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## B370 Operations Management

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**B370 Operations Management**Group 2 Tutorial 9 C.S. Lai December 2012 B370 Operations Management**Agenda**Q & A 15 mins. Operation Scheduling 40 mins. Waiting Line Management 40 mins. Simulation (if time allows) 10 mins. Q & A 15 mins. B370 Operations Management**Operations Scheduling**• Work Center Defined • Typical Scheduling and Control Functions • Job-shop Scheduling • Examples of Scheduling Rules • Shop-floor Control • Principles of Work Center Scheduling B370 Operations Management**Operations Planning Overview**• Long-range planning • Greater than one year planning horizon • Usually with yearly increments • Intermediate-range planning • Six to eighteen months • Usually with monthly or quarterly increments • Short-range planning • One day to less than six months • Usually with weekly increments B370 Operations Management**Weekly Workforce &**Customer Scheduling Daily Workforce & Customer Scheduling Process Planning Exhibit 12.1 Long- range Strategic Capacity Planning Intermediate- range Aggregate Planning Manufacturing Services Master Production Scheduling Material Requirements Planning Order Scheduling Short- range B370 Operations Management**Shop Floor Control**• Loading • Sequencing • Detailed Scheduling • Expediting B370 Operations Management**Work-Center Scheduling Objectives**• Meet due dates • Minimize lead time • Minimize setup time or cost • Minimize work-in-process inventory • Maximize machine utilization B370 Operations Management**Work CenterDefined**• A work center is an area in a business in which productive resources are organized and work is completed. • May be a single machine, a group of machines, or an area where a particular type of work is done. B370 Operations Management**Loading**• Finite Loading – will create a detailed schedule • Infinite Loading – based on what is needed over time, regardless of availability of capacity • Gantt load chart B370 Operations Management**Gantt Load Chart**B370 Operations Management**The Assignment Algorithm**• A special case of linear programming => therefore, the pre-conditions of LN need to be fulfilled! • Only applicable for n jobs processed through n work centers • Must be based on a single criterion, e.g. opportunity cost • Example (refer to p.39, Unit 9 of the Course Guide) B370 Operations Management**Priority Rules for Job Sequencing**1. First-come, first-served (FCFS) 2. Shortest operating time (SOT) 3. Earliest due date first 4. Earliest start date first (due date-lead time) 5. Least slack time remaining (STR) first B370 Operations Management**Priority Rules for Job Sequencing (Continued)**6. Least slack time remaining (per operation as opposed to per job) first 7. Smallest critical ratio (CR) first (due date-current date)/(number of days remaining) 8. Smallest queue ratio (QR) first (slack time remaining in schedule)/(planned remaining queue time) 9. Last come, first served (LCFS) 10. Random order or whim B370 Operations Management**Schedule Performance Measures**• Meeting due dates of customers or downstream operations. • Minimizing the flow time (the time a job spends in the process). • Minimizing work-in-process inventory. • Minimizing idle time of machines or workers. B370 Operations Management**Answer: FCFS Schedule**Example of Job Sequencing: First-Come First-Served Suppose you have the four jobs to the right arrive for processing on one machine. What is the FCFS schedule? Do all the jobs get done on time? No, Jobs B, C, and D are going to be late. Total Flow time: 44, Average Flow time: 11, Average lateness: 5**Answer: Shortest Operating Time Schedule**Example of Job Sequencing: Shortest Operating Time Suppose you have the four jobs to the right arrive for processing on one machine. What is the SOT schedule? Do all the jobs get done on time? No, Jobs A and B are going to be late. Total Flow time: 28, Average Flow time: 7, Average lateness: 2**Answer: Earliest Due Date First**Example of Job Sequencing: Earliest Due Date First Suppose you have the four jobs to the right arrive for processing on one machine. What is the earliest due date first schedule? Do all the jobs get done on time? No, Jobs C and B are going to be late. Total Flow time: 29, Average Flow time: 7.25, Average lateness: 2**Which priority rule is generally the best?(what do you mean**by “the best”?) B370 Operations Management**What priority rule(s) you might use to schedule your TMA?**Why? B370 Operations Management**Since SOT generally offers optimal results in many**evaluation criteria, should the manager of a bank use this rule?Have you noticed the new queuing system in the branches of HSBC? What advantages you think the new system might have? B370 Operations Management**Johnson’s Rule**• Objective: To minimize flow time for n jobs on two machines. • Procedure: • List the operation time for each job • Select the shortest operation time • If the shortest time is for the first machine, do it first; if it is for the last machine, do it last • Repeat 2 & 3 until the schedule is complete B370 Operations Management**Example of Job Sequencing: Johnson’s Rule (Part 1)**Suppose you have the following five jobs with time requirements in two stages of production. What is the job sequence using Johnson’s Rule? Time in Hours Jobs Stage 1 Stage 2 A 1.50 1.25 B 2.00 3.00 C 2.50 2.00 D 1.00 2.00 B370 Operations Management**Example of Job Sequencing: Johnson’s Rule (Part 2)**Time in Hours Jobs Stage 1 Stage 2 A 1.50 1.25 B 2.00 3.00 C 2.50 2.00 D 1.00 2.00 First, select the job with the smallest time in either stage. That is Job D with the smallest time in the first stage. Place that job as early as possible in the unfilled job sequence below. Drop D out, select the next smallest time ( Job A), and place it 4th in the job sequence. Drop A out, select the next smallest time. There is a tie in two stages for two different jobs. In this case, place the job with the smallest time in the first stage as early as possible in the unfilled job sequence. Then place the job with the smallest time in the second stage as late as possible in the unfilled sequence. Job Sequence 1 2 3 4 Job Assigned D B C A B370 Operations Management**Detailed Scheduling**• Specifying: • Start times • Finish times • Work assignments for all jobs at each work centre • Example of tool used : Gantt Chart B370 Operations Management**Expediting**• Track progress • Take special actions to progress the job B370 Operations Management**Input**Output Input/Output Control Work Center • Planned input should never exceed planned output. • Focuses attention on bottleneck work centers. B370 Operations Management**Principles of Work Center Scheduling**1. There is a direct equivalence between work flow and cash flow. 2. The effectiveness of any job shop should be measured by speed of flow through the shop. 3. Schedule jobs as a string, with process steps back-to-back. 4. A job once started should not be interrupted. B370 Operations Management**Principles of Job Shop Scheduling (Continued)**5. Speed of flow is most efficiently achieved by focusing on bottleneck work centers and jobs. 6. Reschedule every day. 7. Obtain feedback each day on jobs that are not completed at each work center. 8. Match work center input information to what the worker can actually do. B370 Operations Management**Principles of Job Shop Scheduling (Continued)**9. When seeking improvement in output, look for incompatibility between engineeringdesign and process execution. 10. Certainty of standards, routings, and so forth is not possible in a job shop, but always work towards achieving it. B370 Operations Management**Waiting Line Management**• Waiting Line Characteristics • Suggestions for Managing Queues • Examples (Models 1, 2, 3, and 4) B370 Operations Management**Servicing System**Servers Waiting Line Customer Arrivals Exit Components of the Queuing System Queue or B370 Operations Management**Finite**Infinite Customer Service Population Sources Population Source Example: Number of machines needing repair when a company only has three machines. Example: The number of people who could wait in a line for gasoline. - Easiler to model B370 Operations Management**Constant**Variable Service Pattern Service Pattern Example: Items coming down an automated assembly line. Example: People spending time shopping. B370 Operations Management**Length**Queuing System Queue Discipline Number of Lines & Line Structures Service Time Distribution The Queuing System B370 Operations Management**One-person**barber shop Car wash Bank tellers’ windows Hospital admissions Examples of Line Structures Single Phase Multiphase Single Channel Multichannel B370 Operations Management**BALK**RENEG Degree of Patience No Way! No Way! B370 Operations Management**Suggestions for Managing Queues**1. Determine an acceptable waiting time for your customers. 2. Try to divert your customer’s attention when waiting. 3. Inform your customers of what to expect. 4. Keep employees not serving the customers out of sight. 5. Segment customers. B370 Operations Management**Suggestions for Managing Queues (Continued)**6. Train your servers to be friendly. 7. Encourage customers to come during the slack periods. 8. Take a long-term perspective toward getting rid of the queues. B370 Operations Management**Waiting Line Models**Source Model Layout Population Service Pattern 1 Single channel Infinite Exponential 2 Single channel Infinite Constant 3 Multichannel Infinite Exponential 4 Single or Multi Finite Exponential Please think of an example for each model These four models share the following characteristics: Single phase · Poisson arrival · FCFS · Unlimited queue length · B370 Operations Management**Model 4**Model 1 Model 2 Model 3 Equations for Solving Three Model Problems**Example: Model 1**Drive-up window at a fast food restaurant. Customers arrive at the rate of 25 per hour. The employee can serve one customer every two minutes. Assume Poisson arrival and exponential service rates. A) What is the average utilization of the employee? B) What is the average number of customers in line? C) What is the average number of customers in the system? D) What is the average waiting time in line? E) What is the average waiting time in the system? F) What is the probability that exactly two cars will be in the system? B370 Operations Management**Example: Model 1**A) What is the average utilization of the employee? B370 Operations Management**Example: Model 1**B) What is the average number of customers in line? C) What is the average number of customers in the system? B370 Operations Management**Example: Model 1**D) What is the average waiting time in line? E) What is the average waiting time in the system? B370 Operations Management**Example: Model 1**F) What is the probability that exactly two cars will be in the system (one being served and the other waiting in line)? B370 Operations Management**1. Calculate the average customer arrival rate and service**rate per hour. The customer arrival rate lambda = 0.0212 patients per hour. This is calculated 62/(8 x 365) = 0.0212. The service rate mu = 0.7427 patients per hour. This calculated 60 min/hour divided by 80.79 minute/patient = 0.7427 patients per hour. 2. Calculate the probability of zero patients in the system (P0), probability of one patient (P1), and the probability of two or more patients simultaneously arriving during the night shift. P(0) = (1 – lambda/mu) = (1 - .0212/.7427) = 0.9714 the probability of no patients in the system is over 97 percent. P(1) = (1 – lambda/mu)(lambda/mu)1 = (1 - .0212/.7427)(.0212/.7427) = 0.0278 the probability of exactly 1 patient in the system is 2.78 percent. The probability that 2 or more patients are in the system is 1 – (P(1) + P(0)) = 1 – (.0278 + 0.9714) = 0.0008. The probability of two or more patients occurring simultaneously on the night shift is less than 0.1% (less than one chance in 1,000). 3. Using a criterion that if the probability is greater than 1 percent, a backup OR team should be employed, make a recommendation to hospital administration. A second OR is not needed at this hospital. B370 Operations Management

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