INVENTORY MANAGEMENT AND JUST IN TIME

Module: Cost and Management Accounting

Why Carry Inventories

Before we can discuss what methods may help the management to ensure an optimum level of inventory to be held, we have to understand the reasons for carrying inventories:

1. Protection Against Uncertainties

There are uncertainties in supply, demand and lead time in inventory systems and so safety stocks may be maintained to protect against those uncertainties. For example, safety stocks of finished goods are maintained to absorb changes in demand in order to avoid an immediate change in production. Similarly, safety stocks of raw materials are maintained to absorb uncertainties in delivery by vendors. Thus, if these sources of variations can be reduced, then safety stocks and so inventories can be correspondingly reduced.

2. Allowing Economic Production and Purchase

It is often economical to produce/purchase materials in lots because it is possible to spread the setup/ordering cost over a large number of items, even though part of the lot is then held in inventory for later use/sale. However, there is a trend today to lower the setup cost by reducing setup times in order to reduce the lot sizes and so inventories.

These two reasons for carrying inventory will influence the methods used for inventory management. (Of course, there are other reasons to carry stocks such as anticipated changes in prices and seasonal variations.) From these reasons, four decision problems in inventory management can be drawn:

• Which items should be carried in stock?

• How much should be ordered?

• When should an order be placed?

• What type of inventory control system should be used?

Elements of Inventory Cost

Many inventory decision rules involve economic criteria. Thus, it is very important to understand the cost of inventory, which may be broken down into the following details (4 parts):

1. Item Cost

This is the cost of buying/producing the individual inventory items. Item cost may be lowered by mass production due to the economies of large scale. Item cost of a bulk purchase is often lowered by a bulk (trade) discount.

Cash (settlement) discounts may not be taken into account because an early payment decision is usually not within the inventory management system.

Freight cost (also import duties and so on) may be part of the item cost if it varies with the number of items purchased.

The item cost can usually be estimated, with good accuracy, directly from historical records.

2. Ordering/Setup cost

The ordering cost is associated with ordering a batch or lot of items. Ordering cost does not depend on the number of items ordered; it is assigned to the entire batch. This cost includes: typing cost and postage of the purchase order, bank charges on letter of credit and bill process, expediting the order, receiving and inspection costs, and so on. Transportation cost and handling charges may be included if they are fixed per order of purchase.

Similarly, for a manufacturing concern, setup cost is those costs associated with placing an order of a batch of items to be produced irrespective of the number of items in the batch. It includes: paperwork of the production order, costs required to set up the production machine for a run, chasing the order, and so on.

The ordering/setup cost can also be determined from company records. However, difficulties are sometimes encountered in separating fixed and variable cost components. The ordering cost should include only the fixed costs for each order irrespective of its size for decision making purposes.

3. Holding (or Carrying) Cost

The holding cost is associated with keeping items in inventory for a period of time. It is typically charged as a percentage of the item cost per unit time. The holding cost usually consists of three components:

1. Opportunity cost of capital - When items are carried in inventory, the capital invested is not available for other purposes.

2. Cost of storage - This cost includes variable space cost, insurance, wages, protective clothing/containers, and so on.

In theory, only variable costs are included because fixed costs remain unchanged for different sizes of reorder quantity when we, say, consider the economic order quantity.

3. Costs of obsolescence, deterioration and loss - Obsolescence costs, including possible rework or scrapping, should be assigned to items which have a high risk of becoming out of fashion. Perishable goods should be charged with deterioration costs which include costs of preventing deterioration. The costs of loss include pilferage and breakage costs associated with holding items in inventory.

The holding cost is more difficult to determine accurately. The opportunity cost of capital cannot be directly derived from historical records but may only be estimated on the basis of current financial considerations. Costs of storage, obsolescence and etc can be estimated from company records plus special cost studies; however, it is difficult to separate the fixed and variable components and only to include those variable ones into the holding cost. The effect of price level changes is the most difficult one for estimation.

4. Stockout Cost

It reflects the economic consequences of running out of stock. There are two cases here. First, items are backordered. Second, the sales are lost. In both cases, the cost of administration on backorders, the loss of profit from the sales forgone, and the savings on holding less inventory may be calculated. However the loss of goodwill or future business associated with both cases is very difficult to calculate and is often handled indirectly by specifying an acceptable stockout risk level.

Conclusion

Inventory costs are often difficult to assess, but with persistence they can be estimated accurately enough for most decision making purposes.

Reorder Level System

Before the reorder level system can be described, the following underlying assumptions should be understood:

1. The lead time is constant and known.

2. Material is ordered or produced in a lot or batch, and the lot is placed into inventory all at one time.

3. The material is an independent product, i.e. its demand has no interaction with the demands of any other products.

In this system, decisions to reorder stock are based on the total on-hand plus on-order quantity. The total of on-hand and on-order material is called stock position. This stock position is monitored after each transaction so that this system is also called continuous review system as contrast to the periodic review system as discussed later. When the stock position drops to a predetermined order point (reorder level), a fixed quantity is placed on order. Since the order quantity is fixed, the time between orders will vary depending on the random nature of demand. A graph of the operation of this system is shown in Figure 1. The stock position drops on an irregular basis. When it reaches the reorder level at R units, an order for Q units is placed. The order arrives later, after a lead time L, and the cycle of usage, reorder, and stock receipt is then repeated.

Stock

Position

Q Q Q

R

L L L

Time

Reorder Level System

Figure 1

Thus, this reorder level system is completely determined by the 2 parameters, Q and R. In more advanced models, Q and R are determined simultaneously. However such models are very complicated; and so in many cases, the parameters are set separately. First, Q is set equal to the EOQ value which will be discussed later. Using the EOQ formula for Q is a reasonable approximation provided that demand is not highly uncertain. Second, the value of R can be based on either stockout cost or stockout probability.

Economic Order Quantity (EOQ)

When we discuss the economic order quantity (EOQ), two more assumptions are added to the underlying assumptions of the reorder level system:

1. The demand rate is constant, recurring and known.

2. No stockouts are allowed. Since demand and lead time are constant, one can determine exactly when to order material to avoid stockouts.

After putting these 2 extra assumptions into the system, the inventory level over time becomes a perfect “sawtooth” pattern as shown in Figure 2.

Stock

Position

order

interval

Q

R

L L L

Time

Reorder Level System without Stockout

Figure 2

From the comparison of Figure 1 and Figure 2, we observe the following essential differences:

1. The order interval becomes constant since demand rate is constant.

2. Each new order is received just at the time when the stock level falls to zero. Thus, the safety stock becomes unnecessary.

For the simplest EOQ model, there is a specific cost structure:

1. The unit item cost is constant (i.e. no bulk discounts/no economies on large scale of production).

2. There is a fixed ordering/setup cost for each lot irrespective of the lot size.

3. The holding cost varies linearly with the average stock level.

4. There is no stockout cost.

Therefore, in choosing the lot size, there is a tradeoff between ordering frequency and inventory level.

EOQ can be determined by three methods:

1. Tabulation method

2. Graphical method

3. Formula method

Example 1

ABC Limited uses 6,000 kg of material X per annum which is $2.5 each to purchase. The ordering costs are $15 per order and carrying costs are 5% of item cost per annum.

Calculate the EOQ of material X.

1. Tabulation method

Under this method, the total annual costs of ordering and carrying inventory are tabulated under various order sizes.

Annual consumption demand	Order quantity (Col. I)	No. of orders per year (6,000 ÷ Col. I) (Col. II)	Annual ordering cost (Col. II x $15) (Col. III)	Average stock (Col. I ÷ 2) (Col. IV)	Annual carrying cost (Col. IV x $0.125) (Col. V)	Total annual cost (Col. III + Col. V)
Kg	Kg		$	Kg	$	$
6,000	6,000	1	15	3,000	375	390
6,000	3,000	2	30	1,500	187.5	217.5
6,000	1,500	4	60	750	93.75	153.75
6,000	1,200	5	75	600	75	150
6,000	1,000	6	90	500	62.5	152.5
6,000	600	10	150	300	37.5	187.5

Notes:

1. The number of order is ascertained by dividing the total annual demand of 6,000kg by the order quantity.

2. If there are no stocks when the order is received and the units received are used at a constant rate, the average stock will be one-half of the quantity ordered.

3. The annual carrying cost is ascertained by multiplying the average stock by the carrying cost of $0.125 per kg ($2.5 x 5%).

4. The economic order quantity is 1,200 kg where the total annual cost $150 is at a minimum.

2. Graphical method

The information tabulated above can be presented in graphical form. The vertical axis represents the annual cost for the investment in stock, and the horizontal axis can be used to represent the various order quantities.

Notes:

1. From the graph, we can see that the carrying cost increases when the order quantity increases. Alternatively, the ordering cost declines as stock levels and order quantities are increased. The total cost line represents the summation of both the carrying and the ordering costs.

2. Note that the total cost line is at a minimum for an order quantity of 1,200kg and occurs at the point where the ordering cost and carrying cost curves intersect.

3. Formula method

The formula underlying the EOQ model is:

EOQ = 2 x D x Co

Cc

Where

D = Demand in units for a specified time period

Co = Ordering costs per order

Cc = Cost of carrying one unit in stock for a time period used for D (usually one year)

Therefore, for this example, the EOQ is

EOQ = 2 x 6,000 x $15

$2.5 x 5%

= 1,200kg

Effect of Quantity Discounts on EOQ

When firms are able to obtain discounts on bulk purchases or economies on large scale of production, the assumption that the unit item cost is constant is no longer applicable. In such circumstances, the item cost cannot be ignored in determining the economic order quantity. That is, the above formula cannot be used to get the economic order quantity directly. We may add the annual item cost for different order quantities to the respective annual ordering cost and annual carrying cost in the tabulation method to get the total annual cost. Again, the order quantity with the lowest total annual cost is the economic order quantity.

Reorder level when demand is certain

To determine the re-order point at which the order should be placed to obtain additional stocks, the lead time that will elapse between placing the order and the actual delivery of the stock need to be ascertained. In a world of certainty, the re-order point will be the number of days/weeks lead time multiplied by the daily/weekly usage during the period.

Example 2

For ABC Limited above, if the weekly usage is constant and there are 50 working weeks in a year, then the weekly usage will be 120 units (6,000 units ÷ 50 weeks).

If the lead time is two weeks, the re-order point is 240 units (120 units x 2).

Re-order level when demand is uncertain

In practice, demand, lead time or the amount that supplier can provide is not known with certainty. To protect itself from conditions of uncertainty, an organisation will maintain a level of safety stocks for all types of inventory. Thus, safety stock is the amount of stock that are carried by an organisation in excess of the expected use during the lead time so as to provide a cushion against unexpected increases in demand, lead time and unexpected unavailability of stock from suppliers.

Example 3 (same data as Example 2)

As calculated in example 2, the firm will place an order when the stock level falls to 240 units. However, if actual demand increases to 140 units per week or if the lead time is three weeks, the firm will out of stock. Therefore, to respond to this possibility, the organisation may set a re-order point of 420 units based on a maximum usage of 140 units per week and a lead time of three weeks. Consequently, this will consist of a re-order point based on expected usage and lead time of 240 units (2 x 120 units) plus the balance of 180 units safety stock to cover the possibility that lead time and expected usage will be greater than expected.

Thus, when demand and lead time are uncertain, the re-order point is computed by adding the safety stock to the average usage during the average lead time.

However, the probability of maximum demand and delivery time occurring at the same time is extremely low and it may not be the interest of the company for maintaining high safety stock if the cost of holding the excessive stock exceeds the cost that will be incurred if the company runs out of stock. It is therefore desirable to establish a sound quantitative procedure for determining an acceptable level of safety stock where stockout cost plus the carrying cost of safety stock are minimised.

Example 4

The total usage for an item of stock over a two weeks lead time is expected to be as follows:

Usage (units)	60	120	180	240	300	360	420
Probability	0.07	0.08	0.20	0.30	0.20	0.08	0.07

Additional information:

1. The average usage during the two weeks lead time is 240 units, and the lead time is known with certainty.

2. The stockout cost is $5 per unit and the carrying cost is $1 per unit for the period.

Calculate the expected stockout cost, carrying cost and total cost for various levels of safety stock.

Solution

Table showing the expected stockout cost, carrying cost and total cost for various levels of safety stock:

Average usage (units)	Safety stock (units)	Re-order point (units)	Stockout (units)	Stockout cost ($5 per unit)	Probab- ility	Expected stockout cost ($)	Carrying cost* ($)	Total expected cost ($)
240	180	420	0	0	0	0	180	180
240	120	360	60	300	0.07	21	120	141
240	60	300	120	600	0.07	42
			60	300	0.08	24
						66	60	126
240	0	240	180	900	0.07	63
			120	600	0.08	48
			60	300	0.2	60
						171	0	171
* To simplify the analysis, it is assumed that a safety stock is maintained throughout the period. The average safety stock will therefore be equal to the total of the safety stock.

Notes:

1. If the firm carries no safety stock, the re-order level will be set at 240 units, and there will be no stockout if actual usage is 240 units or less. However, if usage during the lead time period proves to be 300, 360 or 420 units instead of 240, there will be a stockout of 60, 120 and 180 units respectively.

2. If a safety stock of 180 units is maintained, stockout will not occur.

3. From the table, we can see that a safety stock of 60 units represents the level at which total expected costs are at the lowest. Hence, a re-order point of 300 units will be set, consisting of the average usage during the lead time of 240 units plus a safety stock of 60 units. If the probability distribution for each two-weekly period is expected to remain unchanged throughout the year, this safety stock (60 units) should be maintained. However, if demand is expected to vary throughout the year, the calculations must be repeated for the probability distributions for each period in which the probability distribution changes.

4. This expected value method can also be applied for more complex situations (e.g. both demand and lead time are uncertain).

However, as discussed above, the stockout cost is extremely difficult to estimate. Thus, stockout probability is commonly used as a basis to determine R. “Service level”, a widely used term in inventory management, is the percentage of customer demands satisfied from inventory. The stockout percentage is equal to 100 minus service level.

The reorder level is based on the notion of a probability distribution of demand over the lead time. When an order has been placed, the inventory is exposed to stockout until the order arrives. Figure 3 shows a normal probability distribution of demand over lead time (it is realistic to assume a normal distribution for the demand of an independent stock item). The reorder level (R) in the figure can be set sufficiently high to reduce the stockout probability to any desired level.

The reorder level (R) is defined as follows:

R = m + s

where m = mean demand over the lead time

s = safety stock

Safety stock (s) can be expressed as

s = Zσ

where Z = safety factor

σ = standard deviation of demand over the lead time

Then, we have R = m + Zσ

Thus, the reorder level (R) is set equal to the mean (m) of the probability distribution plus a specified number (Z) of standard deviation (σ) of the distribution. By controlling Z, we can control not only the reorder level but also the service level. A high value of Z will result in a high reorder level and a high service level.

Frequency

Service-level probability

Stockout

probability

s

m R

Demand over lead time

Reorder Level with tolerable stockout probability

Figure 3

Example 5 (same data as Example 4)

If the organisation does not wish the probability of a stockout to exceed 10%, how many safety stocks should be kept?

If the organisation does not wish the probability of a stockout to exceed 10%, it will maintain a safety stock of 120 units and a re-order point of 360 units. A stockout will then occur only if demand is in excess of 360 units; the probability of such an occurrence is 7%.

Periodic Review System

Before we can say what advantages/disadvantages the periodic review system has, we must first understand what a periodic review system is.

The underlying assumptions of a periodic review system are basically the same as those of the reorder level system. However, in a periodic review system, the stock position is reviewed at fixed intervals and the stock position is ordered up to a target inventory level in each of such reviews. A graph of the operation of such a system is shown in Figure 4.

The stock position drops on an irregular basis until the fixed review time is reached (P). At that time, a quantity is ordered to bring the stock position up to the target level (T). The order arrives later, after a lead time (L); then the cycle of usage, reorder, and stock receipt repeats. This system is completely determined by the 2 parameters, P and T.

Stock

Position

T

Q3

Q1 Q4

Q1 Q3

Q2 Q2

P P P

L L L

Time

Periodic Review System

Figure 4

The main disadvantage of a periodic review system is that it always requires more safety stock than the reorder level system for the same service level. It is because the periodic review system must provide coverage over a time of P + L, while the reorder level system must protect against stockout only over the time L. This point can easily been seen when we compare Figure 4 to Figure 1. (This point can also be proved by using mathematical models when the parameters, P and T, are determined. However, such models will not be covered in our discussion.)

However, there are some conditions under which the periodic review system may be preferred over the reorder level system:

1. When orders must be placed and/or delivered at specified intervals, the periodic review system should be used. For example, in some countries, when deliveries of explosive of exceeding the volume specified in law are made, the deliveries must be escorted by police officers. For administration purposes, the vendor, purchaser (usually big construction/engineering company) and police come to agreement for deliveries to be made at fixed intervals (e.g. for every 2 months).

2. The periodic review system may be used when multiple items are ordered from the same supplier and delivered in the same shipment. For example, a supplier of cloth would prefer consolidation of cloth in different colours into a single order rather than to deliver the different colours of cloth at different times.

3. The system may also be used for inexpensive items which are not maintained on perpetual inventory records. An example is nuts or bolts used in a manufacturing process. The bin size determines the target inventory, and the bin is filled up to target at fixed time intervals.

In sum, the periodic review system provides the advantages of scheduled replenishment and in some cases, less record keeping. It requires, however, a larger safety stock.

Just in Time (JIT)

The philosophy of JIT goes far beyond inventory control but encompasses the entire system of production. It aims to eliminate all sources of waste, anything (e.g. inward material inspection cost) which does not add value, in production/trading activities by providing the right parts/goods at the right place at the right time. Parts/goods are therefore produced/purchased just in time to meet manufacturing/selling requirements rather than by the traditional Just-in-case approaches such as those discussed above. The JIT system results in much less inventory, lower cost (including both holding cost and ordering/setup cost to be lower at the same time) and better quality than those traditional approaches.

Another important characteristic of JIT philosophy is utilization of the full capacity of the worker. Workers, in the JIT system, are charged with the responsibility for producing quality parts just in time to support the next production process. They are also charged with improving the production process through quality circles, suggestion systems and any other forms of participation.

Although the major application to date of JIT has been in repetitive manufacturing (i.e. mass production of standardized products), the JIT concept is equally applicable to job lot production or trading business.

In a JIT system, the final assembly schedule must be stabilized and leveled as that the demand on preceding work centers and vendor schedules becomes nearly constant. For example, in Toyota's factory, the final assembly line of Corona has to produce 20,000 units in a month of 20 operating days. This means that 1,000 Coronas must be produced per day and so just sufficient numbers of different parts (e.g. engines, transmissions, accelerators, doors and tires) have to be produced each day and the just sufficient quantities of different materials have to be delivered to the factory each day by the vendors for the production of the different parts.

JIT uses a simple parts withdrawal system (called Kanban) to pull parts from one (preceding) work centre to the next (starting from the final assembly line as described in the Toyota example). A fixed number of containers is provided for each part required. When these containers are full, no more parts are produced, thus limiting the inventory of each part. Constant improvement activities are encouraged to reduce the number/size of the containers and so the inventory.

The objective is to produce parts in a lot size of one. As discussed above, this is not economically feasible because of the high setup cost compared with inventory holding cost. The JIT solution to this problem is to lower the setup cost by reducing the setup time as much as possible, ideally to zero. One of the ways to achieve low setup time is to separate setup procedures into external and internal ones. Internal setups can be carried out only when the machine has been stopped, while external setups can be done when the machine is operating. After separating internal and external setups, as much of the setup as possible is converted from internal to external by having quick change adjustments modified to the machine and/or by employing cleverly designed tools and fixtures. When setup time is reduced, the production lead time is also shortened and so less material and WIP are in the process.

With an emphasis on quick changeovers and smaller lots, multifunction workers are required. Cross-training is needed so that each worker can operate several machines and perform setup, maintenance and inspection activities. JIT also affects the plant layout by requiring much less space (due to much less inventory and elimination of stockrooms) and encouraging movement toward group technology layouts.

As mentioned in the Toyota example above, vendors are required to make deliveries after receiving Kanban cards in every operating day. New vendor relationships are established. Vendors are treated much like internal work centers. Deliveries are made directly to the production lines without receiving or inspection. This requires complete confidence in the vendor's quality. Thus, long-term single-source contracts will often be negotiated with vendors.

The last thing to be mentioned is that a JIT system involves problem-solving activities by management and workers who drive the whole system to eliminate inventory (the root of all evil). Therefore, intensive education of workers and management at all levels is needed in order to have a successful implementation of the JIT system.

Page 5 of 17

Inventory Management & JIT

Cost

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