# Model IV : Manufacturing Model with Shortage

one inventory cycle of this model is given in Fig. 6.5.

Fig. 6.5 Manufacturing model with shortage

Here during Lp inventory is built up at the rate of (k - r),

during t2, inventory is consumed at the rate of r,

during t3, shortage is building at the rate of r,

during t4, shortage is being filled at the rate of (k - r).

The optimum quantities are obtained as given below :

Q1* = maximum inventory level = ( 1- r/k )Q* - Q2*

t* = production cycle time = Q*

Manufacturing time = k

Example 5. The demand for an item is 10000 units per year. Its production rate is 1500 units per month. The holding cost is \$ 20/unit/year and the set up cost is \$ 800 per set up. The shortage cost is \$ 1000 per unit per year. Find the EOQ, maximum shortage and total minimum production inventory cost.

Solution.                                             r = 10000 units/year

k = 1500 units/month = 18000 units/year

c 1 = \$ 20/unit/year

cs = \$ 800

c2 = \$ 1000/unit/year.

Total minimum production inventory cost