Inventory Model Quadratic Back Order Costs, Lead Time Continuous for the (nQ, R, T) Model

The paper considers the continuous lead time to be a gamma distribution backorder costs to be quadratic and demand follows a normal distribution. We obtain the equations for the expected backorder costs and average it over the states of lead time L. The quadratic costs C_β(t) = b1t+b2t+b3t2 for t the duration of a backorder. The backorder costs are computed for each component of the quadratic cost separately. Use it made of the Bessel function of imaginary argument in averaging the backorder costs over the states of the lead time. The on hand inventory is also derived the inventory cost is obtained by summing the expected backorder costs and the on hand inventory costs, over the states of the lead times.