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1) If in the Wilson’s Model, the set up cost instead of being fixed, is equal to
C 2 + BQ ,where B is the set up cost per item produced, then show that there is no
change in the optimum order quantity produced due to change in the set up cost.
Solution:
So in this case;
Total Cost for one cycle = C 2 + BQ +(½) QtC 3
Average Cost for one unit of time = C ( Q ) = C 2 / t + BQ / t +(½) QC 3
Eliminating ‘ t ’, by using ‘ t = Q /D’
C ( Q ) = C 2 D / Q + BD +(½) QC 3
For minimum value, putting the 1 st derivative of above w.r.t ‘ Q ’ equal to zero.
C ’( Q ) = - C 2 D / Q^2 +(½) C 3 = 0
C 2 D / Q^2 =(½) C 3
Q^2 / C 2 D =2/ C 3
Q^2 =2 C 2 D / C 3
^2
3
2C D
Q
C
2) An item is produced at the rate of 50 items per day. The demand occurs at the rate
25 items per day. If the set up cost is Rs.100 per set up and the holding cost is
Rs.0.01 per unit of item per day, find the economic lot size for one run, assuming
that the shortage are not permitted.
Solution:
Here
R = 50/Day, D = 25/Day, C 3 = Rs. 0.01/Day, C 2 = Rs. 100/run
So
Economic Lot Size = Q* =^2
3
C D R
items C R D
t* = Q / D= 1000/25 = 40 Days
3) The demand of an item is uniform at a rate of 25 units per month. The fixed cost
is Rs.15 each time a production is made. The production cost is Rs.1/ item, and
the inventory carrying cost is Rs. 0.30/item/month. If the shortage cost is
Rs.1.50/item/month, determine how often to make a production run and of what
size it should be?
Solution:
In this example the set up cost is variable i-e C 3 + BQ , where B is the production cost per
item. Such a cost is considered in Question-01. Here also it can be shown that the optimal
value of Q remains unchanged. Only the Total cost per unit of time will become
Here
C 1 = Rs. 0.30/item/month
C 2 = Rs. 1.50/item/month
C 3 = Rs.15/set up(fixed)
B =Rs. 1.00/item, R = 25/month
Considering one month as one unit of time optimal value,
3 4
C C C D
Q items C C
And the optimal time = Q */ D = 54/25 = 2.16 months.
4) Group the items given below into an ABC classification.
Solution:
Item no. Annual Usage Accumulated Usage in Rs.
Cumulative Usage Cumulative % of items catagory 9 95000 95000 28.96 10
20
3 75000 17000 51.82 A
B
C
Item no 3 4 2 1 7 8 6 5 9 10
Annual usage
in x 10
3 Rs.
