Question

Marisa Williams runs a retail grocery store and purchases items for resale to her customers. She is facing an ordering decision about how much of a particular item to purchase at one time.. in order t take advantage of supplier discounts (if it makes sense to do so).

Demand = 36,000 units per year

order cost = $25 per order

Carrying cost = $0.45 per unit

purchasing price = $0.85

Discount price= $0.82 (if buy a minimun of 6,000 units per order)

Should she takediscount (show your work)

What other aspectsa bout the purchase decision forthis item should she consider?

If this item were highly perishable and had a carrying cost of $0.65/unit, would it still make sense?

Answer 1

D = annual demand = 36,000
S = fixed ordering cost = $25
C = purchase price = $0.85
H = carrying cost per item = $0.45

Economic Order Quantity (Q*) = (2.D.S/H)^1/2 = SQRT(2*36000*25/0.45) = 2000

Total cost = Total ordering Cost + Total carrying cost + Total purchase cost
= (D/Q*).S + (Q*/2).H + D.C = (36000/2000)*25 + (2000/2)*0.45 + 36000*0.85 = $31,500

If the discount offer is availed, then Q=6000

Total cost = Total ordering Cost + Total carrying cost + Total purchase cost
= (D/Q).S + (Q/2).H + D.C_discounted = (36000/6000)*25 + (6000/2)*0.45 + 36000*0.82 = $31,020

Since the total cost is less in the case of discounted price, the discount makes sense

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For H=$0.65

Q* = SQRT(2*36000*25/0.65) = 1664

Total cost at full price = (36000/1664)*25 + (1664/2)*0.65 + 36000*0.85 = $31,682

Total cost at discounted price = (36000/6000)*25 + (6000/2)*0.65 + 36000*0.82 = $31,620

Yes, still it makes sense to go for discounted offer.