Question

The Economic Order Quantity (EOQ) model is a classical model used for controlling inventory and satisfying demand. Costs included in the model are holding cost per unit, ordering cost and the cost of goods ordered. The assumptions for that model are that only a single item is considered, that the entire quantity ordered arrives at one time, that the demand for the item is constant over time, and that no shortages are allowed.

Suppose we relax the first assumption and allow for multiple items that are independent except for a restriction on the amount of space available to store the products. The following model describes this situation:

Let Dj =	annual demand for item j
Cj =	unit cost of item j
Sj =	cost per order placed for item j
i =	inventory carrying charge as a percentage of the cost per unit
W =	the maximum amount of space available for all goods
wj =	space required for item j

The decision variables are Q_j, the amount of item j to order. The model is:

In the objective function, the first term is the annual cost of goods, the second is the annual ordering cost (D_j/Q_j is the number of orders), and the last term is the annual inventory holding cost (Q_j/2 is the average amount of inventory).

Set up a spreadsheet model for the following data:

	Item 1	Item 2	Item 3
Annual Demand	2,000	2,000	1,500
Item Cost ($)	100	50	80
Order Cost ($)	150	135	125
Space Required (sq. feet)	50	25	40

W = 5,000

i = 0.2

Solve the problem using Excel Solver. Hint: You will need to start with decision variable values that are greater than 0 for Solver to find a solution.

If required, round your answers to two decimal places.

Optimal Solution:

Q₁ = _______

Q₂ = _______

Q₃ = _______

If required, round your answer to the nearest dollar. Do not round intermediate calculations.

Total cost = $________

Answer 1

CALCULATION OF EOQ

fitem 1 = √2×Dj ×Sj / i 2) items 2: √2×2000×135/.20 3) item no:3 √2×1500×125/.20

   = √2× 2000×150/.20 = √2700000 = √1875000

=√3000000 = 1643.167 = 1369.31

=1732.05

H	ANNUAL DEMAND	COST PER UNIT	TOTAL ANNUAL COST OF GOODS ( A)	EOQ	NUMBER OF ORDERS	ORDERING COST PER ORDER	TOTAL ORDERING COST( B)	AVERAGE INVENTORY	INVETORY COST PER UNIT	TOTAL INVENTORY COST( C)	TOTAL COST( A+ B+ C)
ITEM 1	2000	100	2000 X 100 = 200000	1732.05	2000/1732.05= 1.155	150	150 X 1.155=173.25	1732.05/2= 866.025	0.2	173.205	200346.455
ITEM 2	2000	50	2000 X 50   = 100000	1643.18	2000/1643.18=1.217	135	135 X 1.217 = 164.295	1643.18/2= 821.59	0.2	164.318	100328.613
ITEM 3	1500	80	1500 X 80   = 120000	1369.31	2000/1369.31= 1.461	125	125 X 1.461= 182.625	1369.31/2=684.655	0.2	136.931	120319.556
			TOTAL=          420000				TOTAL=          520.17			TOTAL =                      474.454	420994.624