Question

This time, we're going to do a sensitivity analysis. The following is repeated for your convenience. The EOQ is a popular inventory management model (you'll learn more about this in BUS 361). There are two key equations you'll need are for the annual total cost qiven any quantity Q, ATC(9) and the cost minimizing order quantity, Q 0:-, 2DA V VI ATC(q)- Qvr. DA Where D-Annual unit demand 1 - Aggregate cost to place an order v-Unit cost r - Annual holding costas%of unit cost Assuming annual demand of 10,000 units, a $500 cost to place an order, unit cost of $6.95, and an annual holding cost percentage rate of 32%, find the cost minimizing order quantity and its associated annual total cost. Now, calculate the annual total cost for order quantities between 1500 and 2500 (in 100 unit increments). How do these compare to the annual total cost you previously calculated for the cost minimizing order quantity?

Answer 1

As per the question below is the information available which we can use in the formula:

D = 10,000 Units

A = $ 500

v = $ 6.95 per unit

r = 32%

Part 1:

1.1 Find Cost Minimizing Order Quantity (Q*):

Q* =   $^{\sqrt}$ (2* 10,000 * 500) / (6.95 * 32%)

Q* = 2120 Units (Rounded Off)

1.2 Find Annual Total Cost associated to Q*:

ATC(Q) = [(2120 * 6.95 * 32%) / 2] + [(10,000 * 500) / 2120]

ATC(Q) = $ 4,715.9

Part 2:

2.1 Find Annual Total Cost for Quantities 1500 to 2500 (with 100 unit's interval):

ATC(Q) = Qvr / 2 + DA / Q

ATC(1500) = $ 5,001

ATC(1600) = $ 4,904

ATC(1700) = $ 4,832

ATC(1800) = $ 4,779

ATC(1900) = $ 4,744

ATC(2000) = $ 4,724

ATC(2100) = $ 4,716

ATC(2200) = $ 4,719

ATC(2300) = $ 4,713

ATC(2400) = $ 4,752

ATC(2500) = $ 4,780

2.2 Comparision Analysis:

As per Answers shown in the Part 2.1, we can see that the lowest possible cost at ordering level of 2100 units (Cost $4,716). As per the Cost minimizing Order Quantity formula we get the quantity as 2120 units (Cost $4,715.9). So, to conclude the answer if we have the ordering facility only in the multiple of 100 units then the optimum quantity would be at 2100 units.