# P System

Review Period for P System:

The optimal review period is approximately given by

P = 1 / Nopt

Where Nopt is calculated by the basic EOQ formula for a Q-system.

(Nopt = optimal numbers of orders = annual requirement of the material divided by the economic order quantity – EOQ)

Although this approximation is good, there are still some practical difficulties associated with it. The basic idea of using the P system is to club together the orders for various raw materials and place these jointly at every period. If one calculates the review period for each inventory item independently, the very purpose of a P system is defeated. Therefore, in practice, while fixing the review period it may be advisable to also consider other aspects such as the time required to accumulate orders for different raw materials so that an order of sufficiently large quantity can be placed with the supplier, or the financial or budgetary cycle of the organization etc.

Maximum Inventory on Hand Plus on order:

Next is the determination of the maximum level of inventory on hand and on order. This is determined by the addition of two quantities.

1. The average requirement of material for usage during a review period plus lead time.
2. The buffer stock specially determined for the P system. The basic difference between the P system and the Q system is that, in the latter, the buffer stock needs to be carried only for the lead time, whereas in the former the buffer stock requirements are for both the lead time as well as the review period. In the P system, one has to maintain the buffer stock to protect against demand fluctuations during the order (review) period also because there is no flexibility in the order period as in the case with the fixed order quantity system. The latter system absorbs the demand fluctuations during the order period by varying the order period itself and therefore does not require buffer stock for this additional consideration. Remember that in the P system, the buffer stock will be required not only for the order period but also for the lead time.

Example: Consider a case where the average demand during the past is observed to be 100 units per month. The review cycle is one month. A safety stock of 20 units is kept to protect against consumption rate variation during the review period. The lead time is half a month. The maximum inventory we have on hand is 120 units (100 for normal consumption and 20 for safety). Suppose the consumption rate suddenly increases to 120 units per month starting from a time of review period denoted as Review Period No 1. The inventory levels at different points of time will be as follows:

At Review No.1: 70 units (120 – 50 units)

At the end of Lead Time No 1: 70 – 60 = 10;

plus 100 units received due to order placed at

Review Period 1 = 110 units

At Review No.2: 110 – 60 = 50 units

Now an order for 120 units is placed.

At the end of Lead Time No. 2: 50 – 60 = — 10 units

We notice, therefore, that we face a stock out during lead time No.2. This situation has arisen because we did not provide for safety stock for the lead time; our provision of the safety stock was only for the review period.

Let us provide safety stock for review period plus lead time (i.e. for 1½ months). The safety stock will be 30 units and maximum inventory on hand will be 130 units. Now, the stock levels at different points of time are:

At Review Period No. 1: 130 – 50 = 80 units

At the end of Lead Time No. 1: 80 – 60 = 20 units

Plus 100 units received due to order placed at

Review Period 1 = 120 units

At Review Period No.2 : 120 – 60 = 60 units

An order for 120 units is placed.

At the end of Lead Time No.2: 60 – 60 = 0 units

Plus 120 units received due to order placed at Review Period 2.

Note that there is no stock out situation now. In short, in a P system, buffer stock should be kept for consumption variations for amounts of time equal to review period plus lead time.

The same statement is valid even when the review period is equal to or smaller than lead time. Readers can check the validity by similar calculations.

1. Buffer stock is kept for review period + lead time
2. Maximum Inventory on hand plus on order, IH+O = (Normal Consumption + Buffer Stock) both for review period plus lead time.