(3 Points)

1.       The injection molding department of Alvec Inc. uses 40 pounds powder X a day. The plant operates 250 days per year. The daily usage of powder X is normally distributed with a standard deviation of 5 pounds per day. The lead time to obtain powder X from a supplier in 9 days. The annual holding cost is $2.00 per unit and the cost of ordering powder X is $50.

a)      What is Economic Order Quantity? ( 3 points)

2.       Refer to problem 1 and its solution. The injection molding department of Alvec Inc. uses 40 pounds powder X a day. The plant operates 250 days per year. The daily usage of powder X is normally distributed with a standard deviation of 5 pounds per day. The lead time to obtain powder X from a supplier in 9 days. The annual holding cost is $2.00 per unit and the cost of ordering powder X is $50.

a)      If a company has a service level goal is 99.4%. What is the expected pounds of shortage order cycle? (shortages are measured in terms of numbers of units) (2 points)

b)      Determine the order points for a service level of 99.4%. (4 Points)

3.       Draw the Activity-on-Arrow network diagrams for the following PERT problem. Use the minimum number of necessary “dummy” activities. (5 points)

4.       Given the demand of 3000 units and the following bill of materials for the item “A”, determine the low- level- code and the net requirements for all the items (A, B, C, D). (5 points)

5.        (12 Points) The following information is gathered for a project.

a)      Draw the network diagram using the AON (Activity on Node) Convention. (2 points)

b)      Determine the critical path, the amount of slack for each activity and the total completion time of the project. (7 Points)

       Critical Path:                                                                                                                      Project Completion time:

C) Prepare the earliest start schedule (Gantt chart). (3 points)

Question 8

An aegean sea fish market buys swordfish daily for $2.10 per pound and sells it for $3.60 per pound. at the end of each business day any remaining swordfish is sold to a cat food company for $1.20 per pound. Daily demand can be approximated by a normal distribution with a mean of 150 pounds and a standard deviation of 9 pounds.

a) Determine the optimal stocking level for the Aegean sea fish market.

b) if the demand is distributed according to continuous uniform distribution with a mean of 150 pounds and the minimum and the maximum demand values are 130 and 170 pounds respectively, what is the optimal stocking level? Assume that all of the cost values remain the same.

Question 9

A radio manufacturer uses 60000 knobs per year for its popular car stereo series. The firm makes its own knobs, which it can produce at a rate of 600 per day. The radios are assembled uniformly over the entire year. The unit cost of an item is $8 and the carrying rate per year is 15% of the item cost. The setup cost for the production of knobs is $60. The firm operates 300 days per year. Determine each of the following.

a) optimal run size (production quantity)

b)minimum annual carrying cost (show work)

c) minimum annual setup cost (show work)

d) time of usage (cycle time)

e) time of production (run time)

Question 10

A manager has prepared a forecast of expected aggregate demand for the next six months. Develop an aggregate plan to meet this demand given this additional information:

A level regular time production rate of 100 units per month will be used. Backorders are allowed and they are charged at a rate of $5 per unit per month. Inventory holding costs are $3 per unit per month. Develop an aggregate plan to meet demand given the following additional information:

Current inventory is zero

Current employment level is 9 employees

Each employee can produce 10 units per month

Regular time production cost is $20 per unit up to 120 units per month

Inventory holding (carrying) cost is $3 per unit per month

Backorder (backlog) cost -$5 per unit per month

Employee hiring cost  – $20 per employee

Employee firing cost  – $10 per employee

Desired ending inventory -0 units

a) Level plan