The economic order quantity (EOQ) model is a classical model used for controlling inventory and satisfying demand. Costs include
d 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
wj = space required for item j
W = the maximum amount of space available for all goods
N = number of items
The decision variables are Qj, the amount of item j to order. The model is:
Minimize
s.t.
;
In the objective function, the first term is the annual cost of goods, the second is the annual ordering cost (Dj/Qj is the number of orders), and the last term is the annual inventory holding cost (Qj/2 is the average amount of the inventory).
Set up and solve a nonlinear optimization model for the following data. Enter "0" if your answer is zero.
Item 1 Item 2 Item 3
Annual Demand 2,500 2,500 1,500
Item Cost ($) 150 100 130
Order Cost ($) 200 160 150
Space Required (sq. feet) 75 50 65
W = $6,500
i = 0.45
Min + + + + + +
s.t
× Q1 + × Q2 + × Q3
Q1
Q2
Q3
If required, round your answer to three decimals.
Q1 =
Q2 =
Q3 =
If required, round your answer to the nearest dollar.
Total Cost = $
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
wj = space required for item j
W = the maximum amount of space available for all goods
N = number of items
The decision variables are Qj, the amount of item j to order. The model is:
Minimize
s.t.
;
In the objective function, the first term is the annual cost of goods, the second is the annual ordering cost (Dj/Qj is the number of orders), and the last term is the annual inventory holding cost (Qj/2 is the average amount of the inventory).
Set up and solve a nonlinear optimization model for the following data. Enter "0" if your answer is zero.
Item 1 Item 2 Item 3
Annual Demand 2,500 2,500 1,500
Item Cost ($) 150 100 130
Order Cost ($) 200 160 150
Space Required (sq. feet) 75 50 65
W = $6,500
i = 0.45
Min + + + + + +
s.t
× Q1 + × Q2 + × Q3
Q1
Q2
Q3
If required, round your answer to three decimals.
Q1 =
Q2 =
Q3 =
If required, round your answer to the nearest dollar.
Total Cost = $
1 answer:
Answer:
Check the explanation
Explanation:
The above question is based on a non-linear programming model, to answer this question, there will be a need to determine the optimal order quantities of the three different Ferns with diverse values of annual demand, item cost as well as order cost objective of the non-linear programming model is to minimize the overall annual cost.
Step 1: Setup a spreadsheet on Excel, as shown in the first and second attached images below:
Note: The values of quantities of the three items is kept as 1 to for the calculations of total cost.
The Solver dialogue box will appear. Enter the decision variables, objective function and the constraints, as shown in the third attached image below:
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A is the amount you will have.
P is the money you are investing.
r: is the interest rate (in decimals)
n: number of times the interest is compounded per year
t: time (in years)
The first thing is converting the rate from percentage to decimal:
Since the interest is compounded every month and a year has 12 months n=12.
Now we can replace the values in our formula:
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Finally, we can use our calculator to get 288463.33
After 18 your balance in your bank account will be $288463.33
Where:
A is the amount you will have.
P is the money you are investing.
r: is the interest rate (in decimals)
n: number of times the interest is compounded per year
t: time (in years)
The first thing is converting the rate from percentage to decimal:
Since the interest is compounded every month and a year has 12 months n=12.
Now we can replace the values in our formula:
We can simplify the exponents to get:
Finally, we can use our calculator to get 288463.33
After 18 your balance in your bank account will be $288463.33