Chapter 4 Solutions
CHAPTER FOUR
Q4.3. Power Toys
(a) Since every resource has exactly one worker assigned to it, the bottleneck is the assembly station with the highest processing time (#3)
(b) Capacity = 1 / 90 sec = 40 units per hour
(c) Direct labor cost = Labor cost per hour / flow rate = 9*$15/h / 40 trucks per hour = $3.38/truck
(d) Direct labor cost in work cell= (75+85+90+65+70+55+80+65+80) sec/truck * $15/hr = $2.77/truck
(e) Utilization = flow rate / capacity 85 sec / 90 sec = 94.4%
(f)
(g) Capacity = 1 / 145 units/second = 24.83 toy--‐trucks per hour
Q4.4. 12 tasks to 4 workers
(a)
(a) Capacity = 1 / 85 sec = 42.35 units per hour
(b) Direct labor content = (70+55+85+60) sec = 270 sec/unit or 4.5 min/unit
(c) Labor utilization = labor content / (labor content + total idle time) = 270 sec / (270 + 15 + 30+
0 +25 sec) = 79.41%
(d) Note that we are facing a machine paced line, thus the first unit will take 4*85 seconds top go through the empty system. Flow Time = 4 * 85 sec + 99 / (1 / 85 sec) = 8755 sec or 145.92 min or 2.43 hrs
(e) There are multiple ways to achieve this capacity. This table shows only one example.
Capacity = 1 / 70 units/sec = 51.43 units per hour
(f) There are multiple ways to achieve this capacity. This table shows only one example.
Capacity = 1 / 55 units/sec = 65.45 units per hour
(g) We have to achieve a cycle time of 3600/72=50 seconds/unit. The following task allocation includes a lot of idle time, but is the only way to achieve the cycle time, given the constraints we face.
Therefore, a minimum of 8 workers are required to achieve a capacity of 72 units per hour.
Q4.8. Glove Design
(a.) Cutting has a process capacity of 1 glove/2 minutes*60 minutes = 30 gloves/hour. Dyeing has a process capacity of 1 glove/4 minutes*60 minutes = 15 gloves/hour. Stitching has a process capacity of 1 glove/3 minutes*60 minutes = 20 gloves/hour. Packaging has a process capacity of 1 glove/5 minutes*60 minutes = 12 gloves/hour. Therefore, the capacity is a. 12
Q4.3. Power Toys
(a) Since every resource has exactly one worker assigned to it, the bottleneck is the assembly station with the highest processing time (#3)
(b) Capacity = 1 / 90 sec = 40 units per hour
(c) Direct labor cost = Labor cost per hour / flow rate = 9*$15/h / 40 trucks per hour = $3.38/truck
(d) Direct labor cost in work cell= (75+85+90+65+70+55+80+65+80) sec/truck * $15/hr = $2.77/truck
(e) Utilization = flow rate / capacity 85 sec / 90 sec = 94.4%
(f)
(g) Capacity = 1 / 145 units/second = 24.83 toy--‐trucks per hour
Q4.4. 12 tasks to 4 workers
(a)
(a) Capacity = 1 / 85 sec = 42.35 units per hour
(b) Direct labor content = (70+55+85+60) sec = 270 sec/unit or 4.5 min/unit
(c) Labor utilization = labor content / (labor content + total idle time) = 270 sec / (270 + 15 + 30+
0 +25 sec) = 79.41%
(d) Note that we are facing a machine paced line, thus the first unit will take 4*85 seconds top go through the empty system. Flow Time = 4 * 85 sec + 99 / (1 / 85 sec) = 8755 sec or 145.92 min or 2.43 hrs
(e) There are multiple ways to achieve this capacity. This table shows only one example.
Capacity = 1 / 70 units/sec = 51.43 units per hour
(f) There are multiple ways to achieve this capacity. This table shows only one example.
Capacity = 1 / 55 units/sec = 65.45 units per hour
(g) We have to achieve a cycle time of 3600/72=50 seconds/unit. The following task allocation includes a lot of idle time, but is the only way to achieve the cycle time, given the constraints we face.
Therefore, a minimum of 8 workers are required to achieve a capacity of 72 units per hour.
Q4.8. Glove Design
(a.) Cutting has a process capacity of 1 glove/2 minutes*60 minutes = 30 gloves/hour. Dyeing has a process capacity of 1 glove/4 minutes*60 minutes = 15 gloves/hour. Stitching has a process capacity of 1 glove/3 minutes*60 minutes = 20 gloves/hour. Packaging has a process capacity of 1 glove/5 minutes*60 minutes = 12 gloves/hour. Therefore, the capacity is a. 12