Operations Management Question
FALL 2011 2011
Deadline: October 26,
Middle East Technical University – Northern Cyprus Campus
BUS 361 Operations Management
Homework 1 - Solutions
1. Fruit Computer Company manufactures memory chips in lots of ten chips. From past experience, Fruit knows that 80% of all lots contain 10% (1 out of 10) defective chips, 20% of all lots contain 50% (5 out of 10) defective chips. If a good batch (that is, 10% defective) of chips is sent on to the next stage of production, processing costs of $1000 are incurred, and if a bad batch (that is, 50% defective) is sent on to the next stage of production, processing costs of $4000 are incurred. Fruit also has the alternative of reworking a batch at a cost of $1000. A reworked batch is sure to be a good batch. Alternatively, for a cost of $100, Fruit can test one chip from each batch in an attempt to determine whether the batch is defective. Determine how Fruit can minimize the expected total cost per batch.
Expected total cost per batch = $1580. Fruit can minimize the expected total cost per batch by choosing the following decisions: It should test a chip. If the tested chip is defective, Fruit should rework the batch. If the tested chip is not defective, however, Fruit should send batch on to the next stage. See the following figure for details. Probabilities regarding testing a chip are calculated as follows. D: Chip is defective, D’: Chip is not defective, BB: Bad Batch, GB: Good Batch P(GB) = 0.8, P(BB) = 0.2, P(D | GB) = 0.1, P(D’ | GB) = 0.9, P(D | BB) = 0.5, P(D’ | BB) = 0.5, P(D) = (0.8)(0.1) + (0.2)(0.5) = 0.18, P(D’) = 1 – P(D) = 0.82
P(GB | D) = (P(D|GB) P(GB) + P(D|BB)P(BB)) / P(D) = 8/18 P(BB | D) = 1 – P(GB | D) = 10/18 P(GB | D’) = (P(D’|GB) P(GB) + P(D’|BB)P(BB)) / P(D’) = 72/82 P(BB | D’) = 1 – P(GB | D’) = 10/82
1
2. A retailer of electronic products has asked a particular manufacturer to begin daily deliveries rather than on a weekly basis. Currently the manufacturer delivers 2000
Deadline: October 26,
Middle East Technical University – Northern Cyprus Campus
BUS 361 Operations Management
Homework 1 - Solutions
1. Fruit Computer Company manufactures memory chips in lots of ten chips. From past experience, Fruit knows that 80% of all lots contain 10% (1 out of 10) defective chips, 20% of all lots contain 50% (5 out of 10) defective chips. If a good batch (that is, 10% defective) of chips is sent on to the next stage of production, processing costs of $1000 are incurred, and if a bad batch (that is, 50% defective) is sent on to the next stage of production, processing costs of $4000 are incurred. Fruit also has the alternative of reworking a batch at a cost of $1000. A reworked batch is sure to be a good batch. Alternatively, for a cost of $100, Fruit can test one chip from each batch in an attempt to determine whether the batch is defective. Determine how Fruit can minimize the expected total cost per batch.
Expected total cost per batch = $1580. Fruit can minimize the expected total cost per batch by choosing the following decisions: It should test a chip. If the tested chip is defective, Fruit should rework the batch. If the tested chip is not defective, however, Fruit should send batch on to the next stage. See the following figure for details. Probabilities regarding testing a chip are calculated as follows. D: Chip is defective, D’: Chip is not defective, BB: Bad Batch, GB: Good Batch P(GB) = 0.8, P(BB) = 0.2, P(D | GB) = 0.1, P(D’ | GB) = 0.9, P(D | BB) = 0.5, P(D’ | BB) = 0.5, P(D) = (0.8)(0.1) + (0.2)(0.5) = 0.18, P(D’) = 1 – P(D) = 0.82
P(GB | D) = (P(D|GB) P(GB) + P(D|BB)P(BB)) / P(D) = 8/18 P(BB | D) = 1 – P(GB | D) = 10/18 P(GB | D’) = (P(D’|GB) P(GB) + P(D’|BB)P(BB)) / P(D’) = 72/82 P(BB | D’) = 1 – P(GB | D’) = 10/82
1
2. A retailer of electronic products has asked a particular manufacturer to begin daily deliveries rather than on a weekly basis. Currently the manufacturer delivers 2000