Assignment 1 - Case Study

Assignment 1 - Case Study (Individual Assignment)
Name of the Student
Name Of the University
Author Note

Answer to question 1:
Annual demand = 10000
Ordering cost = $504
Holding cost = $3
Optimal order quantity (EOQ) = sqrt(2*504*10000/3) = 1833
Now, total cost = annual ordering cost + annual holding cost
= (10000/1833)*504 + (1833/2)*3
=$5499.09
Frequency of orders = 10000/1833 = 5.46 = 6 times
Time between orders = 12/6 = 2 months
Answer to question 2:
Let St is the set up cost or ordering cost in period t
It is the inventory holding cost in period t
Dt is the demand in period t
Xt is the production quantity in period t
Yt is dummy variable representing 1, if Xt >0, else 0
M is very large number
Et is ending inventory in period t carried to next period
Therefore, the objective function will be:
Min = ∑
t =1
12
( I ¿ ¿ t∗Et +Y t∗St )¿
Constraints:
Ordering Cost = M Y t ≥ Xt
Production quantity = Xt ≥ 0
Ending Inventory = Et ≥ 0
Production quantity = Xt =Integer
Dummy variable = Y t =binary

Excel model:
Period 1 2 3 4 5 6 7 8 9 10 11 12
Demand (D) 300 700 800 900 3300 200 600 900 200 300 1000 800
Beginning Inventory 0 0 0 0 0 0 0 0 0 0 0 0
Set up Cost (S) 504 504 504 504 504 504 504 504 504 504 504 504
Holding Cost (I) 3 3 3 3 3 3 3 3 3 3 3 3
Production quantity (X) 300 700 800 900 3300 200 600 900 200 300 1000 800
Total inventory 300 700 800 900 3300 200 600 900 200 300 1000 800
Ending inventory (E) 0 0 0 0 0 0 0 0 0 0 0 0
Dummy Variable (Y) 0.03 0.07 0.08 0.09 0.33 0.02 0.06 0.09 0.02 0.03 0.1 0.08
Constraint 300 700 800 900 3300 200 600 900 200 300 1000 800
Inventory Holding 0 0 0 0 0 0 0 0 0 0 0 0
Set up Cost 15.12 35.28 40.32 45.36 166.32 10.08 30.24 45.36 10.08 15.12 50.4 40.32
Large Number (M) 10000
Total Cost 504
The above table is showing that to minimise the total cost, in this specific case production unit will be equivalent to demand for each month. Hence,
there will be monthly order. In other words, 12 orders needs to be placed.
Excel model:
Period 1 2 3 4 5 6 7 8 9 10 11 12
Demand (D) 300 700 800 900 3300 200 600 900 200 300 1000 800
Beginning Inventory 0 0 0 0 0 0 0 0 0 0 0 0
Set up Cost (S) 504 504 504 504 504 504 504 504 504 504 504 504
Holding Cost (I) 3 3 3 3 3 3 3 3 3 3 3 3
Production quantity (X) 300 700 800 900 3300 200 600 900 200 300 1000 800
Total inventory 300 700 800 900 3300 200 600 900 200 300 1000 800
Ending inventory (E) 0 0 0 0 0 0 0 0 0 0 0 0
Dummy Variable (Y) 1 1 1 1 1 1 1 1 1 1 1 1
Constraint 10000 10000 10000 10000 10000 10000 10000 10000 10000 10000 10000 10000
Inventory Holding 0 0 0 0 0 0 0 0 0 0 0 0
Set up Cost 504 504 504 504 504 504 504 504 504 504 504 504
Large Number (M) 10000
Total Cost 6048