Question: R. C. Coleman distributes a variety of food products that are sold through grocery store and supermarket outlets. The company receives orders directly from the individual outlets, with a typical order requesting the delivery of several cases of anywhere from 20 to 50 different products. Under the company’s current warehouse operations, warehouse clerks dispatch order-picking personnel to fill each order and have the goods moved to the warehouse shipping area. Because of the high labor costs and relatively low productivity of hand order-picking, management decided to automate the warehouse operation by installing a computer-controlled order-picking system, long with a conveyor system for moving goods from storage to the warehouse shipping area.

R. C. Coleman’s director of material management has been named the project manager in charge of the automated warehouse system. After consulting with members of the engineering staff and warehouse management personnel, the director compiled a list of activities associated with the project. The optimistic, most probably and pessimistic times (in weeks) have also been provided for each activity.

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Activity Description Immediate Predecessor

A Determine equipment needs none

B Obtain vendor proposals none

C Select vendor A, B

D Order system C

E Design new warehouse layout C

F Design warehouse E

G Design Computer interface C

H Interface computer D, F, G

I Install system D, F

J Train system operators H

K Test system I, J

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Time

Activity Optimistic Most Probable Pessimistic

A 4 6 8

B 6 8 16

C 2 4 6

D 8 10 24

E 7 10 13

F 4 6 8

G 4 6 20

H 4 6 8

I 4 6 14

J 3 4 5

K 2 4 6

Draw the network. Calculate early starts, early finishes, latest starts, latest finishes, and slack for each activity. Determine the critical path.

What is the expected finish time?

What is the probability that the project will take at least three weeks longer than the expected finish time?

What is the probability that the project will be completed at least two weeks sooner than expected?

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