. to obtain the required output reports or results. 5. Evaluate results. The output or results in setup 4 are subject to validation and analysis for making effective decision 6. Implementation. Results of validated simulation exercise can lead to further experimentation in which the problem definition is charged slightly or differently decision rules are employed. It can be utilized for actual operation.