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 operation, warehouse clerks dispatch orderpicking 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 has decided to automate the warehouse operation by installing a computercontrolled order-picking system, along 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 has compiled a list of activities associated with the project. The optimistic, most probable, and pessimistic times (in weeks) have also been provided for each activity. Activity Description Immediate Predecessor Optimistic time Most probable time Pessimistic time A Determine equipment needs ----- 5 6 7 B Obtain vendor proposals ----- 2 4 12 C Select vendor A, B 1 4 7 D Order system C 6 9 18 E Design new warehouse layout C 7 10 13 F Design warehouse E 3 5 7 G Design computer interface C 4 6 20 H Interface computer D, F, G 4 6 8 I Install system F 4 6 14 J Train system operators and test system H, I 3 5 7 The project manager asks you to analyze this project. You must write a managerial report, which should be turned in this afternoon by 4 p.m. The report should address the following issues:

a) Draw the project network

b) Develop an activity schedule

c) What is the expected completion time for this project?

d) Identify the critical path and the non-critical activities?

e) What are the chances of completing this project within the expected time computed in question c). Why? Justify your answer

f) R.C. Coleman's top management has established a required 35-week completion time for the project. Can this completion time be achieved? Include probability information in your discussion.

g) What are the chances of completing this project in 44 weeks or less? 48 weeks or less?

h) If the variance of the project completion time is the same (does not change) as you found previously, by how much time should the expected project completion time be shortened to achieve the goal of 80% chance of completion within 35 weeks?