Modeling with Queuing Theory System Characteristics – Population source: finite, infinite – No. of servers – Arrival and service patterns: e.g. exponential distribution for inter-arrival time – Queue discipline: e.g. first-come-first-serve
Measuring Performance Performance Measurement: – System utilization – Average no. of customers: in line and in system – Average waiting time: in line and in system e.g. infinite source, single server, exponential inter-arrival and service times, first-come-first- serve: (see handout)
Optimum Cost of service capacity Cost of customers waiting Total cost Cost Service capacity Total cost Customer waiting cost Capacity cost =+ Basic Tradeoff
System Utilization Average number on time waiting in line 0 100% Basic Tradeoff (cont.)
Applying Queuing Theory In Process Design: – Describe the process and establish a model – Collect data on incoming and service patterns – Find formulas and/or tables, software to calculate performance measures – Use performance measures to guide process design decisions
Applying Queuing Theory In Operations: – Monitor performance measures – Use performance measures to guide process improvement and operations decisions
Statistical Process Control Emphasis on the process instead of the product/material Focus on “prevention”
0123456789101112131415 UCL LCL Sample number Mean Out of control Normal variation due to chance Abnormal variation due to assignable sources Control Chart
Sample number UCL LCL 1234 In-Control: random only
Control Charts for Variables Mean Chart: measuring sample means Range Chart: measuring sample ranges i.e. max-min
UCL LCL UCL LCL R-chart x-Chart Detects shift Does not detect shift process mean is shifting upward Sampling Distribution Out-of-Control: assignable & random shifted mean
UCL LCL R-chart Reveals increase x-Chart UCL Does not reveal increase (process variability is increasing) Sampling Distribution Out-of-Control: assignable & random increased variability
Mean LCLUCL /2 Probability of Type I error Type I Error:
Mean LCLUCL Type II Error: In-Control Out-of-Control
p-Chart - Control chart used to monitor the proportion of defectives in a process c-Chart - Control chart used to monitor the number of defects per unit Control Charts for Attributes
Counting Above/Below Median Runs(7 runs) Counting Up/Down Runs(8 runs) U U D U D U D U U D B A A B A B B B A A B Counting Runs Figure 10-11 Figure 10-12
Lower Specification Upper Specification Process variability matches specifications Lower Specification Upper Specification Process variability well within specifications Lower Specification Upper Specification Process variability exceeds specifications Process Capability
Process mean Lower specification Upper specification 1350 ppm 1.7 ppm +/- 3 Sigma +/- 6 Sigma Process Capability: 3-sigma & 6-sigma
Input/Output Analysis Change in inventory = Input - Output Average throughput time is proportional to the level of inventory.
Input flow of materials Inventory level Scrap flow Output flow of materials Flow and Inventory Figure 11.1
MRP A general framework for MRP Inputs: Bill of Materials, Inventory Files and Master Production Schedule MRP Processing
A General Framework of MRP Aggregate Plan Master Production Schedule MRP Capacity Requirements Planning Production Scheduling
Item: Seat subassembly Lot size: 230 units Lead time: 2 weeks Gross requirements 150 123 120 45 150 6 120 78 Planned receipts Planned order releases Week 0000 230 Item: Seat frames Lot size: 300 units Lead time: 1 week Gross requirements 0 1 0 23 0 45678 Scheduled receipts Projected on-hand inventory Planned receipts Planned order releases 40 Week 230 0 000 300000 Item: Seat cushion Lot size: L4L Lead time: 1 week Gross requirements 0 1 0 23 0 45678 Scheduled receipts Projected on-hand inventory Planned receipts Planned order releases 0 Week 230 0 000 0000 Usage quantity: 1 MRP Explosion Figure 15.11
Issues in MRP Two basic concepts: – Net requirements – Lead time offset Lot size Safety stock/Safety lead time Inventory records Validity of the schedules
JIT and Inventory Management Inventory as delay in work flow Why inventory? – Dealing with fluctuations in demand – Dealing with uncertainty – Reducing transaction costs – Taking advantage of quantity discount – Hedging against inflation, etc.
JIT and Inventory Management Inventory costs: – Holding cost – Long response time – Low flexibility – Slow feedback in the system
JIT and Inventory Management The objective of JIT: – General: reduce waste – Specific: avoid making or delivering parts before they are needed Strategy: – very short time window – mixed models – very small lot sizes.
JIT and Inventory Management Prerequisites: – Reduce set up time drastically – Keep a very smooth production process Core Components: – Demand driven scheduling: the Kanban system – Elimination of buffer stock
JIT and Inventory Management Core Components: (cont.) – Process Design: Setup time reduction Manufacturing cells Limited work in process – Quality Improvement
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