GATE Mechanical Engineering (ME) 2020 Shift 2 Solved Paper

Question : 56 of 65

Marks: +1, -0

For a single item inventory system, the demand is continuous, which is 10000 per year. The replenishment is instantaneous and backorders (S units) per cycle are allowed as shown in the figure.

As soon as the quantity (Q units) ordered from the supplier is received, the backordered quantity is issued to the customers. The ordering cost is Rs. 300 per order. The carrying cost is Rs. 4 per unit per year. The cost of backordering is Rs. 25 per unit per year. Based on the total cost minimization criteria, the maximum inventory reached in the system is _______ (round off to nearest integer).

Your Answer:

Validate

Solution:

In back order model,

(Q^{*}-S^{*}) C_{n}=S^{*} × C_{b}

S^{*}=(\;{Q^{*} C_{h}}/{C_{h}+C_{b}})

Maximum inventory level

=( {Q}^{*}- {S}^{*})

=Q^{*}-\;{Q^{*} C_{h}}/{C_{h}+C_{b}}

=(\;{Q^{*} C_{b}}/{C_{h}+C_{b}})

M^{*}=√{\;{2 D C_{0}}/{C_{h}} ×(\;{C_{b} × C_{h}}/{C_{b}})} ×(\;{C_{b}}/{C_{h}+C_{b}})

M^{*}=√{\;{2 D C_{0}}/{C_{h}} ×(\;{C_{b}}/{C_{b}+C_{b}})}

=√{\;{2 × 10000 × 300}/{4} ×(\;{25}/{29})}

=1137.147

unit

≅ 1137

units

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