IEOR 130 Methods of Manufacturing Improvement Practice Examination Problems Part II of Course Prof. Leachman Fall, 2017

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1 IEOR 130 Methods of Manufacturing Improvement Practice Examination Problems Part II of Course Prof. Leachman Fall, For a particular semiconductor product, the customer orders received to date are as follows, sorted by date due to ship to customer: Delivery date Total orders due The current finished goods inventory of the product is 80 units. The production plan for the product is as follows: Output date Output quantity (a) A new customer calls and asks for delivery of 10 units per period beginning in period 4 and ending in period 6. Can the company provide delivery as requested? (b) Calculate the best delivery schedule the company can offer the customer. (c) Assuming the customer accepts the quote you calculated in part (b), calculate the new available-to-promise (ATP) quantities by period. Indicate whether you use cumulative ATP or incremental ATP. 2. For a particular semiconductor product, the customer orders received are as follows, sorted by date due to ship to customer: Delivery date Total orders due The current finished goods inventory of the product is 120 units. The production plan for the product is as follows: Output date Output quantity (a) A new customer calls and asks for delivery of 30 units per period beginning in period 3 and ending in period 6. Can the company provide delivery as requested? (b) Calculate the best delivery schedule the company can offer the customer. 1

2 (c) Assuming the customer accepts the quote you calculated in part (b), calculate the new available-to-promise (ATP) quantities by period. Indicate whether you use cumulative ATP or incremental ATP. 3. The finished goods inventory of a particular device is 100 units. The projected output over the next 6 weeks is 50, 50, 40, 40, 50, 50, respectively. The on-hand orders due for delivery over the next 6 weeks are 100, 60, 60, 40, 40, 20, respectively. (a) Calculate the availability of the device. (b) A prospective customer calls and asks for a delivery quote. The customer requests a delivery of 15 units per week in weeks 3, 4, 5, 6. If these quantities can not be met, the customer would like a quote of deliveries catching up to this schedule as quickly as possible. Calculate the best delivery quote that can be offered to the customer. (c) The same company sells a different device type that has bin splits into high-speed, mediumspeed and low-speed versions. These bin splits are 25%, 25% and 50%, respectively. Customers for the low speed version will accept shipment of either the medium-speed or the high-speed version in lieu of a low-speed version; customers for the medium-speed version will accept shipment of the high-speed version in lieu of the medium-speed version; and customers for the high-speed version will not accept any version substitution. Currently the company has 50 units in inventory of the low-speed version, but no inventory of the other versions. There are orders for 25 units of the high-speed version, 50 units of the medium-speed version, and 100 units of the low-speed version that need to be filled as soon as possible. Given the bin splits, the orders and the initial inventory, determine the minimum number of units of the device type that should be manufactured. 4. For a particular semiconductor product, the customer orders received are as follows, sorted by date due to ship to customer: Delivery date Total orders due The current finished goods inventory of the product is 200 units. The production plan for the product is as follows: Output date Output quantity (a) A new customer calls and asks for delivery of 10 units in period 2, 10 units in period 3 and 10 units in period 5. Can the company provide delivery as requested? 2

3 (b) Calculate the best delivery schedule the company can offer the customer. (c) Assuming the customer accepts the quote you calculated in part (b), calculate the new available-to-promise (ATP) quantities by period. (d) Now suppose that because of yield problems, the output quantity in period 5 is reduced to 60 (instead of 70). How does the quote to the new customer change? 5. A semiconductor company sells a device type that has bin splits into high-speed and lowspeed versions. These bin splits are 25% and 75%, respectively. Customers for the low speed version will accept shipment of the high-speed version in lieu of a low-speed version. Customers for the high-speed version will not accept version substitution. Currently the company has 100 units in inventory of the low-speed version, but no inventory of the high-speed version. The production plan for the product is as follows: Output date Output quantity before bin split The total customer orders received are as follows, sorted by date due to ship to customer: Delivery date Total orders due for high-speed Total orders due for low-speed (a) Calculate the available-to-promise (ATP) quantities for both versions by period. Indicate whether you use cumulative ATP or incremental ATP. (b) A new customer calls and asks for a delivery quote. The customer requests a delivery of 10 units of high-speed version and 20 units of low-speed version per day on day 2 and day 3. If these quantities cannot be met, the customer would like a quote of deliveries catching up to this schedule as quickly as possible. Calculate the best delivery quote that can be offered to the customer. (c) Suppose the fab experienced unexpected machine down when the new customer calls. The fab management is forced to adjust the production plan so that the actual output will be as follows: Output date Output quantity before bin split Can the company still ship as planned? How should it respond to the new customer in this case? 3

4 6. Formulate linear programs to accomplish requirements planning of binning products for the simplified case below. The goal is to efficiently translate demands for final products into demands for starts of assembly products. The notation and parameters are as follows. Indices t time period, t = 1,, T. i assembly product, i = 1,, I. j quality bin of assembly product, j = 1,., J. k final product, k = 1,, K. r demand class, r = 1,2. Class 1 consists of customer commitments that must be fulfilled as ontime as possible. Class 2 includes class 1 commitments plus all other forecasted demand. Demands d = demand in class r for final product k during period t. r kt Product structure i j denotes that assembly product i generates bin j. j k denotes that bin j is suitable for fulfilling demands for final product k. k j denotes that final product k is an allowed usage of bin j. aij = fraction of output of assembly product i that falls into bin j. L = cycle time for assembly products (assumed to be integer). Economic parameters cit = discounted cost of output of one unit of assembly product i in period t. skt = discounted revenue for one unit of final product k in period t. bkt = discounted backorder cost for one unit of final product k committed in period t. Initial conditions Ij0 = initial inventory of bin j. wit = projected WIP-out of assembly product i in period t, t = 1,, L. BOk0 = initial shortage to customer commitments of final product k. 7. The process flow for making an advanced DRAM device requires the use of a 193nm scanner photolithography machine at the photo steps in layers 1, 5 and 9. The cycle times from fab start to the photo steps in layers 1, 5 and 9 are 0.2 weeks, 0.8 weeks and 1.8 weeks, respectively. The fab line yield is 100%. The UPH (units per hour) factors at the photo steps in layers 1, 5 and 9 are 50, 48 and 45, respectively. There are 3 193nm scanners in service. The CEE of the 193nm scanners is 72%. The fab operates 24 hours a day, 7 days per week. The 193nm scanner is believed to be the fab bottleneck equipment type. It is desired to develop a capacity constraint on weekly fab starts for the purposes of production planning. 4

5 (a) Let xt denote the fab starts in week t. Express the 193nm scanner capacity constraint on xt, xt-1 and xt-2. You may assume the fab will operate every day of every week. You do not need to simplify your expression. (b) (6 points) In steady state, how many wafers may be started per week? (c) Suppose 4,000 wafer starts were made last week, and 6,000 wafer starts were made the week before that. What is the maximum number of wafers that may be started this week without extending 193nm scanner cycle time? 8. A small fabrication line operates two process flows, flow A and flow B. The important steps in each flow are as follows: Flow A Flow B Qualified CT up Qualified CT up Step UPH Machine_types to Step Step UPH Machine_types to Step 1 50 M M1 or M M1 or M M1 or M2 or M M1 or M M1 or M2 or M3 2 Note: UPH = units per hour, the speed of the machine when it performs that step. CT up to step is the average cycle time from fab start to arrival at the process step, expressed in weeks. Data on the photo machines is as follows: Machine_type Quantity CEE M M M The factory operates 168 hours per week and line yield losses are negligible. (a) Let xt denote the constant rate of starts of flow A in week t, and let yt denote the constant rate of starts of flow B in week t. Express capacity constraints on xt and yt in an arbitrary week t. You do not need to simplify numerical expressions. (b) Suppose no starts of flow B are allowed. What is the maximum steady-state starts rate for flow A? In that case, which machine type(s) is (are) the bottleneck(s)? (c) Suppose no starts of flow A are allowed. What is the maximum steady-state starts rate for flow B? In that case, which machine type(s) is (are) the bottleneck(s)? (d) The starts rates in the last two weeks for each flow were as follows: 5

6 Week Flow A Flow B 0 9,000 12, ,000 14,000 If in week 1 the starts for flow A are required to be zero, what is maximum amount of starts of flow B that should be allowed in week 1? Why is this number different from your answer to part (c)? Which machine type(s) will be the bottleneck(s) in week 1? 9. A small fabrication line operates two process flows, 180nm and 250nm. The photo steps are as follows: 180nm 250nm CT up CT up Step UPH Machine_type to Step Step UPH Machine_type to Step 1 50 Scanner DUV stepper DUV stepper I Line stepper DUV stepper I Line stepper DUV stepper I Line stepper Scanner DUV stepper 4 Note: UPH = units per hour, the speed of the machine when it performs that step. CT up to step is the average cycle time from fab start to arrival at the process step, in weeks. Data on the photo machines is as follows: Machine_type Quantity CEE Scanner DUV stepper I Line stepper The factory operates 168 hours per week and line yield losses are negligible. (a) Let xt denote the constant rate of 180nm starts in week t, and let yt denote the constant rate of 250nm starts in week t. Express capacity constraints on xt and yt for each type of photo machine in an arbitrary week t. You do not need to simplify numerical expressions. (b) If in every week t, xt = yt, what is the maximum steady-state starts rate for each process flow? (c) For your answer to (b), which machine type(s) is (are) the bottleneck(s)? (d) Can the starts rate of either the 180nm or 250nm processes be increased from your answer to (b) without exceeding capacities? If so, how much? 6

7 (e) Considering your answer to (d), has (have) the bottleneck(s) changed? If so, what is (are) the bottleneck(s) now? 10. Consider a factory that has two products in production, A and B. Sales of product A are a steady 1,000 wafers per week and its remaining product life is two years. The average selling price per wafer is $5,000 and that price is declining 30% per year. Sales of product B are a steady 5,000 wafers per week and the remaining product life is one year. The average selling price per wafer is $2,000 and that selling price is declining 60% per year. (a) The cycle time to make product A is 30 days. The cycle time to make product B is 45 days. Compute the remaining lifetime revenue for each product. (b) There are 17 photo machines in the factory and they achieve 88% availability operating 168 hours per week. The mean and standard deviation of a down time event on photo machines at the factory are 9 and 6 hours, respectively. There are 17 photo steps to make product A and 20 photo steps to make product B. The process time to perform any photo step is 0.5 hours per 25-wafer lot and the standard cycle time per lot is 0.75 hours. Assume line yields for both products are 100%. Assuming utilization is balanced across all 10 photo machines, compute the utilization of availability of the photo machines. (c) Let m denote the number of photo machines qualified to perform a given photo step. Management is considering engineering work to qualify more photo machines at various photo steps to make Product A as follows: Step m # of Required Type steps engineering hours in flow to add 1 more to m for all steps of that type Management also is considering engineering work to qualify more photo machines at various photo steps to make Product B as follows: Step m # of Required Type steps engineering hours in flow to add 1 more to m for all steps of that type Estimate the current total cycle time for each type of photo step on each product. You may assume ca 2 =1, and c0 2 = 1 for all step types. 7

8 (d) If all of the proposed work for Product A is undertaken, what additional revenue will the company obtain over the life of Product A? If all of the proposed work for Product B is undertaken, what additional revenue will the company obtain over the life of Product B? (e) Because of other engineering tasks and limited engineering staff, the company might not be able to undertake all of the photo qualification work above. Order the product-step-type projects listed above in the order of decreasing economic return per engineering hour expended. 11. The photolithography department is considering doing the engineering work to qualify one more photo machine at various photo steps. There are different possible steps where this work could be done. Information is as follows: Step m MTTR cr 2 PT (per A U/A # of Required Type step) steps engineering hours in flow to add 1 more to m to each step of that type (a) Estimate the cycle time per step for each machine type. You may assume fab line yield is 100%, ca 2 =1, c0 2 = 1 and SCT = 1.5 per step for all step types. (b) Considering the number of steps in the overall process flow within each step type, estimate the total cycle time of each step type. (c) For each step type, estimate the total cycle time reduction if one more machine is qualified for every step of that type. Assume no more machines are installed and the fab starts rate is kept constant. (d) Considering the cycle time reduction per engineering hour expended, which step type qualification effort has the highest return on investment? 12. The management of a wafer fab with one process flow is considering the purchase of an additional process machine in order to reduce cycle time. At present, there is room in the fab for one more machine of either Type 1 or Type 2. Statistics about these machines are as follows: Type m MTTR cr 2 PT (per A U/A SCT (per No. of steps step) step) in process flow (a) Estimate the cycle time per step for each machine type. You may assume fab line yield is 100%, ca 2 =1, and c0 2 = 1. 8

9 For type 1, the queue time per step is 9.4 hours and the cycle time per step is 10.9 hours. For type 2, the queue time per step is 5.0 hours and the cycle time per step is 6.6 hours. (b) Considering the number of steps in the process flow performed by each machine type, estimate the total cycle time in the process flow contributed by each machine type. (c) Estimate the total cycle time reduction if one more machine of type 1 is installed, while keeping the fab starts rate constant. (d) Repeat (c) for one more machine of type 2. (e) The cost to install one more machine of type 1 is 1.0 million dollars. The cost to install one more machine of type 2 is 1.5 million dollars. Which installation would offer the greatest cycle time reduction per capital dollar expended? 13. The photolithography department in a semiconductor fabrication plant has 10 identical photo machines. Manufacturing lots move through a series of 100 steps in the plant, including five photolithography steps. At present, any of the ten machines can be used to perform any of the five photo steps. To improve the die yield, the photo process engineer proposes a lot-to-lens dedication policy, whereby each manufacturing lot would be required to visit the same photo machine for processing of photo steps 2, 3, 4 and 5 that the lot visited for photo step 1. It still would be the case that a lot could be processed by any of the ten machines at photo step 1. Suppose the photo machines average 90% availability, the factory works 168 hours per week, and the total hours of processing work that the ten photolithography machines perform is 1250 hours per week. a. Assuming utilization of the ten machines is balanced, what is the utilization of availability for the photo machines? b. Assume all lots at all photo steps have the same process time. Assume the proposed change in policy would not have any effect on the lot inter-arrival times at each step nor any effect on equipment down times or process times. Estimate the RATIO of lot queue time at photo step 2 if lot-to-lens dedication is implemented to lot queue time at photo step 2 at present. c. Estimate the percentage increase in total lot queue time for all five photo steps if lot-to-lens dedication is implemented. You may assume there is no line yield loss, i.e., each step has an equal production volume. 14. The processing cycle for a diffusion furnace consists of three phases: load, run, and unload. During the load portion of the cycle, an operator transfers wafers from incoming lots into a boat accommodating 150 wafers. If the incoming lots include less than 150 wafers, the operator inserts dummy wafers to raise the total wafers in the boat up to 150. During the run portion of the cycle, the boat is mechanically inserted into the furnace, the wafers are cooked for a specified length of time, and then the boat is mechanically withdrawn from the furnace. During the unload portion of the cycle, the operator unloads the product wafers from the boat into lots 9

10 to be sent to follow-on operations, and he/she unloads the dummy wafers for re-use in subsequent furnace runs as may be required. For a particular furnace, the run portion of the cycle takes exactly 6 hours every cycle. The theoretical times to perform the load and unload portions of the cycle are 0.5 hours each, but sometimes the operators take longer to complete these tasks. The average load time is estimated to be 0.6 hours (and the average unload time also is 0.6 hours). Last week this furnace completed 20 process cycles and experienced 4.5 hours of down time. The average batch size was 5.7 lots (i.e., product wafers). (a) Estimate the utilization of total time, utilization of availability, and OEE of this furnace last week. Assume the factory is operated 24 hours per day, seven days per week. (b) Identify the two reasons that rate efficiency was less than 100% for this furnace. (c) The equipment vendor offers a modification to the furnace whereby the furnace would be equipped with dual boats instead of a single boat. If equipped with dual boats, the operator could load boat B while the furnace was running boat A. After the run on boat A was completed, the furnace could immediately start the run on boat B. In parallel with the run on boat B, the operator could unload boat A. When loading and unloading are conducted in parallel with processing, the furnace is said to be backloaded. If equipped with dual boats, what is the reduction in theoretical process time per cycle? (d) Assuming the same number of process cycles were run with the same average batch size, estimate the OEE and utilization of availability last week if the furnace had been equipped with dual boats and all batches could be backloaded. (e) Assuming the same number of process cycles were run with the same average batch size, estimate the reduction in cycle time last week if the furnace had been equipped with dual boats and all batches could be backloaded. Assume there are no alternative furnaces, i.e., this is the only one that can be used, and assume down time statistics and process time variability would be unchanged if dual boats are installed. Other data: c0 = 1, MTTR = 4.5, cr = 1.0, ca = 1, lot arrival rate = lots per hour. (f) Suppose the current revenue from one lot is $25,000 and is declining 25% per year. The current fab cycle time is 40 days. The remaining product lifetime is 3 years. Assuming last week s processing rate is maintained, estimate the revenue gain from installation of dual boats in the furnace. 15. A wet bench consists of a series of tanks served by a robot arm. Two production lots (50 wafers total) form one batch that travels down the bench. The batch is dunked in each tank by the robot arm. One of the tanks contains sulfuric acid that strips an undesired film off the wafers. With repeated use, the acid bath contains more and more residue from previously stripped wafers, and there is increasing probability that the film on the wafers in the next batch may be inadequately stripped. An inspection step carried out after the wet bench step would detect this, 10

11 in which case the batch must be re-worked. At some point the acid bath must be dumped and repoured with fresh acid; this involves one hour of down time to the wet bench as well as the expenses for new sulfuric acid and disposing of the old acid. The process time in the sulfuric acid tank is 30 minutes per batch, whether for a first-time batch or a re-worked batch. Each batch is dunked for a lesser amount of time in the other tanks on the bench (pre-cleaning, rinsing and drying); the total time for a batch to traverse the bench is 90 minutes. The wet etch engineer estimates the probability that rework is required is a linear function of bath usage: P(n) = 0.05*n, where n is the number of first-time batches processed since the acid bath was re-poured and P(n) is the probability that the n th batch must be re-worked. You may assume that with probability one a batch that is reworked will be successfully stripped of the undesired film on the second pass through the tank, and that reworking does not cause the acid bath to deteriorate. (a) Suppose our objective is maximum wet-bench capacity. What frequency of re-pour is best? (By frequency, we mean how many batches between re-pours of the sulfuric acid bath.) (b) Now suppose our objective is minimum cycle time. Assume the following data for the wet bench: m=1, ca = 1, ce = 1, the wet bench receives 250 lots per week (i.e., 125 batches per week, excluding rework), and the only down time is for re-pouring the acid bath. Now what frequency of re-pour is best? (Hint: You can calculate the availability and average rework rate as functions of the re-pour frequency. And be sure to include rework in utilization.) (c) Now suppose our objective is maximum profit. What factors should be taken into account to decide the best frequency of re-pour? What other data would you request in order to make this determination? 16. A wafer fab operates a single process flow that has a photo step at the end of layers one through five. Layer six includes the remaining process steps after the last photo step. A detailed simulation of the fab has been run and stable steady-state statistics were collected as follows: Layer Avg. Wait time Std. Dev. Of Wait time Avg. No. of Lots in the layer (days) in the layer (days) in the layer The average output rate in the steady-state statistics of the simulation is 20 lots per day. (a) What was the steady-state average total cycle time in the simulation? 11

12 (b) Suppose management sets the target cycle time for the process flow to be equal to the simulated average total cycle time. For an output rate of 20 lots per day, recommend target WIP levels in each layer. (c) Suppose fab outs to date are on time, and suppose the target output rate of 20 lots per day will be maintained for many weeks. The fab operates two 12-hour shifts per day. Suppose it is the start of a shift and the current WIP levels in each layer are as follows: Layer WIP (no. of lots) Calculate IPQs and Schedule Scores for each photo step. What is the priority order for scheduling the photo steps? (d) In the etch area of the fab, the process time is 0.5 hours for all etch steps. There are two etch machines, M1 and M2. Each machine can perform any etch step. At the start of the shift, the etch area has the following data: Step IPQ (lots) Available WIP (lots) A 6 4 B 2 4 C D 2 8 The following shift schedule has been prepared by the etch area supervisor: Machine M1: Run 4 lots of A, then run 2 lots of B, then run 6 lots of C Machine M2: Run 8 lots of C, then run 4 lots of D Can this schedule be improved upon? If so, suggest the best schedule you can, and briefly note the reasons why your schedule should be preferred over the schedule above. 17. A fabrication process includes 4 visits to the photo bottleneck, one each at the end of layers 1, 2, 3 and 4. Recent statistics about the fabrication process are as follows: Layer Avg. total WIP Avg. active WIP (no. of lots) (no. of lots)

13 The average production rate during the period of data collection was 10 lots per shift. No line yield losses were experienced. (a) Recommend target cycle times by layer assuming line yields are 100% and the overall target cycle time is 50 shifts. (b) Current WIP status is as follows. Data concerning the photo steps also is displayed. Layer Actual WIP WIP at Photo Photo process Qualified (lots) (lots) time (hours/lot) Machines A, B, C B, C A, B C 5 15 Assume it is now the start of a shift and that fab-outs to date are on time. The target production rate continues to be 10 lots per shift. Calculate the ideal production quantity (IPQ) and the schedule score (SS) for each photo step for this shift. (c) Assume one shift lasts 8 hours. Using the data in part (b), determine an efficient shift schedule for the steppers. Assume only the WIP at photo may be scheduled and assume all 3 steppers will be available for all 8 hours. (An efficient schedule has the following properties: as much of the IPQs are completed as possible, steppers are utilized as much as possible, and changeovers of the steppers are minimized.) 18. A fabrication process includes 4 visits to the photo bottleneck, one each at the end of layers 1, 2, 3 and 4. Recent statistics about the process are as follows: Layer Avg. cycle time Standard Avg. number of (shifts) cycle time (shifts) active lots (a) Assuming the current production rate is the same as the rate during the period the above statistics were tabulated, recommend target WIP levels by layer, assuming line yields are 100% and the target cycle time is 40 shifts. (b) The current WIP status is as follows. Data concerning the photo steps at the end of each layer also are displayed. 13

14 Layer Actual WIP WIP at Photo Photo process Qualified (lots) (lots) time (hours/lot) Machines A, B, C B, C A, B C 5 15 Assume it is currently the start of a shift. Calculate the ideal production quantity (IPQ) and the schedule score (SS) for each photo step for the upcoming shift. (c) Assume one shift lasts 8 hours. Using the data in part (b), determine an efficient shift schedule for the steppers. Assume only the WIP at photo may be scheduled and assume all 3 steppers will be available for all 8 hours. (An efficient schedule has the following properties: as much of the IPQs are completed as possible, steppers are utilized as much as possible, and changeovers of the steppers are minimized.) 19. A fabrication process includes 4 visits to the photo bottleneck, one each at the end of layers 1, 2, 3 and 4. A simulation of the fabrication process produced the following statistics: Layer Avg. cycle time Standard deviation Avg. number of (shifts) of cycle time (shifts) active lots (Note: Active lots are lots that are not waiting, i.e., they are experiencing processing or transport between steps.) The simulated average production rate was 10 lots per shift. No line yield losses were simulated. (a) Recommend target cycle times by layer assuming line yields are 100% and the target cycle time is 40 shifts. (b) The fab outs at the end of the simulation had achieved the target output. The WIP status at the end of the simulation was as follows. Data concerning the photo steps also is displayed. Layer Actual WIP WIP at Photo Photo process Qualified (lots) (lots) time (hours/lot) Machines A, B, C B, C A, B C

15 Assume the simulation ended at the start of a shift. Calculate the ideal production quantity (IPQ) and the schedule score (SS) for each photo step for that shift. (c) Assume one shift lasts 8 hours. Using the data in part (b), determine an efficient shift schedule for the steppers. Assume only the WIP at photo may be scheduled and assume all 3 steppers will be available for all 8 hours. (An efficient schedule has the following properties: as much of the IPQs are completed as possible, steppers are utilized as much as possible, and changeovers of the steppers are minimized.) 20. A fabrication process includes three steps performed on the bottleneck equipment type. Layer 1 of the process ends at the first bottleneck step; layer 2 ends at the second bottleneck step; layer 3 ends at the third bottleneck step; and layer four includes all steps of the process after the third bottleneck step. The machines performing the bottleneck steps are inflexible whereby each bottleneck step must be performed by a different machine. Data on cycle times is as follows: Layer Actual Avg. Standard Theoretical i Cycle Time Deviation of Cycle Time (ACTi) ACTi ( i) (SCTi) Management of the factory operating the process has decided to set the target cycle time for the process to be 90% of the actual average cycle time (ACT). The total WIP level in the process in the most recent week was 400. (a) According to management s target cycle time for the process, what is the target for the total WIP in the process? (b) Compute efficient target WIP levels for each layer. (c) Instead of your answer to (b), suppose management decides to set the target WIP level in each layer to be 90% of the actual WIP level in that layer. If management implements their target WIP levels, which of the three bottleneck steps will have the greatest idle time over the long run? And in this layer, will the amount of idle time be higher or lower than it would be using the target WIP levels in your answer in (b)? Explain. 21. A simulation of a factory with a single process flow achieves steady-state. Various machines are used to perform the steps of the process flow; each machine performs one step on one production lot at a time. The steady-state statistics show that, on average, 63.5 out of 80 machines are busy processing lots. Summing across all steps in the process flow, the average total waiting time for each lot is 8.5 days, and the average total number of lots in queues is (a) What is the production rate of the factory? 15

16 (b) What is the level of active WIP in the factory? (c) What is the standard cycle time of the process flow? (d) What is the actual cycle time of the process flow? 22. A wafer fab has a single process flow with five masking layers. The standard deviation of the WIP level at each photo exposure operation has been computed as follows: Layer 1-11 lots Layer 2-19 lots Layer 3-25 lots Layer 4-25 lots Layer 5-20 lots The sum of standard cycle times for the process steps in each layer has been computed as follows: Layer 1-2 days Layer 2-4 days Layer 3-4 days Layer 4-4 days Layer 5-4 days Layer 6-2 days (a) The target cycle time for the entire fab process is 60 days. The target production rate is 10 lots per day. Determine the target WIP level for each layer. (b) Currently, layer 5 has a WIP level of 150 lots. The photo stepper machines can process two lots per hour when they are up; average availability of these machines is 90% and the average utilization (of total time) is 75%. If two steppers are qualified to perform the layer 5 exposure, how long will it take to reduce the WIP in layer 5 to the target level? (c) How many steppers need to be qualified for layer 5 if the recovery time is to be within one shift, i.e., less than 8 hours? 16

17 23. A wafer fab has a single process flow with five masking layers. The standard deviation of the cycle time between photo exposure operations has been computed as follows: Fab-in to Layer 1 exposure shifts (where one shift equals 8 hours) Layer 1 exposure to Layer 2 exposure shifts Layer 2 exposure to Layer 3 exposure shifts Layer 3 exposure to Layer 4 exposure shifts Layer 4 exposure to Layer 5 exposure shifts Layer 5 exposure to fab-out shifts The sum of standard cycle times for the process steps in each layer has been computed as follows: Layer 1-2 shifts Layer 2-4 shifts Layer 3-4 shifts Layer 4-4 shifts Layer 5-4 shifts Layer 6-2 shifts (a) The target cycle time for the entire fab process is 40 shifts. The target production rate is 10 lots per shift. Determine the target WIP level for each layer. (b) Currently, layer 5 has a WIP level of 110 lots. The photo stepper machines each can process two lots per hour when they are up; average availability of these machines is 90% and the average utilization (of total time) is 65%. If two steppers are qualified to perform the layer 5 exposure, estimate how long it will take to reduce the WIP in layer 5 to the target level. (c) How many steppers would need to be qualified for layer 5 if the recovery time is to be within four hours, i.e., less than 0.5 shifts? (d) Now suppose at the start of a shift the actual WIP levels (expressed in lots) are as follows: Layer Total WIP WIP On-Hand Qualified in Layer at Photo step Steppers A,B,C,D 17

18 C,D A,B,C,D D B Assuming fab-outs up until the start of the shift are exactly on time, determine the ideal production quantity (IPQ) and schedule score (SS) for each photo operation. (Each photo operation is the last operation in its layer.) (e) The fab has four total steppers (A,B,C,D). Each stepper is qualified to perform only certain photo operations, as specified in the table above. Assume that all four steppers will be available all 8 hours during the shift, and that the process time per lot is 0.5 hours for all photo operations. Suggest an efficient shift schedule for the four steppers. Assume that only WIP on-hand at photo may be scheduled for processing by the steppers. 24. A wafer fab has a single process flow with five masking layers. The standard deviation of the WIP level at each photo exposure operation has been computed as follows: Layer 1-5 lots Layer 2-8 lots Layer 3-10 lots Layer 4-10 lots Layer 5-7 lots The sum of standard cycle times for the process steps in each layer has been computed as follows: Layer 1-1 day Layer 2-2 days Layer 3-2 days Layer 4-2 days Layer 5-2 days Layer 6-1 day 18

19 (a) The target cycle time for the entire fab process is 20 days. The target production rate is 8 lots per day. Determine the target WIP level for each layer. Identify the active WIP and buffer WIP levels for each layer. (b) Currently, the total WIP in each layer and the WIP at the photo operation in each layer are as follows. Layer Total WIP WIP at photo Compute the schedule score for the photo operation in each layer. Assume there is no shortage or surplus in fab outs to date. Assume there are two 12-hour shifts per day. (c) Suppose one of the steppers is about to run out of lots for its current operation. According to the schedule scores, which photo operation has the highest priority for next setup? (d) Suppose downstream WIP continues to move from layer to layer according to the target production rate, and suppose one stepper is set up to process the photo operation you identified in part (c). Estimate how long it will take to raise the schedule score for this operation to zero. Assume steppers have 90% availability, and assume the standard process time for photo operations is 2 hours per lot. 25. In a wafer fab with a single process flow and five masking layers, the following information on standard deviation of the cycle time between photo steps is available: Fab start to Layer 1 photo step shifts Layer 1 photo step to Layer 2 photo step shifts Layer 2 photo step to Layer 3 photo step shifts Layer 3 photo step to Layer 4 photo step shifts Layer 4 photo step to Layer 5 photo step shifts Layer 5 photo step to Fab out shifts The sum of the standard cycle times for the process steps in each layer has been computed as follows: Layer 1-1 shift 19

20 Layer 2-1 shift Layer 3-2 shifts Layer 4-3 shifts Layer 5-2 shifts Layer 6-1 shift (Note: "Layer 6" is just the portion of the fab process after the Layer 5 photo step until fab out.) (a) The target cycle time for the entire fab process is 25 shifts. The target production rate is 10 lots per shift. The photo machines are the bottleneck. Determine the target WIP level for each layer. (b) Currently, the total WIP in each layer, the WIP at the photo operation in each layer, and the qualified steppers in each layer are as follows: Layer Total WIP WIP at Photo Qualified Steppers A,C,D,E B,C C,D,E B,E D Assuming fab-outs up until the start of the shift are exactly on time, determine the ideal production quantity (IPQ) and schedule score (SS) for each photo operation. (c) The fab has five total steppers (A,B,C,D,E). Each stepper is qualified to perform only certain operations, as specified in the table above. Assume all five steppers are available for all 8 hours during the shift and that the process time per lot is 0.5 hours for all photo operations. Suggest an efficient schedule for the five steppers. Assume that only WIP on hand at the photo may be scheduled for processing by the steppers. 20