By the end of the chapter the student should be able to:
(1) Define the term inventory
(2) Explain the different types of inventory
(3) Distinguish between dependent and independent demand
(4) Calculate the EOQ
(5) Calculate the minimum stock level
Inventory is a stock or store of goods. It includes raw materials or stock incoming suppliers.
Types of inventory
(i) Raw materials and purchased parts
(ii) Partially completed goods
(iii) Finished-goods inventories or merchandise
(iv) Replacement parts, tools, and suppliers
(v) Goods-in-transit to warehouses or Goods In progress
Types of Demand:
1) Dependent Demand
These are items that are typically subassemblies or component parts that will be used in the production of a final or finished product. Subassemblies and component a part is derived from the number of finished units that will be produced. Example: Demand for wheels for new cars.
2) Independent Demand
These are items that are the finished goods or other end items. These items are sold or at least shipped out rather than used in making another product.
Functions of Inventory
1. To meet anticipated customer demand. These inventories are referred to as anticipation stocks because they are held to satisfy planned or expected demand.
2. To smooth production requirements. Firms that experience seasonal patterns in demand often build up inventories during off-season to meet overly high requirements during certain seasonal periods. Companies that process fresh fruits and vegetable deal with seasonal inventories
3. To decouple operations. The buffers permit other operations to continue temporarily while the problem is resolved. Firms have used buffers of raw materials to insulate production from disruptions in deliveries from suppliers, and finished goods inventory to buffer sales operations from manufacturing disruptions.
4. To protect against stock-outs. Delayed deliveries and unexpected increases in demand increase the risk of shortages. The risk of shortages can be reduced by holding safety stocks, which are stocks in excess of anticipated demand.
5. To take advantage of order cycles. Inventory storage enables a firm to buy and produce in economic lot sizes without having to try to match purchases or production with demand requirements in short run.
6. To hedge against price increase. The ability to store extra goods also allows a firm to take advantage of price discounts for large orders.
To permit operations. Production operations take a certain amount of time means that there will generally be some work-in-process inventory.
Effects of inadequate inventory controls
Inadequate control of inventories can result into two categories of consequences:
1) Under stocking results in missed deliveries, lost sales, dissatisfied customers and production bottlenecks.
2) Overstocking unnecessarily ties up funds that might be more productive elsewhere
Objectives of Inventory Management
To achieve satisfactory levels of customer service while keeping inventory costs within reasonable bounds. Specifically Decision maker tries to achieve a balance in stocking and Fundamental decision must be made related to the timing and size of orders
Requirements for Effective Inventory Management
To be effective, management must have the following:
1. A system to keep track of the inventory on the hand on order.
2. A reliable forecast of demand that includes an indication of possible forecast error.
3. Knowledge of lead times and lead time variability.
4. Reasonable estimates of inventory holding costs, ordering costs, and shortage costs.
5. A classification system for inventory items.
Stock taking systems
1) Periodic System
This is a physical count of items in inventory is made at periodic intervals (e.g. weekly, monthly) in order to decide how much to order of each item. Major users: Supermarkets, discounts stores, and department stores.
Orders for many items occur at the same time, which can result in economies in processing and shipping orders
a) Lack of control between reviews.
b) The need to protect against shortages between review periods by carrying extra stock.
c) The need to make a decision on order quantities at each review
2) Perpetual Inventory System (also known as a continual system)
This keeps track of removals from inventory on a continuous basis, so the system can provide information on the current level of inventory for each item.
1. The control provided by the continuous monitoring of inventory withdrawals.
2. The fixed-order quantity; management can identify an economic order size.
2. The added cost of record keeping.
3) Two-bin-system method
Is two containers of inventory; reorder when the first is empty. The advantage of this system is that there is no need to record each withdrawal from inventory; the disadvantage is that the reorder card may not be turned in for a variety of reasons.
4) Tracking System
Universal Product Code (UPC) bar code printed on a label that has information about the item to which it is attached. Bar coding represents an important development for other sectors of business besides retailing. In manufacturing, bar codes attached to parts, subassemblies, and finished goods greatly facilitate counting and monitoring activities.
Demand Forecast and Lead time Information
Managers need to know the extent to which demand and lead time might vary; the greater the potential variability, the greater the need for additional stock to reduce the risk of a shortage between deliveries.
Inventory Cost
1. Holding or Carrying Cost is the costs to carry an item in inventory for a length of time usually a year. Cost includes interest, insurance, taxes, depreciation, obsolescence, deterioration, spoilage, pilferage, breakage, etc.
2. Ordering Cost is cost of ordering and receiving inventory. These include determining how much is needed, preparing invoices, inspecting goods upon arrival for quality and quantity, and moving the goods to temporary storage.
3. Storage Cost is cost resulting when demand exceeds the supply of inventory on hand. These costs can include the opportunity cost of not making a sale, loss of customer goodwill, late charges, and similar costs
Inventory Decisions
The main concern of inventory management is the trade-off between the cost of not having an item in stock against the cost of holding and ordering the inventory. A stock-out can either be to an internal customer in which case a loss of production output may occur, or to an external customer when a drop in customer service level will result. In order to achieve a balance between inventory availability and cost the following inventory management aspects must be addressed of
volume – how much to order and timing – when to order.
The Economic Order Quantity (EOQ) Model
The Economic Order Quantity (EOQ) calculates the inventory order volume which minimises the sum of the annual costs of holding inventory and the annual costs of ordering inventory. The model makes a number of assumptions including:
– Stable or Constant Demand
– Fixed and identifiable ordering cost
– The cost of holding inventory varies in a linear fashion to the number of items held
– The item cost does no tvary with the order size
– Delivery lead time does not vary
– No quantity discounts are available
– Annual demand exists
These assumptions have led to criticisms of the use of EOQ in practice. The assumption of one delivery per order, and then the use of that stock over time increases inventory levels and goes against a JIT approach. Also annual demand will not exist for products with a life-cycle of less than a year. However, the EOQ approach still has a role in inventory management in the right circumstances and if its limitations are recognised.
Using the EOQ each order is assumed to be of Q units and is withdrawn at a constant rate over time until the quantity in stock is just sufficient to satisfy the demand during the order lead time (the time between placing an order and receiving the delivery). At this time an order for Q units is placed with the supplier. Assuming that the usage rate and lead time are constant the order will arrive when the stock level is at zero, thus eliminating excess stock or stock-outs.
The order quantity must be set at a level which is not too small, leading to many orders and thus high order costs and not too large leading to high average levels of inventory and thus high holding costs.
The annual holding cost is the average number of items in stock multiplied by the cost to hold an item for a year. If the amount in stock decreases at a constant rate from Q to 0 then the average in stock is Q/2. Thus if CH is the average annual holding cost per unit, the total annual holding cost is:
Annual Holding Cost = Q * CH
The annual ordering cost is a function of the number of orders per year and the ordering cost per order. If D is the annual demand, then the number of orders per year is given by D/Q. Thus if CO is the ordering cost per order then the total
annual ordering cost is:
Annual Ordering Cost = D * CO Q
Thus the total annual inventory cost is the sum of the total annual holding cost and the total annual ordering cost: Total
Annual Cost = Q * CH + D * CO 2 Q
Q=order quantity
CH = holding cost per unit
D = annual demand
Co = ordering cost per order

Total cost =annual ordering cost + annual stock holding cost=1250+1248=2498
The Re-Order Point (ROP) Model
The EOQ model tells us how much to order, but not when to order. The Reorder point model identfiies the time to order when the stock level drops to a predetermined amount. This amount will usually include a quantity of stock to cover for the delay between order and delivery (the delivery lead time) and an element of stock to reduce the risk of running out of stock when levels are low (the safety stock).
The previous economic order quantity model provides a batch size that is then depleted and replenished in a continuous cycle within the organisation. Thus the EOQ in effect provides a batch size which the organisation can work to. However this assumes that demand rates and delivery times are fixed so that the stock can be replenished at the exact time stocks are exhausted. Realistically though both the demand rate for the product and the delivery lead-time will vary and thus the risk of a stock-out is high. The cost of not having a item in stock when the customer requests it can obviously be costly both in terms of the potential loss of sales and the loss of customer goodwill leading to further loss of business.
Safety Stock and Service Level
Safety stock is used in order to prevent a stock-out occurring. It provides an extra level of inventory above that needed to meet predicted demand, to cope with variations in demand over a time period. he level of safety stock used, if any, will vary for each inventory cycle, but an average stock level above that needed to meet demand will be calculated. To calculate the safety stock level a number of factors should be taken into account including:
– cost due to stock-out
– cost of holding safety stock
– variability in rate of demand
– variability in delivery lead time
It is important to note that there is no stock-out risk between the maximum inventory level and the reorder level. The risk occurs due to variability in the rate of demand and due to variability in the delivery lead time between the reorder point and zero stock level.
The reorder level can of course be estimated by a rule of thumb, such as when stocks are at twice the expected level of demand during the delivery lead time. However to consider the probability of stock-out, cost of inventory and cost of stock-out the idea of a service level is used. The service level is a measure of the level of service, or how sure, the organisation is that it can supply inventory from stock. T his can be expressed as the probability that the inventory on hand during the lead time is sufficient to meet expected demand (e.g. a service level of 90% means that there is a 0.90 probability that demand will be met during the lead time period, and the probability that a stock-out will occur is 10%. the service level set is dependent on a number of factors such as stockholding costs for the extra safety stock and the loss ofsalesif demand cannot be met.
The ABC Inventory Classification System
Normally a mix of fixed-order-interval and fixed order quantity inventory systems are used within an organisation. When there are many inventory items involved this raises the issue of deciding which particular inventory systems hould be used for a particular item. The ABC classification system sorts inventory items into groups depending on the amount of annual expenditure they incur. This will depend on both the estimated number of items used annually multiplied by the unit cost. To instigate an ABC system a table is produced listing the items in expenditure order (with largest expenditure at the top), and showing the percentage of total expenditure and cumulative percentage ofthe total expenditure for each item. By reading the cumulative percentage figure it is usually found, following Pareto‟s Law, that 10-20% of the items account for 60-80% of annual expenditure. These items are called A items and need to be controlled closely to reduce overall expenditure. This often implies a Fixed quantity system with perpetual inventory checks or a fixed-interval system employing a small time interval between review periods. It may also require a more strategic approach to management of these items which may translate into closer buyer-supplier relationships. The B items account for the next 20-30% of items and usually account for a similar percentage of total expenditure. These items require fewer inventory level reviews than A items. A fixed order interval system with a minimum order level may be appropriate here. Finally C items represent the remaining 50-70% of items but only account for less than 25% of total expenditure. Here much less rigorous inventory control methods can be used, as the cost of inventory tracking will outweigh the cost of holding additional stock.
It is important to recognise that overall expenditure may not be the only appropriate basis on which to classify items. Other factors include the importance of a component part on the overall product, the variability in delivery time, the loss of value through deterioration and the disruption caused to the production process if a stock-out occurs.
Review questions
1. Define the term inventory
2. List the types of inventory that may be held by an organization
3. Explain the ABC stock classification system
4. Discuss the reorder point model
5. List five assumptions of the EOQ model
Slack, N. and Lewis, M. (2011) Operations Strategy, 3rd edn, Pearson Education Limited, Harlow.
Vonderembse, M.A. and White,G.P.(2004)Core Concepts of Operations Management, JohnWiley
and Sons Ltd., Chichester.
Hayes, R.H. and Wheelwright, S.C. (1984) Restoring our Competitive Edge,John
Wiley & Sons Ltd.
Hill, T 2005, Operations Management, 2 nd edn, Palgrave Macmillan, Basingstoke.
Ohno, T. 1988 Toyota Production System: Beyond Large-Scale Production, Productivity Press.

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