a) Optimal order quantity:-

1. Let supply of goods at uniform rate be ‘R’ per unit.
2. Demand is fixed & known. No shortages are allowed. Order is placed every ‘t’ time units where ‘t’ is fixed.
3. The ordering cost per unit is $C_m \ \ \& \ \ C_2$ is the cost of shortages.
4. 17 orders are placed at intervals ‘t’ quantity ‘q’ = Rt.
5. The cost of holding inventory during the time $‘t’ = 1/2 C_1 Rt_2$.

$C_1$ is the cost of holding 1 unit inventory for unit time.

The ordering cost to place and order = $C_3$

Total cost during time $‘t’ = ½ C_1 Rt_2 + C_3$

Optimal time interval

$‘to’ = \sqrt{\dfrac{2 C_3}{C_1 R}}$

Optimal order quantity is given by :

$q0 = \sqrt{\dfrac{2 R C_3}{C_1}}$

It indicates any other quantity will result in higher cost.

b) Lead time :-

1. The time gap between the movement of placing an order and actually receiving the order is referred as ‘Lead time’.
2. The lead time can be deterministic constant, variable or probabilistic.
3. If there is no such a gap, then lead time is said to be zero.
4. If lead time exists, then it requires to place an order in advance by an amount equal to lead time.
5. Lead time consists of internal lead time and external lead time.
6. Internal lead time consists of servicing time which includes time required for obtaining quotations, negotiating price, entering into which includes time needed for inspecting goods, moving them between stores and making entries in stock records.
7. External lead time comprises of administrative manufacturing & delivery time taken by the suppliers.