After making some wise short-term investments at a race track, Chris Low had some additional cash to invest in a business. The most promising opportunity at the time was in building supplies, so Low bought a business that specialized in sales of one size of nail. The annual volume of nails was 2,000 kegs, and they were sold to retail customers in an even flow. Low was uncertain of how many nails to order at any time. Initially, only two costs concerned him: order-processing costs, which were $60 per order without regard to size, and warehousing costs, which were $1 per year per keg space. This meant that Low had to rent a constant amount of warehouse space for the year, and it had to be large enough to accommodate an entire order when it arrived. Low was not worried about maintaining safety stocks, mainly because the outward flow of goods was so even. Low bought his nails on a delivered basis.
Question 1: Using the EOQ methods outlined in Chapter 9, determine how many kegs of nails Low should order at one time.
EOQ = √ (2)(annual usage)(cost of placing order)/annual carrying cost
EOQ = √ 2*2000*60/(1*2)
EOQ = √120,000 = 346.41
EOQ = 346 kegs per order
Question 2: Assume that all conditions in Question 1 hold, except that Low’s supplier now offers a quantity discount in the form of absorbing all or part of Low’s order-processing costs. For orders of 750 or more kegs of nails, the supplier will absorb all order-processing costs; for orders between 249 and 749 kegs, the supplier will absorb half. What is Low’s new EOQ? (It might be useful to lay out all costs in tabular form for this and later questions.)
Orders/year
Order Size
Processing Costs
Carrying Costs
Sum of processing and warehousing costs ($)
1
2000
Free
$2,000
$2,000
2
1000
Free
$1,000
$1,000
Order-Processing Costs
60
3
667
$90
$667
$757
Warehousing Costs
1.0
4
500
$120
$500
$620
5
400
$150
$400
$550
6
334
$180
$334
$514...