Capacity Management with Set-Ups – Focused on Set-Up Time Set-up times dominate Compute Capacity as function of batch size Compute cycle time (CT) of the rest of the process Compute set-up costs & inventory costs Use EOQ model or one of its variants Solve for batch size: Cap(B)=1/CT Analyze Set-up times & Set-up Costs Set-up costs dominate Reduce the need for batches • Set-up time reduction, SMED • Process lay-out •10-minute rule • Externalize internal set-ups Figure 7.11.: Summary of batching Batching Under Set-Up Times Capacity Management with Set-Ups – Focused on Set-Up Time Set-up times dominate Compute Capacity as function of batch size Compute cycle time (CT) of the rest of the process Compute set-up costs & inventory costs Use EOQ model or one of its variants Solve for batch size: Cap(B)=1/CT Analyze Set-up times & Set-up Costs Set-up costs dominate Reduce the need for batches • Set-up time reduction, SMED • Process lay-out •10-minute rule • Externalize internal set-ups Figure 7.11.: Summary of batching An Example Application Single bottleneck recourse – a milling machine – which produces two components (one steer support and two ribs) for manufacturing a single scooter A steer support requires 1 minute per unit, & A rib requires 0.5 minutes per unit Other remaining step in the process is an assembly operation which does not require any setup and the per unit time for this process is 3 minutes/unit Step 1 Activity Time one Steer support: 1 min/part Two Rib: 0.5 min/part x 2 parts = 1min Step 2 3 min/unit Set-Up Times To switchover from one product to another on the milling machine requires a 60 minute delay for resource set up. 60 min 1 min/unit Step 1 Activity Time one Steer support: 1 min/part Two Rib: 0.5 min/part x 2 parts = 1min 60 min 2x(.5 min/unit) Step 2 3 min/part No setup If there were no set up, then given batch size Q and the total time to produce one unit would be equal to p, the total capacity of the bottleneck resource would be = [Q/(p*Q)] = 1/p (capacity/unit time) Capacity WO Set-up= Batch Size Batch-size*Time per unit = 1 Time per unit Thus, in this case, the batch size Q does not matter. No setup (example) In fact, the time per unit for our example application would be p=1+(2*.5)=2 minutes per unit and with zero setup times, the capacity would be 0.5 units/minutes (since 1/p=1/2=0.5) Activity Time 60/2 = 30 unit/hr 60/3 = 20 unit/hr Step 1 Step 2 one Steer support: 1 min/part Two Rib: 0.5 min/part Total processing 1 x 1min + 2 x 0.5 min = 2 min/unit 3 min/part Setup Set-up time + Batch-size*Time per unit 1-unit 122 min/unit 60 min 1 min/unit 1/122 = 0.00819 unit/min Step 1 Activity Time Batch Size Capacity given Batch Size= one Steer support: 1 min/part Two Rib: 0.5 min/part 60 min 2x(.5 min/unit) 1/3 = .333 unit/min Step 2 3 min/part Setup Set-up time + Batch-size*Time per unit 12-unit 144 min/12unit 60 min (1 min/unit)x12 1/144 x 12 = 0.0833 unit/min Step 1 Activity Time Batch Size Capacity given Batch Size= one Steer support: 1 min/part Two Rib: 0.5 min/part 60 min [2x(.5 min/unit)]x12 1/3 = .333 unit/min Step 2 3 min/part Setup Set-up time + Batch-size*Time per unit 24-unit 168 min/24unit 60 min (1 min/unit)x24 1/168 x 24 = 0.1428 unit/min Step 1 Activity Time Batch Size Capacity given Batch Size= one Steer support: 1 min/part Two Rib: 0.5 min/part 60 min [2x(.5 min/unit)]x24 1/3 = .333 unit/min Step 2 3 min/part Setup Capacity given Batch Size= Set-up time + Batch-size*Time per unit 48-unit 216 min/48unit 1/216 x 48 = 0.2222 unit/min Step 1 Activity Time Batch Size one Steer support: 1 min/part Two Rib: 0.5 min/part 1/3 = .333 unit/min Step 2 3 min/part Setup Capacity given Batch Size= Batch Size Set-up time + Batch-size*Time per unit 92-unit Step 1 Activity Time one Steer support: 1 min/part Two Rib: 0.5 min/part Step 2 3 min/part Capacity as a function of Batch Size Capacity given Batch Size= Batch Size Batch Size Set-up time + Batch-size*Time per unit Supports Ribs Total Capacity Set-Up Prododuction Time Set-Up Prododuction Time Time per minute 1 60 1 60 1 122 0.01 12 60 12 60 12 144 0.08 24 60 24 60 24 168 0.14 36 60 36 60 36 192 0.19 48 60 48 60 48 216 0.22 60 60 60 60 60 240 0.25 120 60 120 60 120 360 0.33 240 60 240 60 240 600 0.40 360 60 360 60 360 840 0.43 720 60 720 60 720 1560 0.46 1440 60 1440 60 1440 3000 0.48 2880 60 2880 60 2880 5880 0.49 Process Analysis with Batching Note: Capacity increases with batch size: 0.5 Capacity 1/p 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 650 610 570 530 490 450 410 370 330 290 250 210 170 130 90 50 10 Batch Size So why not choose a large batch size to increase capacity? Larger Batch Leads to a Lot of Inventory(either in process or in storage) Production with large batches Cycle Inventory Production with small batches Cycle Inventory Produce Sedan Produce Station wagon Beginning of Month End of Month Example: 2 car models. Average demand is 400 per day. Beginning of Month End of Month Choosing a “Good” Batch Size Requires balance of capacity and inventory since both increase with increases in batch size. General principals Capacity at a bottleneck is extremely valuable; If setup occurs at a bottleneck, increase batch size. If setup occurs at non-bottleneck, decrease batch size Capacity as a function of Batch Size (60) Batch Size Supports Ribs Total Capacity Set-Up Prododuction Time Set-Up Prododuction Time Time per minute 1 60 1 60 1 122 0.01 12 60 12 60 12 144 0.08 24 60 24 60 24 168 0.14 36 60 36 60 36 192 0.19 48 60 48 60 48 216 0.22 60 60 60 60 60 240 0.25 120 60 120 60 120 360 0.33 240 60 240 60 240 600 0.40 360 60 360 60 360 840 0.43 720 60 720 60 720 1560 0.46 1440 60 x 60 = 0.25 unit/min 1440 60 1440 1/3 = 3000 (1/240) .333 unit/min 0.48 2880 60 2880 60 2880 5880 0.49 Step 1 Activity Time one Steer support: 1 min/part Two Rib: 0.5 min/part Step 2 3 min/part Capacity as a function of Batch Size (240) Batch Size Supports Ribs Total Capacity Set-Up Prododuction Time Set-Up Prododuction Time Time per minute 1 60 1 60 1 122 0.01 12 60 12 60 12 144 0.08 24 60 24 60 24 168 0.14 36 60 36 60 36 192 0.19 48 60 48 60 48 216 0.22 60 60 60 60 60 240 0.25 120 60 120 60 120 360 0.33 240 60 240 60 240 600 0.40 360 60 360 60 360 840 0.43 720 60 720 60 720 1560 0.46 1440 60 x240 = 0.4 unit/min 1440 60 1440 1/3 = 3000 (1/600) .333 unit/min 0.48 2880 60 2880 60 2880 5880 0.49 Step 1 Activity Time one Steer support: 1 min/part Two Rib: 0.5 min/part Step 2 3 min/part Capacity as a function of Batch Size (120) Batch Size Supports Ribs Total Capacity Set-Up Prododuction Time Set-Up Prododuction Time Time per minute 1 60 1 60 1 122 0.01 12 60 12 60 12 144 0.08 24 60 24 60 24 168 0.14 36 60 36 60 36 192 0.19 48 60 48 60 48 216 0.22 60 60 60 60 60 240 0.25 120 60 120 60 120 360 0.33 240 60 240 60 240 600 0.40 360 60 360 60 360 840 0.43 720 60 720 60 720 1560 0.46 1440 60 x120 = 0.333 unit/min 1440 60 1440 1/3 = 3000 (1/360) .333 unit/min 0.48 2880 60 2880 60 2880 5880 0.49 Step 1 Activity Time one Steer support: 1 min/part Two Rib: 0.5 min/part Step 2 3 min/part Batch size for our example For our example, the milling machine is the bottleneck (p=2 min/unit) plus a setup time of 120 minutes, as compared to the assembly process of 3 minutes/unit. To find the recommended batch size we need to have a target CT. The CT is variable for the bottleneck depending on the batch size because of setup. Therefore, we will use the CT for smallest capacity of the non-bottleneck steps. Step 1 Activity Time Setup time: one Steer support: 1 min/part Two Rib: 0.5 min/part 60 minutes x 2 = 120 minutes Step 2 3 min/part Batch size for our example Capacity given Batch Size = Batch Size Set-up time + Batch-size*Time per unit And we will set Capacity = Capacity for the slowest non-bottleneck SO: Batch Size Cap for the slowest non-bottleneck = Batch Size 0 + Batch-size*3 = Set-up time + Batch-size*Time per unit Batch Size 120 + Batch-size*2 Therefore we can solve for recommended batch size: B = 120 0 + Batch-size*3 = 120 + Batch-size*2 Choosing a “Good” Batch Size 0.5 Capacity 1/p 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 Batch<120 no products in non-bottleneck Batch>120 piles up inventory 650 610 570 530 490 450 410 370 330 290 250 210 170 130 90 50 10 Batch Size Example (Batch sizes are 50, 249, and 251) Step 1 Step 2 Activity Time 0.2 min/part 0.10 min/part Setup Time 15min 40 min Compute the capacity of the system when the batch sizes are 50, 249 or 251 parts. What is the bottleneck? Processing time for one batch = Setup Time + Batch size * runtime (min) Q=50 Processing time for one batch Step 1 Step 2 What is a bottleneck? Capacity (# of batches per hour) Capacity (# of units per hour) Example Step 1 Step 2 Activity Time 0.2 min/part 0.10 min/part Setup Time 15min 40 min Compute the capacity of the system when the batch size is 50 parts. What is the bottleneck? Processing time for one batch = Setup Time + Batch size * runtime (min) Processing time for one batch Capacity (# of batches per hour) Capacity (# of units per hour) Step 1 15 + 0.2 x 50 = 25 60/25 = 2.4 2.4*50 = 120 Step 2 40 + 0.1 x 50 = 45 60/45 = 1.33 1.33*50 = 66.66 Example (Batch sizes are 50, 249, and 251) Step 1 Step 2 Activity Time 0.2 min/part 0.10 min/part Setup Time 15min 40 min Compute the capacity of the system when the batch sizes are 50, 249 or 251 parts. What is the bottleneck? Processing time for one batch = Setup Time + Batch size * runtime (min) Q=100 Processing time for one batch Step 1 Step 2 What is a bottleneck? Capacity (# of batches per hour) Capacity (# of units per hour) Example Step 1 Step 2 Activity Time 0.2 min/part 0.10 min/part Setup Time 15min 40 min Compute the capacity of the system when the batch size is 100 parts. What is the bottleneck? Processing time for one batch = Setup Time + Batch size * runtime (min) Processing time for one batch Capacity (# of batches per hour) Capacity (# of units per hour) Step 1 15 + 0.2 x 100= 35 60/35 = 1.714 1.714*100 = 171.4 Step 2 40 + 0.1 x 100= 50 60/50 = 1.2 1.2*100 = 120 Example (Batch sizes are 50, 249, and 251) Step 1 Step 2 Activity Time 0.2 min/part 0.10 min/part Setup Time 15min 40 min Compute the capacity of the system when the batch sizes are 50, 249 or 251 parts. What is the bottleneck? Processing time for one batch = Setup Time + Batch size * runtime (min) Q=249 Processing time for one batch Step 1 Step 2 What is a bottleneck? Capacity (# of batches per hour) Capacity (# of units per hour) Example Step 1 Step 2 Activity Time 0.2 min/part 0.10 min/part Setup Time 15min 40 min Compute the capacity of the system when the batch size is 249 parts. What is the bottleneck? Processing time for one batch = Setup Time + Batch size * runtime (min) Processing time for one batch Capacity (# of batches per hour) Capacity (# of units per hour) Step 1 15 + 0.2 x 249= 64.8 60/64.8 = 0.9259 0.9259 x 249 = 230.549 Step 2 40 + 0.1 x 249= 64.9 60/64.9 = 0.9244 0.9244 x 249 = 230.176 Example (Batch sizes are 50, 249, and 251) Step 1 Step 2 Activity Time 0.2 min/part 0.10 min/part Setup Time 15min 40 min Compute the capacity of the system when the batch sizes are 50, 249 or 251 parts. What is the bottleneck? Processing time for one batch = Setup Time + Batch size * runtime (min) Q=251 Processing time for one batch Step 1 Step 2 What is a bottleneck? Capacity (# of batches per hour) Capacity (# of units per hour) Example Step 1 Step 2 Activity Time 0.2 min/part 0.10 min/part Setup Time 15min 40 min Compute the capacity of the system when the batch size is 251 parts. What is the bottleneck? Processing time for one batch = Setup Time + Batch size * runtime (min) Processing time for one batch Capacity (# of batches per hour) Capacity (# of units per hour) Step 1 15 + 0.2 x 251= 65.2 60/65.2 = 0.9202 0.9202 x 251 = 230.97 Step 2 40 + 0.1 x 251= 65.1 60/65.1 = 0.9217 0.9217 x 251 = 231.34 Example (Batch sizes are 50, 249, and 251) Step 1 Step 2 Activity Time 0.2 min/part 0.10 min/part Setup Time 15min 40 min Compute the capacity of the system when the batch sizes are 50, 249 or 251 parts. What is the bottleneck? Processing time for one batch = Setup Time + Batch size * runtime (min) Q=300 Processing time for one batch Step 1 Step 2 What is a bottleneck? Capacity (# of batches per hour) Capacity (# of units per hour) Example Step 1 Step 2 Activity Time 0.2 min/part 0.10 min/part Setup Time 15min 40 min Compute the capacity of the system when the batch size is 300 parts. What is the bottleneck? Processing time for one batch = Setup Time + Batch size * runtime (min) Processing time for one batch Capacity (# of batches per hour) Capacity (# of units per hour) Step 1 15 + 0.2 x 300= 75 60/75 = 0.8 0.8 x 300 = 240 Step 2 40 + 0.10 x 300 = 70 60/70 = 0.857 0.857 x 300 = 257.1 Example Step 1 Step 2 Activity Time 0.2 min/part 0.10 min/part Setup Time 15min 40 min Example Step 1 Step 2 Activity Time 0.2 min/part 0.10 min/part Setup Time 15min 40 min For what maximum value of batch size does step 2 become a bottleneck in the system? Example Step 1 Step 2 Activity Time 0.2 min/part 0.10 min/part Setup Time 15min 40 min For what maximum value of batch size does step 2 become a bottleneck in the system? Compare the processing times (including setup) of two steps. If processing time at Step 1 is greater than at Step 2, Step 1 becomes a bottleneck. Processing time @step 1 >= Processing time @step 2 Set up (@ step 1) + B x processing time (@ step 1) >= Set up (@ step 2) + B x processing time (@ step 2) 15 min + 0.2 x B >=40 min + 0.1 B 0.1B >=25 B >=250 Answer: If batch size is less than 250, Step 2 is a bottleneck. Example Step 1 Step 2 Activity Time 0.2 min/part 0.2 min/part Setup Time 15min 20 min Step 3 0.10 min/part 40 min Compute the capacity of the system when the batch size is 1 part. What is the bottleneck? Processing time for one batch = Setup Time + Batch size * runtime (min) Processing time for one batch Step 1 Step 2 Step 3 Capacity (# of batches per hour) Capacity (# of units per hour) Example Step 1 Step 2 Activity Time 0.2 min/part 0.2 min/part Setup Time 15min 20 min Step 3 0.10 min/part 40 min Compute the capacity of the system when the batch size is 1 part. What is the bottleneck? Processing time for one batch = Setup Time + Batch size * runtime (min) Processing time for one batch Capacity (# of batches per hour) Step 1 15 + 0.2 x 1= 15.2 60/15.2 Step 2 20 + 0.2 x 1 = 20.2 60/20.2 Step 3 40 + 0.10 x 1 = 40.1 60/40.1 Capacity (# of units per hour) Example Step 1 Step 2 Activity Time 0.2 min/part 0.2 min/part Setup Time 15min 20 min Step 3 0.10 min/part 40 min Compute the capacity of the system when the batch size is 50 parts. What is the bottleneck? Processing time for one batch = Setup Time + Batch size * runtime (min) Processing time for one batch Capacity (# of batches per hour) Capacity (# of units per hour) Step 1 15 + 0.2 x 50= 25 60/25 = 2.4 2.4*50 = 120 Step 2 20 + 0.2 x 50 = 30 60/30 = 2.0 2 * 50 = 100.0 Step 3 40 + 0.10 x 50 = 45 60/45 = 1.33 1.33*50 = 66.66 Example Step 1 Step 2 Activity Time 0.2 min/part 0.2 min/part Setup Time 15min 20 min Step 3 0.10 min/part 40 min Compute the capacity of the system when the batch size is 199 parts. What is the bottleneck? Processing time for one batch = Setup Time + Batch size * runtime (min) Processing time for one batch Capacity (# of batches per hour) Capacity (# of units per hour) Step 1 15 + 0.2 x 199= 54.8 60/54.8 = 1.095 1.095*199 = 217.88 Step 2 20 + 0.2 x 199 = 59.8 60/59.8 = 1.003 1.003 *199 = 199.67 Step 3 40 + 0.10x199 = 59.9 60/59.9 = 1.0016 1.0016 * 199 = 199.33 Example Step 1 Step 2 Activity Time 0.2 min/part 0.2 min/part Setup Time 15min 20 min Step 3 0.10 min/part 40 min Compute the capacity of the system when the batch size is 200 parts. What is the bottleneck? Processing time for one batch = Setup Time + Batch size * runtime (min) Processing time for one batch Capacity (# of batches per hour) Capacity (# of units per hour) Step 1 15 + 0.2 x 200= 55 60/55 = 1.09 1.09*200 = 218.18 Step 2 20 + 0.2 x 200 = 60 60/60 = 1.0 1 * 200 = 200.0 Step 3 40 + 0.10 x 200 = 60 60/60 = 1.0 1 * 200 = 200.0 Example Step 1 Step 2 Activity Time 0.2 min/part 0.2 min/part Setup Time 15min 20 min Step 3 0.10 min/part 40 min Compute the capacity of the system when the batch size is 201 parts. What is the bottleneck? Processing time for one batch = Setup Time + Batch size * runtime (min) Processing time for one batch Capacity (# of batches per hour) Capacity (# of units per hour) Step 1 15 + 0.2 x 201= 55.2 60/55.2 = 1.087 1.087*201 = 218.487 Step 2 20 + 0.2 x 201 = 60.2 60/60.2 = 0.9967 0.9967 * 201 = 200.337 Step 3 40 + 0.10 x 201 = 60.1 60/60.1 = 0.9983 0.9983 * 201 = 200.6583 Example Step 1 Step 2 Activity Time 0.2 min/part 0.2 min/part Setup Time 15min 20 min Step 3 0.10 min/part 40 min Compute the capacity of the system when the batch size is 500 parts. What is the bottleneck? Processing time for one batch = Setup Time + Batch size * runtime (min) Processing time for one batch Capacity (# of batches per hour) Capacity (# of units per hour) Step 1 15 + 0.2 x 500= 115 60/115 (60/115) x 500 Step 2 20 + 0.2 x 500 = 120 60/120 (60/120) x 500 Step 3 40 + 0.10 x 500 = 90 60/90 (60/90) x 500 Example Step 1 Step 2 Activity Time 0.2 min/part 0.2 min/part Setup Time 15min 20 min Step 3 0.10 min/part 40 min Example Step 1 Step 2 Activity Time 0.2 min/part 0.2 min/part Setup Time 15min 20 min Step 3 0.10 min/part 40 min For what maximum value of batch size is step 3 bottleneck in the system? Example Step 1 Step 2 Activity Time 0.2 min/part 0.2 min/part Setup Time 15min 20 min Step 3 0.10 min/part 40 min For what maximum value of batch size is step 3 bottleneck in the system? Set up (@ step 3) + B x processing time (@ step 3) = Set up (@ step 2) + B x processing time (@ step 2) 40 + B x 0.1 = 20 + B x 0.2 20 = 0.1 B B = 200 Example Step 1 Step 2 Activity Time 0.15 min/part 0.2 min/part Setup Time 30 min 20 min Step 3 0.10 min/part 40 min Practice Problem Q5.5 (JCL Inc.) (a) Practice Problem Q5.5 (JCL Inc.) (b) Practice Problem Q5.5 (JCL Inc.) (c) Observations Setups have an impact on process capacity so it is important to integrate them when choosing batch size: Use either setup time or setup cost to determine batch size If we adopt a process flow perspective, then setup TIMEs should be used to determine batch size If we are incurring out-of-pocket cost and the focus is on a single resource, then use setup COSTS to determine batch sizes. If we encounter both, then compute the Q based on both and choose one for implementation