Abstract: During olden days, in the inventory models of Health service firms, the demand and cost of holding the things were fixed. Now in the modern world, the above cannot be considered as fixed. It is changing from time to time and place to place. So we have to formulate a model of demand in quadratic with time function. The cost of holding the things are considered as parabolic equations of time where changing of fixed deterioration is taken. The shortage of stocks is allowed. Using this inferences, a mathematical model have developed and find the solution and represented using graph. The scope is time should be optimal, order quantity is more of very least overall average cost. This result has more importance in Health service firms.