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# Operations Management Inventory Quantity Discounts

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A retailer needs to choose between two suppliers for one of its products. The only criterion used for the decision is the cost. The following information about the product is available:

Demand 200 a week
Ordering cost (for all suppliers) \$75 per order
Holding cost 20% of the unit cost
Working weeks 50 a year

The retailer has narrowed down the choices to two suppliers. The following shows the price-break schedule for each supplier:
SUPPLIER A SUPPLIER B
Quantity Unit Price Quantity Unit Price
1-299 \$14.00 1-249 \$14.10
300-699 13.80 250-449 13.90
700+ 13.60 450+ 13.70

A. Which supplier should the retailer choose? Explain and support your answer with appropriate calculations.
B. What is the optimal lot size for the item? (Note: There has to be only ONE choice, regardless of supplier).
C. What is the total annual cost of inventory for the chosen (best) lot size?

#### Solution Preview

Operations Management - Inventory Management Quantity Discount
A retailer needs to choose between two suppliers for one of its products. The only criterion used for the decision is the cost. The following information about the product is available:
Demand 200 a week
Ordering cost (for all suppliers) \$75 per order
Holding cost 20% of the unit cost
Working weeks 50 a year
The retailer has narrowed down the choices to two suppliers. The following shows the price-break schedule for each supplier:
SUPPLIER A SUPPLIER B
Quantity Unit Price Quantity Unit Price
1-299 \$14.00 1-249 \$14.10
300-699 13.80 250-449 13.90
700+ 13.60 450+ 13.70
A. Which supplier should the retailer choose? Explain and support your answer with appropriate calculations.
B. What is the optimal lot size for the item? (Note: There has to be only ONE choice, regardless of supplier).
C. What is the total annual cost of inventory for the chosen (best) lot size?

D = 200
Ordering Cost = CO = 75
Holding Cost = CH = .20

Let's calculate the Annual Demand
Annual Demand = Weekly Demand X Number Operation Weeks Per Year
D ...

#### Solution Summary

Inventory management has two main types of quantity discount models. We examine the all units discounts to determine which supplier to select and the best ordering quantity.

\$2.19
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## Operation Management: Economic Order Quantity and Delay During Lead Time

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, &#61510;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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