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A particular raw material is available to a company at three different prices, depending on the size of the order:

Less than 100 pounds

\(20 per pound

100 pounds to 1,000 pounds

\)19 per pound

More than 1,000 pounds

\(18 per pound

The cost to place an order is \)40. The annual demand is 3,000 units. Holding (or carrying) cost is 25 percent of the material price. What is the economic order quantity to buy each time?

Short Answer

Expert verified

Answer

The economic order quantity aids in lowering inventory holding costs. The firm does not have to order surplus inventories that must be held in warehouses, saving money that would otherwise be spent on rent and other storage-related expenditures.

Step by step solution

01

The economic order quantity

The goal of the EOQ formulais to find the optimal number of product units to order. If this target is attained, the costs of acquiring, distributing, and storing units will be decreased. Firms with complicated supply chains and large variable costs produce EOQ using an algorithm in their computer software, and the EOQ formula may be altered to provide various production levels or order intervals.

The EOQ is a useful cash flow tool. The strategy can help a company control the amount of cash tied up in its inventory balance. Inventory is frequently a company's most important asset, second only to human resources, and as a result, organizations must have adequate inventory on hand to meet the expectations of their customers.

02

Step 2:

Given,

Annual demand (A) = 3000 units

Ordering cost per unit (S) = $40 per order

Holding cost (H) = 25% of cost

EOQ=2×A×SHwhere,A=AnnualdemandS=OrderingcostperunitH=Carryingcostperunit

Hence, the 225 units lie within the given range and therefore it is feasible and considered an Optimal order quantity

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Most popular questions from this chapter

Contrast the significance of the term lead time in the traditional EOQ context and an MRP system.

This drives the MRP calculations and is a detailed plan for how we expect to meet demand.

Famous Albert prides himself on being the Cookie King of the West. Small, freshly baked cookies are the specialty of his shop. Famous Albert has asked for help to determine the number of cookies he should make each day. From an analysis of past demand, he estimates demand for cookies as

Demand

Probability of Demand

1,800 dozen

0.05

2,000

0.10

2,200

0.20

2,400

0.30

2,600

0.20

2,800

0.10

3,000

0.05

Each dozen sells for \(0.69 and costs \)0.49, which includes handling and transportation. Cookies that are not sold at the end of the day are reduced to $0.29 and sold the following day as day-old merchandise.

a. Construct a table showing the profits or losses for each possible quantity.

b. What is the optimal number of cookies to make?

c. Solve this problem by using marginal analysis.

Discuss the meaning of MRP terms such as planned order release and the scheduled order receipt.

SY Manufacturers (SYM) is producing T-shirts in three colors: red, blue, and white. The monthly demand for each color is 3,000 units. Each shirt requires 0.5 pounds of raw cotton that is imported from Luft-Geshfet-Textile (LGT) Company in Brazil. The purchasing price per pound is \(2.50 (paid only when the cotton arrives at SYM’s facilities) and the transportation cost by sea is \)0.20 per pound. The traveling time from LGT’s facility in Brazil to the SYM facility in the United States is two weeks. The cost of placing a cotton order, by SYM, is $100 and the annual interest rate that SYM is facing is 20 percent.

a. What is the optimal order quantity of cotton?

b. How frequently should the company order cotton?

c. Assuming that the first order is needed on April 1, when should SYM place the order?

d. How many orders will SYM place during the next year?

e. What is the resulting annual holding cost?

f. What does the resulting annual ordering cost?

g. If the annual interest cost is only 5 percent, how will it affect the annual number of orders, the optimal batch size, and the average inventory? (You are not expected to provide a numerical answer to this question. Just describe the direction of the change and explain your answer.)

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