Project Network and Activity

6. Consider the following project network and activity times (in weeks):

1. Identify the critical path.
2. How much time will be needed to complete this project?
3. Can activity D be delayed without delaying the entire project? If so, by how many weeks?
4. Can activity C be delayed without delaying the entire project? If so, by how many weeks?
5. What is the schedule for activity E?
6. Davison Construction Company is building a luxury lakefront home in the Finger Lakes region of New York. Coordination of the architect and subcontractors will require a major effort to meet the 44-week (approximately 10-month) completion date requested by the owner. The Davison project manager prepared the following project network:

1. Find the critical path.
2. What is the expected project completion time?
3. Based only on the critical path, what is the estimated probability the project can be completed in 44 weeks as requested by the owner?
4. Based only on the critical path, what is the estimated probability the building project could run more than 3 months late? Use 57 weeks for this calculation.
5. What should the construction company tell the owner?

Chapter 10

4. Westside Auto purchases a component used in the manufacture of automobile generators directly from the supplier. Westside’s generator production operation, which is operated at a constant rate, will require 1000 components per month throughout the year (12,000 units annually). Assume that the ordering cost are $25 per order, the unit cost is $2.50 per component, and annual holding cost are 20% of the value of the inventory. Westside has 250 working days per year and a lead time of 5 days. Answer the following inventory policy questions:
5. What is the EOQ for this component?
6. What is the reorder point?
7. What is the cycle time?
8. What are the total annual holding and ordering cost associated with your recommended EOQ?

6. The manager at a local university bookstore wishes to apply the EOQ model to determine the respective order quantities for two products: ballpoint pens and mechanical pencils. The annual demand for pens and pencils is 1500 and 400, respectively. The ordering cost for each product is $20 per order and the wholesale price of a pen and pencil is $1.50 and $4, respectively. Assume the bookstore’s annual holding rate is 10% and that the bookstore operates 240 days per year.
7. Determine the optimal order quantity and the order cycle time for each product. What is the total cost (summed over both products)?
8. The bookstore orders the pens and pencils from the same supplier. If these two products had the same cycle time, the corresponding shipment consolidation would reduce the ordering cost to $15. How much money does the bookstore save by consolidating the orders for these two products? (Hint: By setting the cycle times equal, we have Q pens/(1500/240) = Q pencils/(400/240) or Q pens = 3.75Q pencils. Make this substitution into the combined cost equation so that it is a function only of Q pencils and apply equation (10.5) with the appropriate values to determine Q pencils (and subsequently Q pens).

8. Nation-Wide Bus Lines is proud of its six-week bus driver-training program that it conducts for all new Nation-Wide drivers. As long as the class size remains less than or equal to 35, a six-week training program cost Nation-Wide $22,000 for instructors, equipment, and so on. The Nation-Wide training program must provide the company with approximately five new drivers per month. After completing the training program, new drivers are paid $1600 per month paid to each idle new driver as a holding cost necessary to maintain a supply of newly trained drivers available for immediate service. Viewing new drivers as inventory-type units, how large should the training classes be to minimize Nation-Wide’s total annual training and new driver idle-time cost? How many training classes should the company hold each year? What is the total annual cost associated with your recommendation?