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Suppose that the probability function of the kanban number is known and given according to the table below
Suppose that the probability function of the kanban number is known and given according to the table below. It is assumed that the inventory holding and stocking costs for each carrier per unit time are 50 and 250, respectively. Determine the optimum number of kanbans that will minimize the total expected inventory carrying and outsourcing costs.
Probability 0.00 0.15 0.20 0.30 0.20 0.15
Kanban number 0 1 2 3 4 5
Expert Solution
Calculation of optimum number of kanbans :
The situation should be satisfied for that :
P (n-1) <stockings cost/ holding cost + stockings cost <p(n)
250/300=0.833
Let the kanbans at 4
Pn= summation 4x=0 p(x)
Cumulative probability at = 0.00+0.15+0.20+0.3+0.20= o.85
So the optimum number kanbans satisfied at 4 where expected inventory carrying cost and outsourcing cost is minimum .
But if take kanban number at 3 then probability summation is 0.65 that not satisfy the condition.
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