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Operation Management: Economic Order Quantity and Delay Duri

Please see the attached file for the fully formatted problems.

Problem #1- This is a production type EOQ problem, where the units produced each day go directly to inventory. Most production problems are treated as gradual delivery problems. Note that the carrying cost is 30% of the cost of making an individual DVD (.30 x 2.40).

The production rate of final assembly is 2,400 digital video discs (DVDs) per day. After DVDs are assembled, they go directly to finished-goods inventory. Customer demand averages 1,300 DVDs per day, or about 325,000 per year. It costs $700 to set up the assembly line for the DVDs, the cost per DVD is $2.30, and the carrying cost rate is 30 percent of product cost per year.

A. How many DVDs should be in production batch at final assembly?

B. What is the annual TSC at the EOQ?

Problem #2- This is a quantity discount EOQ problem.

E Office Supplies, Inc., sells discounted office supplies over the internet. One popular product sold is legal-size notepads, which are ordered by many law firms. E Office Supplies offers the following quantity discount structure, based on how many dozen notepads are ordered: 1-19 dozen, $21.95 per dozen; 20-99, $19.95 per dozen; 100-199, $18.95 per dozen; 200+, $17.95 per dozen. The law firm of Sanders, Taylor, Hernandez, Donahue and Smith (STHDS) would like to decide how many legal notepads to order using the EOQ model for quantity discounts. Its ordering cost is $35 per order, its anticipated need in the coming year is for 1,500 dozen notepads, and its annual carrying cost rate is 40 percent of acquisition cost.

A. How many dozen notepads should STHDS order each time?

B. What would be the resulting total inventory cost per year (ordering plus carrying plus materials)?

C. How many orders per year should be expected?

D. What is the expected maximum inventory level of notepads?

E. If STHDS has only enough storage space for 150 dozen notepads, how many should it order each time?

Problem #3 - This problem requires the determination of the order point. The distribution of demand during lead times (DDLT) is discrete.

An auto dealership has experienced the following historical demands during lead times for Ford half-ton pickup trucks:

Actual DDLT # of Occurrences Actual DDLT # of Occurrences
7 2 12 6
8 6 13 11
9 4 14 9
10 8 15 3
11 7 16 1

This data covers the dealerships past 57 orders to Ford. The replenishment lead time is five days to receive an order of trucks.
A. Compute the order point using a 90 percent service level
B. Compute the expected demand during lead time
C. What is the effective level of safety stock resulting from this order point?

Problem #4 - This problem requires determination of the order point when the DDLT is normally distributed.

If EDDLT = 65.5 unites, DDLT = 10.5 units, DDLT is normally distributed, and service level is 95 percent:

A. What is the order point?
B. What is the safety stock level?

Problem #5 - This problem requires the determination of the order point, etc. for demand that is normally distributed, however the lead time is relatively constant and the DDLT is estimated from the demand per period of time.

A part used to repair machines has a normally distributed monthly demand with a mean of 65.0 and a standard deviation of 5.2. If lead time is so predictable that it can be considered a constant 0.25 month and the service level is 90 percent.
A. What is the order point?
B. What is the safety stock level?

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Solution Preview

Please see the attached file for the full solution.

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For 4)

Order Point = point where demand < order point is greater than service level

since demand is normally distributed, we have to find a point ...

Solution Summary

Operations Management problems that are solved for optimal inventory policies under uncertain demand conditions