BUSI 3010 Week 7 EOQ and Reorder Point Analysis Example

How Many Slabs of the Best-Selling Quartz to Order and When: An Economic Order Quantity of 33, a Reorder Point of 18 and Why a 3 Percent Discount at 60 Slabs Changes the Answer Once Rack Space Is Counted

Student Name

Walden University

BUSI 3010: Operations Management

Instructor Name

Month Day, Year

How Many Slabs of the Best-Selling Quartz to Order and When: An Economic Order Quantity of 33, a Reorder Point of 18 and Why a 3 Percent Discount at 60 Slabs Changes the Answer Once Rack Space Is Counted

The Item and the Question

Red River Stone & Surface stocks about forty colors of quartz and granite. One color, a white quartz with gray veining, outsells every other and accounts for roughly a third of the shop's slab use. This analysis calculates how many slabs of that color to order at a time and at what stock level to reorder, then tests the result against the conditions the basic model ignores.

Inputs

Table 1

Inputs for the White Quartz Slab

Red River Stone & Surface and its figures are composite; demand is from 2027 usage records.

The holding rate of 20 percent covers the cost of money tied up in stone, insurance, and the risk of slabs being chipped or cracked while stored. Both the holding cost and the demand are expressed per year so that the formula is consistent.

Economic Order Quantity

Ordering often raises delivery charges, and ordering rarely raises the cost of stone sitting in the yard; the economic order quantity finds the size where the two are equal (Harris, 1990).

EOQ = √(2DS ÷ H)

EOQ = √(2 × 520 × 240 ÷ 230)

EOQ = √(249,600 ÷ 230) = √1,085.2 = 32.9, rounded to 33 slabs.

At 33 slabs per order, the shop would place 520 ÷ 33 = 15.8 orders a year.

Annual ordering cost = 15.8 × $240 = $3,782.

Annual holding cost = (33 ÷ 2) × $230 = $3,795.

Total annual inventory cost = $7,577.

The two costs are nearly equal, as they should be at the economic order quantity.

Reorder Point

Daily demand is d = 520 ÷ 250 = 2.08 slabs per day.

Demand during lead time = 2.08 × 6 = 12.5 slabs.

Daily demand varies, so the shop needs safety stock to avoid running out while an order is on its way. The shop wants to run short no more than about one cycle in twenty, which sets z at 1.65.

Safety stock = z × σd × √L = 1.65 × 1.2 × √6 = 4.85, rounded to 5 slabs.

Reorder point = 12.5 + 4.85 = 17.3, rounded up to 18 slabs.

When the rack holds 18 slabs of this color, the programmer places an order for 33.

What the Model Assumes

The economic order quantity rests on assumptions that should be checked before the answer is used. It assumes demand is steady through the year; in this shop it is not, since summer months run about 40 percent above winter months. It assumes the cost per order and the price do not change with order size. It assumes each order arrives all at once and that there is space to store it. Silver et al. (2017) note that the total cost curve is flat near the optimum, so small departures from the computed quantity cost little, which makes the result robust to modest errors in the inputs. But the assumptions about price and space matter more here.

The Discount the Model Leaves Out

The distributor offers 3 percent off the slab price on orders of 60 slabs or more. At 60 slabs the price falls to $1,115.50 and the holding cost to $223.10 per slab per year.

Table 2

Annual Cost at 33 and at 60 Slabs per Order

Purchase cost is annual demand times unit price.

Ordering 60 slabs at a time saves about $16,700 a year, almost all of it from the lower price. The basic model, which treats price as fixed, cannot see this.

The Constraint the Model Leaves Out

The A-frame rack for this color holds 40 slabs. At the economic order quantity, the most on hand at once is about 33 plus 5 of safety stock, or 38, which fits. At 60 slabs, peak stock would reach about 65, which does not fit. A second A-frame rack costs about $4,500 installed and would take floor space in the slab yard that is now used to stage remnants.

The space constraint therefore turns the decision into a comparison of the discount against the rack. Even after paying for the rack once, the discount would save about $12,200 in the first year and $16,700 in each year after. The larger order also ties up about $15,000 more in stone on average, and it increases the risk that slabs are damaged in storage or left over if the color falls out of fashion.

Recommendation

Order this color 60 slabs at a time, with a reorder point of 18 slabs plus the time needed to receive the larger load, and install a second rack before the next order. Review the decision quarterly: if monthly demand falls below about 30 slabs for two quarters, return to orders of 33. For colors without a discount and with steady demand, the basic economic order quantity remains a sound starting point. Stevenson (2021) cautions that quantity discounts require comparing total cost, including purchases, at each price break, which is exactly where the basic answer and the better answer diverge here.

References

Harris, F. W. (1990). How many parts to make at once. Operations Research, 38(6), 947-950. https://doi.org/10.1287/opre.38.6.947 (Original work published 1913)

Silver, E. A., Pyke, D. F., & Thomas, D. J. (2017). Inventory and production management in supply chains (4th ed.). CRC Press.

Stevenson, W. J. (2021). Operations management (14th ed.). McGraw Hill.