Models with fixed cycle and order quantaty

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Russian: Модели с фиксированной периодичностью и размером заказа

Consider two basic models in inventory management [1], [2]:

1. Fixed quantity system (Q-system);

2. Fixed period system (P- system).

In the first system the quantity ordered per order is fixed and new order is made when inventory level reaches a certain minimum level. It could happen in arbitrary moment of time and it depends on demand rate. To implement fixed quantity system one should continuously monitor current inventory level. In the second case the successive order is placed in a fixed time periods. Order quantity could be different in different orders. Continuous monitoring of inventory level is not required: surplus of inventory is counted just at the end of the corresponding cycle.

In general case neither fixed quantity system nor fixed period system is preferable. A system choosing depends on goods characteristics, nature of demand, service level, supply chain management etc. Particularly inventory management under fixed quantity system takes more efforts in comparison with fixed period system, since Q-system needs continuous counting of consumption and replenishment. In the fixed period system average inventory exceeds the one in the Q-system, since one should have safety stock before the next replenishment.

Inventory management under Q-system is preferable in the following cases:

a) vital goods (items without which the system or a company cannot operate)

b) valuable goods (items with high value)

Inventory management under P-system is preferable in the following cases:

• Annual replenishment;

• Two-bin system;

• Max-min system;

• Max system.

Annual replenishment

In the planning system of inventory management the amount of materials could be calculated for the whole planning period: week, month, year. Particularly it occurs when demand for finished goods could be precisely estimated (functional product), or when a production program is planned for an enterprise or industry.

Two-bin system

Inventory is allocated between two bins. We start to spend inventory from the second bin. The volume of the first bin should be enough to satisfy the demand during leadtime. When the second bin is empty one places the new order and starts to spend inventory from the first bin. Two-bin system is fixed quantity system (Q-system).

Size of each bin are defined as a solution to an optimization problem subject to demand rate, holding cost, leadtime etc. Two-bin system could be used to reduce workload in a Q-system.

Max-min system

When costs for monitoring of inventory and costs to make an order are high one it could be implemented max-min system. In such a system monitoring of inventory acquires at fixed points of time. New order is set only if inventory level equals to or less than a certain minimum level. Safety stock is defined to satisfy demand in case of late supply. Order quantity is defined to get the maximum inventory at the next supply. Dynamics of inventory level in the max-min system is shown at fig. 1. Vertical lines correspond to the moment of inventory monitoring, L – leadtime, Т – suspend in delivery.


fig. 1 Max-min inventory system dynamics.

Periodic system with order size up to max level

When demand is unpredictable one may implement max-system [3]. In such a system orders could be placed either in certain moment of time with a constant cycle period or when inventory level approaches a certain minimum level. Safety stock is defined to satisfy demand in case of late supply. Order quantity is defined to get the maximum inventory at the next supply.


  1. Bowersox D.J., Closs D.J. Logistical Management: The Integrated Supply Chain Process, McGraw-Hill, New York, 1996 .
  2. Ramamurthy P. Operations Research - New Age International, 2007..
  3. Zipkin P. Foundations of Inventory Management - McGraw-Hill Education, 2000.
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