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 Dy-annual demand for item C₂-unit cost of item Sy-cost per order placed for item i-inventory carrying charge as a percentage of the cost per unit W- the maximum amount of space available for all goods Wyspace required for item The decision variables are Q, the amount of itemj to order. The model is:
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 Dy-annual demand for item C₂-unit cost of item Sy-cost per order placed for item i-inventory carrying charge as a percentage of the cost per unit W- the maximum amount of space available for all goods Wyspace required for item The decision variables are Q, the amount of itemj to order. The model is:
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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![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
C₁ = unit cost of item j
S;= cost per order placed for item j
¡ = inventory carrying charge as a percentage of the cost per unit
W = the maximum amount of space available for all goods
W;= space required for item j
The decision variables are Q₁, the amount of item j to order. The model is:
Minimize Σ
s.t
£% [C,D, +²
Σ₁w₂Q₁ = W
Q₁ = 0
Annual Demand
Item Cost ($)
SD+i
Q2 =
2₁
X
X
In the objective function, the first term is the annual cost of goods, the second is the annual ordering cost (D;/Q; is the number of orders), and the last term is the annual inventory holding cost (Q;/2 is the average amount of inventory).
Set up a spreadsheet model for the following data:
- iC;
j = 1, 2, ... N
2
Item 1
2,500
90
150
50
Item 2
2,500
50
135
25
Order Cost ($)
Space Required (sq. feet)
W = 4,000
i = 0.3
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 =
Item 3
2,000
70
125
40
Q3 =
If required, round your answer to the nearest dollar. Do not round intermediate calculations.
Total cost = $](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F21c26dd5-6855-4bd8-8f94-032cd6f44579%2F406e4641-b18f-4e9a-813f-2bb0d7b9903e%2Fk4ffhzi_processed.png&w=3840&q=75)
Transcribed Image Text:The Economic Order Quantity (EOQ) model is a classical model used for controlling inventory and satisfying demand. Costs included in the model are holding cost per unit, ordering cost and the cost of goods ordered. The assumptions for that model are that only a single item is considered, that the entire quantity ordered arrives at one
time, that the demand for the item is constant over time, and that no shortages are allowed.
Suppose we relax the first assumption and allow for multiple items that are independent except for a restriction on the amount of space available to store the products. The following model describes this situation:
Let Dj = annual demand for item j
C₁ = unit cost of item j
S;= cost per order placed for item j
¡ = inventory carrying charge as a percentage of the cost per unit
W = the maximum amount of space available for all goods
W;= space required for item j
The decision variables are Q₁, the amount of item j to order. The model is:
Minimize Σ
s.t
£% [C,D, +²
Σ₁w₂Q₁ = W
Q₁ = 0
Annual Demand
Item Cost ($)
SD+i
Q2 =
2₁
X
X
In the objective function, the first term is the annual cost of goods, the second is the annual ordering cost (D;/Q; is the number of orders), and the last term is the annual inventory holding cost (Q;/2 is the average amount of inventory).
Set up a spreadsheet model for the following data:
- iC;
j = 1, 2, ... N
2
Item 1
2,500
90
150
50
Item 2
2,500
50
135
25
Order Cost ($)
Space Required (sq. feet)
W = 4,000
i = 0.3
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 =
Item 3
2,000
70
125
40
Q3 =
If required, round your answer to the nearest dollar. Do not round intermediate calculations.
Total cost = $
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