2. Objectives of Material Control
3. Requirements of Material Control
8. Just-in-time Analysis—The Origin
10. Perpetual Inventory System
12. Stock/Material Turnover Ratio
After reading this chapter, you will be able to understand:
The meaning of material control
Objectives of material control
Requirements of material control
Duties of a storekeeper
Different levels of stock
Different inventory systems
Stock turnover ratio
Formulae used
Material control is a way of regulating the purchase, storage and use of materials required for production because material constitutes an important factor of production. Material also forms an important part in determining the cost of a product. Material control is given importance to ensure uninterrupted production and to minimize the investment of funds in material. Thus, material control is aimed at having proper control over production, production cost, investment in material and increase in profitability.
The fundamental purpose of material control is to obtain the requisite quantity of material at the right price, at the right quantity, at the right quality and from the right source. The other objectives of material control are as follows:
Since material forms a major part of the cost of a product, proper controlling and recording is essential:
The requirements of material control are as follows:
The duties of a storekeeper are as follows:
Material control means maintaining a right level of stock by taking into account the production requirement and the financial resources of a business. The inflow and outflow of materials have to be regulated in such a manner that neither is production adversely affected for want of material nor is there unnecessary blocking of capital funds due to overstocking of raw materials. This implies there is always a limit to the minimum and maximum quantities of materials to be stored.
In order that the correct quantity of materials is purchased and stocked, the storekeeper applies some scientific techniques of material control. Fixing of certain levels for materials is one such technique.
The minimum level or minimum stock is that level of stock below which stock should not be allowed to fall. In case the stock of any item falls below this level, there is the danger of stopping production and, therefore, the management should give top priority to the acquisition of new supplies.
It is the level below which the stock of an item should not normally be allowed to fall. In the case of stock falling below this level, there is a danger of stopping production of the item. This level is also known as “safety stock” because such stock is normally not touched. This level is fixed after considering (a) rate of consumptions and (b) time required to acquire the stock:
The main factors considered in fixing the minimum level of inventory are as follows:
The maximum stock limit is the upper level of inventory and the quantity that must not be exceeded without specific instruction from the management. In other words, the maximum stock level is that quantity of material above which the stock of any item should not normally be allowed to go.
It is the level above which the stock of any item should not generally be allowed to go. This level of stock is maintained for avoiding overstocking of materials and its associated risks. This level is fixed after considering (a) rate of consumption, (b) amount of capital needed and available, (c) storage space available, (d) insurance costs, (e) cost of storing above normal cost and (f) risk of wastage and deterioration:
The important considerations that govern the fixing of maximum level for various inventory items are as follows:
The reorder level of stock is the point at which stock of a particular item has diminished to a point where it needs to be replenished. It is the level at which a new order for a material is to be placed. It is the level at which a purchase requisition is made. It is the level between maximum and minimum. It is also known as the ordering level. This level is fixed after considering rate of consumption (r), minimum level (b), delivery time (c) and variation in delivery time (d).
This is the level at which issue of material is stopped. This level indicates emergency of stock position. The storekeeper at this level obtains material at any cost. But issues are made only under specific instructions.
Danger level is a level of stock fixed usually below the minimum level. When the stock reaches danger level, an urgent action for purchase is initiated. When stock reaches the minimum level, the storekeeper must make special arrangements to get fresh material so that production is not interrupted due to the shortage of material.
It is the normal level of stock held by a firm:
Economic order quantity (EOQ) is the size of the order that gives maximum economy in purchasing any material and ultimately contributes towards maintaining the material at the optimum level and at the minimum cost. In other words, it is the ideal quantity of a material to be purchased at a time. The quantity is fixed in such a way that carrying cost and ordering cost are minimized. Carrying cost refers to the cost of holding the materials in the store. Ordering cost refers to the cost of placing orders for the purchase of materials.
EOQ is essentially an accounting formula that determines the point at which the combination of order costs and inventory carrying costs is the least. The result is the most cost-effective quantity to order. In purchasing this is known as the order quantity, whereas in manufacturing it is known as the production lot size.
EOQ is the number of units that a company should add to its inventory with each order to minimize the total costs of inventory, such as holding costs, order costs and shortage costs. EOQ is used as part of a continuous review inventory system, in which the level of inventory is monitored at all times and a fixed quantity is ordered each time the inventory level reaches a specific reorder point.
Not all companies use EOQ. Companies that deal with a large volume of stock use EOQ. It is used in industries where the ordering of stock is repetitive. Another type of business also uses EOQ, that is, business that has multiple orders and has to plan for their components. Businesses that have a steady demand for stock adopt EOQ.
When implementing EOQ
The underlying assumptions of EOQ are
EOQ is calculated as follows:
A = annual consumption
B = buying cost per order
or
C = cost per unit
S = storage and carrying cost
C = annual usage of material
O = cost of placing one order
I = annual carrying cost of one unit
Annual usage is expressed in units. Order cost is the sum of the fixed costs that are incurred each time an item is ordered. Carrying cost is the cost associated with having the inventory at hand.
ABC analysis is a business term used to define an inventory categorization technique often used in materials management. It is also known as selective inventory control. It is a part of inventory management, in which items included in the inventory are classified into different categories such as items of higher value occupying lesser space, those of lower value occupying more space and others.
ABC analysis provides a mechanism for identifying items that have significant impact on overall inventory cost, while also providing a mechanism for identifying different categories of stock that require different management and controls. When carrying out an ABC analysis, inventory items are valued (item cost multiplied by quantity issued/consumed in a period) with the results and then ranked. The results are then grouped typically into three bands. These bands are called ABC codes.
ABC analysis is similar to the Pareto principle in that the ‘A class’ group typically accounts for a large proportion of the overall value but a small percentage of the overall volume of inventory.
ABC codes
Another breakdown of ABC classes
Under this system, materials are classified into three categories in the order of their respective values. Materials that are costly are grouped into ‘A’ category. Materials that are moderate in value are grouped into ‘B’ category, and materials that are cheap are grouped into ‘C’ category. In other words, high-priced materials are grouped into the A category, medium-priced materials are grouped into the B category and low-priced materials are grouped into the ‘C’ category.
Materials in the A category form a small part of the total inventory. Utmost care should be taken in storing and using these materials. Materials in the B category form a medium part of the total inventory. Moderate care and control should be exercised in storing and using these materials. Materials in the C category form a large part of the total inventory. Such materials need not be given much importance as such.
Category | Percentage of items | Percentage of cost |
---|---|---|
A | 8 | 75 |
B | 25 | 20 |
C | 67 | 5 |
Total | 100 | 100 |
Just-in-time (JIT) analysis was developed by Toyota's Vice President Taiichi Ohno. The JIT concept was first transferred to the United States around 1980 at Kawasaki's Lincoln, Nebraska. Since then many corporations in the United States have followed suit and have begun implementing JIT. But even today the concept is just beginning to be understood and used by many industrial enterprises throughout the world.
JIT analysis is nothing but just-in-time inventory system. It is the purchase of material in such a way that materials are delivered before their use. Timely deliveries have special significance in JIT analysis.
JIT is an inventory strategy that strives to improve a business's return on investment by reducing in-process inventory and associated carrying costs. Ability to provie quick notice that stock depletion requires personnel to order new stock is critical to inventory reduction at the centre of JIT. This saves warehouse space and costs. However, the complete mechanism for making this work is often misunderstood.
The benefits of JIT are
VED analysis is used mainly for the control of spare parts, where V stands for vital, E stands for essential and D stands for desirable. Absence of vital spare parts will immediately affect production, absence of essential spare parts will affect production after a few hours or so and absence of desirable spare parts will affect production only after a week or so.
It is the analysis for monitoring and controlling stores and spare parts inventory by classifying them into three categories, viz, vital, essential and desirable. The mechanics of VED analysis is similar to that of ABC analysis. Whereas in ABC classification inventories are classified on the basis of their consumption value and in HML analysis the unit value is the basis, criticality of inventories is the basis for vital, essential and desirable categorization.
VED analysis is done to determine the criticality of an item and its effect on production and other services. It is specially used for the classification of spare parts. If a part is vital it is given ‘V’ classification, if it is essential then it is given ‘E’ classification and if it is not so essential the part is given ‘D’ classification. For V items, a large stock of inventory is generally maintained, whereas for D items minimum stock is enough.
VED Analysis
VED analysis can be defined as the analysis of maintenance spares into
V items—items of vital importance
E items—items of essential importance
D items—items of desirable importance
Perpetual inventory means the system of records, whereas continuous stocktaking means the physical checking of those records with actual stocks. The perpetual inventory method has the following advantages:
Under the periodic method, the entire book inventory is verified at a given date by an actual count of materials at hand. This physical inventory is usually taken near the end of the accounting period. This method provides for the recording of purchases, purchase returns and purchase allowances on a daily basis.
The costs of goods sold are computed by deducting closing inventory from the sum of opening inventory and purchases made during the current period. It is assumed that goods not on hand at the end of the accounting period have been sold. There is no system and accounting for shrinkage, losses, theft and waste throughout the accounting period and they can be discovered only after the end of the period.
Taking a physical inventory at the end of a year is an important task in the periodic inventory system. It must be ensured that all items are counted accurately. Counting procedures usually involve teams of people assigned to specific sections of the factory and to inventory storage areas. Large items are counted individually, whereas small items are weight-counted. Counted items are tagged to prevent double counting and information from the tags concerning each item's description and quantity is recorded on the inventory sheet.
Periodic inventory system refers to knowing the level of every item of stock at all times. It is a method of recording stores’ balances after every receipt and issue. This system implies continuous maintenance of stock.
Material turnover (MT) ratio refers to the rate of consumption of materials. It indicates the fast- and slow-moving materials. A high ratio indicates that an item is fast moving and investment in it is low. A lower ratio indicates the item is not consumed in more quantity and the locking of working capital in undesirable items.
Illustration 1
Find out the EOQ and the number of orders per year.
Annual usage: | 1,000 units | |
Cost of material per unit: | Rs 20 | |
Cost of placing one order: | Rs 40 |
Annual carrying cost of one unit; 10% of inventory value.
Solution:
The answer is five orders per year.
Problem 1. Find out the EOQ and the number of orders per year
Annual usage: | 2,000 units | |
Cost of material per unit: | Rs 20 | |
Cost of placing one order: | Rs 40 |
Annual carrying cost of one unit; 10% of inventory value.
Illustration 2
Monthly consumption | 4,200 units |
Cost per unit | Rs 63 |
Ordering cost | Rs 125 per order |
Inventory carrying cost | 20% of the average inventory |
Calculate EOQ.
Solution:
Problem 2.
Monthly consumption | 6,200 units |
Cost per unit | Rs 63 |
Ordering cost per order | Rs 125 |
Inventory carrying cost | 20% of the average inventory |
Calculate EOQ.
Illustration 3
Consumption of material per annum | Rs 12,500 |
Ordering cost per order | Rs 100 |
Carrying and storage cost | 10% of the average inventory |
Calculate EOQ.
Solution:
Problem 3.
Consumption of material per annum | Rs 14,500 |
Ordering cost per order | Rs 100 |
Carrying and storage cost | 10% of the average inventory |
Calculate EOQ.
Illustration 4
A factory consumes 30 units of material per day, which is supplied by a wholesaler in lots of 480 units each at Rs 4,800 per lot. On an average the factory works for 300 days in a year. Each order involves handling charges of Rs 400 and freight charges of Rs 600. The storage cost is Rs 1.40 per unit per annum. Carrying cost is 0.50% per month. Calculate EOQ.
Solution:
Where
A = annual usage of material
B = buying cost per order
C = cost per unit
S = storage and carrying cost
(s) Storage and carrying cost:
∴ Number of units to be ordered each time to minimize overall inventory cost = 3,000 units
(b) Frequency of placing orders:
Problem 4. A factory consumes 30 units of material per day, which is supplied by a wholesaler in lots of 480 units each at Rs 6,800 per lot. On an average the factory works for 300 days in a year. Each order involves handling charges of Rs 400 and freight charges of Rs 600. The storage cost is Rs 1.40 per unit per annum. Carrying cost is 0.50% per month. Calculate EOQ.
Illustration 5
A company is able to obtain quantity discount on its order of material in the following manner:
Price per tonne | Tonnes |
---|---|
Rs 6.00 | Less than 100 |
Rs 5.80 | 100 and less than 600 |
Rs 5.20 | 600 and less than 1,200 |
Rs 4.60 | 1,200 and less than 2,000 |
Rs 4.00 | 2,000 and above |
Annual demand is 3,000 tonnes. Storage cost is 10% per annum. Delivery cost per order is Rs 6. Calculate EOQ.
Solution:
Where
A = annual usage
B = buying cost per order
C = cost per unit
S = storage and carrying cost per unit
Tabular method
It can be observed from the aforementioned table that when five orders are placed for 100 units each time, the total cost is the lowest. So EOQ = 100 units per order.
Problem 5. A company is able to obtain quantity discount on its order of material in the following manner:
Price per tonne | Tonnes |
---|---|
Rs 7.00 | Less than 100 |
Rs 6.80 | 100 and less than 600 |
Rs 6.20 | 600 and less than 1,200 |
Rs 5.60 | 1,200 and less than 2,000 |
Rs 5.00 | 2,000 and above |
Annual demand is 3,000 tonnes. Storage cost is 10% per annum. Delivery cost per order is Rs 6. Calculate EOQ.
Illustration 6
Calculate EOQ using tabular method.
Annual consumption | 3,000 units |
Ordering cost | Rs 6 per order |
Price per unit | Rs 4 |
Carrying cost per annum | 10% |
Solution:
Problem 6. Calculate EOQ using tabular method.
Annual consumption | 700 units |
Ordering cost | Rs 20 per order |
Price per unit | Rs 20 |
Carrying cost per annum | 10% |
Illustration 7
ARR Limited got an offer on its order of materials as under
Price per tonne | Tonnes |
---|---|
1,400 | Less than 800 |
1,380 | 800 and less than 1,600 |
1,360 | 1,600 and less than 2,500 |
1,340 | 2,500 and less than 3,500 |
1,320 | 3,500 and above |
The annual requirement for material is 6,000 tonne. The ordering cost per order is Rs 1,200 and the stockholding cost is estimated at 20% of material cost per annum. The purchase quantity options to be considered are 600, 900, 1,800, 2,400 and 3,600 tonne. You are required to compute the most economical purchase level. What will be your answer to the question if no discounts are offered and the price per tonne is Rs 2,100.
Solution: Computation of the most economical purchase level is as follows:
From the aforementioned table we see that the minimum cost is Rs 83,65,100. When the order quantity is 2,400 tonne, the most economical purchase level is 2,400 tonne.
(b)
Problem 7. ARR Limited got an offer on its order of materials as unde
Price per tonne | Tonne |
---|---|
2,400 | Less than 800 |
2,380 | 800 and less than 1,600 |
2,360 | 1,600 and less than 2,500 |
2,340 | 2,500 and less than 3,500 |
2,320 | 3,500 and above |
The annual requirement for material is 6,000 tonne. The ordering cost per order is Rs 1,200 and the stockholding cost is estimated at 20% of material cost per annum. The purchase quantity options to be considered are 600, 900, 1,800, 2,400 and 3,600 tonne. You are required to compute the most economical purchase level. What will be your answer to the question if no discounts are offered and the price per tonne is Rs 2,100.
Illustration 8
Calculate inventory turnover ratio and express in number of days the average inventory held.
Value of material | Rs 2/kg | |
Opening stock | 1,200 kg | |
Purchases | 1,400 kg | |
Closing stock | 600 kg |
Solution:
Problem 8. Calculate inventory turnover ratio and express in number of days the average inventory held.
Value of material | Rs 2/kg | |
Opening stock | 1,400 kg | |
Purchases | 1,600 kg | |
Closing stock | 800 kg |
Illustration 9
Calculate the material turnover ratio from the following particulars:
Material A | Material B | |
---|---|---|
Rs | Rs | |
Opening stock | 8,000 | 10,000 |
Purchases | 60,000 | 70,000 |
Closing stock | 4,000 | 8,000 |
Solution:
For material A,
For material B,
Problem 9. Calculate the material turnover ratio from the following particulars:
Material A | Material B | |
---|---|---|
Rs | Rs | |
Opening stock | 10,000 | 12,000 |
Purchases | 70,000 | 80,000 |
Closing stock | 4,000 | 8,000 |
Illustration 10
Calculate the material turnover ratio from the following particulars and determine the fast-moving item:
Material X | Material Y | |
---|---|---|
Rs | Rs | |
Materials on 1 January 2005 | 40,000 | 60,000 |
Materials on 31 December 2005 | 10,000 | 20,000 |
Materials purchased | 1,40,000 | 2,10,000 |
Solution:
For material X,
For material Y,
Comment: The inventory turnover ratio of material X is higher than that of Y. Therefore, material X is fast moving compared with material Y.
Problem 10. Calculate the material turnover ratio from the following particulars and determine the fast-moving item:
Material X | Material Y | |
---|---|---|
Rs | Rs | |
Materials on 1 January 2005 | 40,000 | 60,000 |
Materials on 31 December 2005 | 10,000 | 20,000 |
Materials purchased | 1,40,000 | 2,10,000 |
Illustration 11
Material X is used as follows: | |
Maximum usage in a month | 800 units |
Minimum usage in a month | 200 units |
Average usage in a month | 400 units |
Head time: maximum—8 months, minimum—4 months | |
Reorder quantity | 1,200 numbers |
Maximum reorder period for emergency purchases | 1 month |
Calculate (a) reorder level, (b) maximum level, (c) minimum level, (d) average level and (e) danger level.
Solution: The terms lead time and reorder period mean the same thing. Usage and consumption are also used as alternative terms.
= 800 units × 8 months
= 6,400 units
= 6,400 + 1,200 − (200×4)
= 7,600 − 800 = 6,800 units
= 400 × 1 = 400 units
Problem 11.
Material X is used as follows: | |
Maximum usage in a month | 900 units |
Minimum usage in a month | 200 units |
Average usage in a month | 400 units |
Head time: maximum—8 months, minimum—4 months | |
Reorder quantity | 1,200 numbers |
Maximum reorder period for emergency purchases | 1 month |
Calculate (a) reorder level, (b) maximum level, (c) minimum level, (d) average level and (e) danger level.
Illustration 12
Two materials X and Y are used as follows:
Particulars | Material X | Material Y |
---|---|---|
Reorder quantity | 2,200 | 2,000 |
Reorder period | 2–4 week | 4–6 week |
Normal usage | 400 units/week | 300 units/week |
Minimum usage | 300 units/week | 200 units/week |
Maximum usage | 600 units/week | 400 units/week |
Calculate (a) reorder level, (b) maximum level, (c) minimum level, (d) average level
Solution:
Material X = 600 units × 4 weeks = 2,400 units
Material Y = 400 units × 6 weeks = 2,400 units
Material X = 2,400 + 2,200 [300 × 2]
= 4,600 − 600 = 4,000 units
Material Y = 2,400 + 2,000 [200 × 4]
= 4,400 − 800 = 3,600 units
Problem 12. Two materials X and Y are used as follows:
Particulars | Material X | Material Y |
---|---|---|
Reorder quantity | 2,400 | 2,200 |
Reorder period | 2–4 weeks | 4–6 weeks |
Normal usage | 400 units/week | 300 units/week |
Minimum usage | 300 units/week | 200 units/week |
Maximum usage | 600 units/week | 400 units/week |
Illustration 13
Calculate (a) EOQ, (b) reorder level, (c) maximum level and (d) minimum level from the following information:
Normal usage | 250 units per day | |
Minimum usage | 150 units per day | |
Maximum usage | 350 units per day | |
Reorder period | 60–70 days | |
Annual usage | 75,000 units | |
Cost of purchase per order | Rs 1.50 | |
Cost per unit | Rs 2 | |
Carrying cost per annum | 20% |
Solution:
Where
A = annual usage
B = buying cost per order
C = cost per unit
S = storage and carrying cost
= 350 units × 70 days
= 24,500 units
= 24,500 + 7,500 − (150 × 60)
= 32,000 − 9,000
= 23,000
Problem 13. Calculate (a) EOQ, (b) reorder level, (c) maximum level and (d) minimum level from the following information:
Normal usage | 350 units per day | |
Minimum usage | 250 units per day | |
Maximum usage | 450 units per day | |
Reorder period | 60–70 days | |
Annual usage | 75,000 units | |
Cost of purchase per order | Rs 1.50 | |
Cost per unit | Rs 2 | |
Carrying cost per annum | 20% |
Illustration 14
Two components X and Y are used as follows:
Normal usage | 50 units each per week | |
Minimum usage | 25 units each per week | |
Maximum usage | 100 units each per week | |
Reorder quantity | X—500 units, Y—700 units | |
Reorder period | X—4–6 weeks, Y—2–4 weeks |
Calculate for each component the (1) reorder level, (2) minimum level (3) maximum level and (4) average level.
Solution:
Component X = 100 units × 6 weeks = 600 units
Component Y = 100 units × 4 weeks = 400 units
Component X = 600 + 500 − [25 × 4]
= 1,100 − 100 = 1,000 units
Component Y = 400 + 700 − [25 × 2]
= 1,100 − 50 = 1,050 units
Problem 14. Two components X and Y are used as follows:
Normal usage | 75 units each per week | |
Minimum usage | 50 units each per week | |
Maximum usage | 200 units each per week | |
Reorder quantity | X—500 units, Y—700 units | |
Reorder period | X—4–6 weeks, Y—2–4 weeks |
Calculate for each component the (1) reorder level, (2) minimum level, (3) maximum level and (4) average level.
Illustration 15
Two components X and Y are used as follows:
Normal usage | 600 units each per week | |
Maximum usage | 800 units each per week | |
Minimum usage | 250 units each per week | |
Reorder quantity | X—4,500 units, Y—7,500 units | |
Reorder period | X—4–6 weeks, Y—2–4 weeks |
Calculate for each component the (a) reorder level, (b) minimum level, (c) maximum level and (d) average stock level.
Solution:
Component X = 800 units × 6 weeks = 4,800 units
Component Y = 800 units × 4 weeks = 3,200 units
Component X = 4,800 + 4,500 − [25 × 4]
= 9,300 − 1,000 = 8,300 units
Component Y = 3,200 + 7,500 − [25 × 2]
= 10,700 − 500 = 10,200 units
Problem 15. Two components X and Y are used as follows:
Normal usage | 800 units each per week | |
Maximum usage | 900 units each per week | |
Minimum usage | 450 units each per week | |
Reorder quantity | X—4,500 units, Y—7,500 units | |
Reorder period | X—4–6 weeks, Y—2–4 weeks |
Illustration 16
Two components A and B are used as follows:
Normal usage | 100 units each per week |
Minimum usage | 50 units each per week |
Maximum usage | 200 units each per week |
Reorder quantity | A—800 units, B—1,000 units |
Reorder period | A—6–8 weeks, B—3–5 weeks |
Calculate for each component the (a) minimum level, (b) maximum level and (c) average stock level.
Solution:
Reorder level = Maximum consumption × Maximum reorder period
Component A = 200 × 8 = 1,600 units
Component B = 200 × 5 = 1,000 units
Component A = 1,600 + 800 − [25 × 6]
= 2,400 − 300 = 2,100 units
Component B = 1,000 + 1,000 − [25 × 3]
= 2,000 − 150 = 1,850 units
Problem 16. Two components A and B are consumed as follows:
Normal usage | 200 units each per week |
Minimum usage | 100 units each per week |
Maximum usage | 300 units per each week |
Reorder quantity | A—800 units, B—1,000 units |
Reorder period | A—6–8 weeks, B—3–5 weeks |
Calculate for each component the (a) minimum level, (b) maximum level and (c) average stock level.
Illustration 17
From the following particulars, calculate (a) reorder level, (b) minimum level and (c) maximum level:
Normal usage | 150 units per day | |
Minimum usage | 70 units per day | |
Maximum usage | 150 units per day | |
Economic order quantity | 8,000 units | |
Reorder period | 25–30 days |
Solution:
= 150 × 30 = 4,500 units
= 4,500 + 8,000 − [70 × 25
= 12,500 − 1,750 = 10,750 units
Problem 17. From the following particulars, calculate (a) reorder level, (b) minimum level and (c) maximum level:
Normal usage | 300 units per day | |
Minimum usage | 100 units per day | |
Maximum usage | 250 units per day | |
Economic order quantity | 8,000 units | |
Reorder period | 25–30 days |
Illustration 18
Calculate (a) EOQ, (b) maximum level, (c) minimum level and (d) reordering level from the following data:
Reorder period | 4–6 weeks | |
Maximum consumption | 150 units per week | |
Minimum consumption | 50 units per week | |
Normal consumption | 100 units per week | |
Annual consumption | 36,000 units | |
Cost per unit | Re 1 | |
Ordering cost | Rs 25 |
Inventory carrying cost is 20% of unit value.
Solution:
Where
A = annual usage
B = buying cost per order
C = cost per unit
S = storage and carrying cost
= 150 × 6 = 900 units
= 900 + 3,000 − [50 × 4
= 3,900 − 200 = 3,700 units
Problem 18. Calculate (a) EOQ, (b) maximum level, (c) minimum level and (d) reordering level from the following data:
Reorder period | 4–6 weeks | |
Maximum consumption | 250 units per week | |
Minimum consumption | 100 units per week | |
Normal consumption | 200 units per week | |
Annual consumption | 36,000 units | |
Cost per unit | Re 1 | |
Ordering cost | Rs 25 |
Inventory carrying cost is 20% of unit value.
Illustration 19
In a manufacturing firm, a material is used as follows:
Maximum consumption | 14,000 units per week | |
Minimum consumption | 3,000 units per week | |
Normal consumption | 10,000 units per week | |
Reorder quantity | 52,000 units | |
Average consumption | 8,000 units per week | |
Emergency delivery time | 2 weeks | |
Minimum | 6 weeks; maximum: 10 weeks |
Calculate (a) reorder level, (b) minimum level, (c) maximum level, (d) average stock level and (e) danger level.
Solution:
= 1,40,000 + 52,000 − [3000 × 6]
= 1,92,000 − 18,000 = 1,74,000 units
= 8,000 units × 2 weeks = 16,000 units
Problem 19. In a manufacturing firm, a material is used as following:
Maximum consumption | 16,000 units per week | |
Minimum consumption | 5,000 units per week | |
Normal consumption | 12,000 units per week | |
Reorder quantity | 52,000 units | |
Average consumption | 8,000 units per week | |
Emergency delivery time | 2 weeks | |
Minimum | 6 weeks; maximum: 10 weeks |
Calculate (a) reorder level, (b) minimum level, (c) maximum level, (d) average stock level and (e) danger level.
Illustration 20
In manufacturing its products, a company uses three raw materials, A, B and C, for which the following particulars apply:
Weekly production varies from 225 to 275 units, averaging 250. What would you expect the quantities of (a) minimum stock of A, (b) maximum stock of B, (c) reorder level of C and (d) average stock of A to be?
Solution:
Maximum stock of B = Reorder level + Reorder quantity − (Minimum consumption × Minimum reorder period)
6,700 + 6,000 − (1,125 × 3) = 9,325 lb
(Minimum production per week = 225 units
Usage per unit of product = 5 lb
∴ Minimum consumption of material per week = 225 × 5 = 1,125 lb)
Reorder level of C = Maximum consumption × Maximum reorder period
2,200 × 4 = 8,800 lb
(Maximum production per week = 275 units)
Usage per unit = 8 lb
∴ Maximum consumption of material C = 275 × 8 = 2,200 lb
Problem 20. In manufacturing its products, a company uses three raw materials, A, B and C, for which the following particulars apply:
Weekly production varies from 225 to 275 units, averaging 250. What would you expect the quantities of (a) minimum stock of A, (b) maximum stock of B, (c) reorder level of C and (d) average stock of A to be?
Illustration 1
Develop the formula for economic order quantity.
Solution:
A = annual consumption
B = buying cost per order
CS = carrying cost per unit
*Since on an average 50% of E will be in stock.
At the EOQ level, total storage costs are equal to total order placing costs.
Illustration 2
If the minimum stock level and average stock level of raw material A are 4,000 and 9,000 units, respectively, find its reorder quantity.
Solution:
Minimum stock level of material | A4,000 units |
Average stock of material | A9,000 units |
Average stock level | minimum stock level + ½ reorder quantity |
½ Reorder quantity | 9,000–4,000 |
5,000 units | |
Reorder quantity | 10,000 units |
Illustration 3
G Ltd produces a product that has a monthly demand of 4,000 units. The product requires a component X, which is purchased at Rs 10 for every finished product one unit at component is required. The ordering cost is Rs 60 and the holding cost is 10% per annum. You are required to calculate
Solution:
(i) If the order size is 4,000 units
When the order size is 2,400
The carrying or storage cost depends upon the size of the order. Its value will be minimum when the order size is the lowest. In the question, the two order sizes are 2,400 units and 4,000 units. Hence, 2,400 units is the least of the two order sizes. At this size, the carrying cost will be minimum. The minimum carrying cost in this case will be as follows:
Illustration 4
A gardener is deciding on the EOQ for two brands of lawn fertilizers: Super Grow and Nature's Own. The following information is collected:
Fertilizer | ||
---|---|---|
Particulars | Super Grow | Nature's Own |
Annual demand | 2,000 bags | 1,280 bags |
Relevant ordering cost per purchase order | 600 | 700 |
Annual relevant carrying cost per bag | 240 | 280 |
You are required to calculate
Solution:
Super Grow:
Nature's Own:
Total annual relevant costs for Nature's Own:
Number of Deliveries:
Illustration 5
In a company, weekly minimum and maximum consumptions of material A are 25 and 75 units, respectively. The reorder quantity as fixed by the company is 300 units. The material is received within 4–6 weeks from the issue of supply order. Calculate minimum level and maximum level of material A.
Minimum level = Reorder level − Average consumption × Average reorder period)
= 455 − (50 units × 4 weeks)
= 650 units
Reorder level = Maximum usage × Maximum reorder period
= 75 units × 6 weeks
= 450 units
Illustration 6
About 50 items are required every day for a machine. A fixed cost of Rs 25 per order is incurred for playing an order. The inventory carrying cost per item amounts to Rs 0.01 per day. The lead period is 32 days. Compute (i) economic order quantity and (ii) reorder level.
Solution:
Annual consumption | = 50 × 365 = 18,250 units |
Order cost | = 25 |
Inventory carrying cost per item per annum | = 0.01 × 365 |
= 3.65 |
= 50 × 32
= 1,600 items
Illustration 7
A company uses three raw materials A, B and C for a particular product for which the following data apply:
Weekly production varies from 175 to 225 units, averaging 200 units, of the said product. What would be the values of the following quantities?
Solution:
= 8,000 − (2,000 × 2)
= 4,000 kg
= 4,750 + 5,000 − (700 × 3)
= 4,750 + 5,000 − 2,100
= 7,650
= 4 × 1,350
= 5,400kg
After reading this chapter, you should be able to understand the importance of material for production. You should have also understood the levels, essentials and techniques of material control.
Where
First formula:
A = annual consumption
O = ordering cost per order
C = carrying cost per unit per year
Second formula:
B = buying cost per order
C = cost per unit
S = storage and carrying cost
Third formula:
C = annual usage of material
O = cost of placing one order
I = annual carrying cost of one unit
or
Average stock level = minimum level + ½ of ROQ or EOQ
Objective-Type Questions
I. State whether the following statements are true or false:
[Ans: 1—false, 2—true, 3—true, 4—false, 5—false, 6—false, 7—true, 8—true, 9—true, 10—true]
II. Choose the correct answer:
Ans: 1—(c), 2—(b), 3—(c), 4—(b), 5—(a), 6—(b), 7—(b), 8—(b), 9—(b), 10—(b).
Short Answer-Type Questions
Essay-Type Questions
Ans:
Annual usage | 6,000 units |
Cost per unit | Re 0.30 |
Buying cost | Rs 7 per order |
Carrying cost | 15% of average inventory holding |
[Ans: 1,366 units]
Annual return on investments | 10% | |
Rent, insurance, taxes per unit per year | Re 1 | |
Cost of placing an order | Rs 100 |
Determine the economic order quantity
[Ans: 200 units]
Annual consumption | 120 units |
Buying cost per order | Rs 20 |
Price per unit | Rs 100 |
Storage and carrying cost as a percentage of average inventory 12%.
[Ans: 20 units, 6 orders]
Monthly usage | 150 units |
Buying cost | Rs 2 per order |
Cost per unit | 0.32 paise |
Storage cost | 25% per annum |
(Osmania, B.Com.)
[Ans: EOQ = 300 units]
Annual consumption | 600 units |
Order cost | Rs 12 per order |
Cost price per unit | Rs 20 |
Storage and carrying cost | 20% |
(Madras, 1990)
[Ans: EOQ = 60 units]
Annual usage | 20,000 units |
Buying cost per order | Rs 10 |
Cost per unit | Rs 100 |
Cost of carrying inventory | 10% of cost |
(Madras, 1996)
[Ans: EOQ = 200 units]
Annual consumption | 90,000 units |
Cost per unit | Rs 50 |
Buying cost per order | Rs 10 |
Cost of carrying inventory | 10% of cost |
(Madras, 1996)
[Ans: EOQ = 600 units]
Annual usage | 6,000 units |
Cost of materials per unit | Rs 20 |
Cost of placing and receiving one order | Rs 60 |
Annual carrying cost | Rs 2 per unit |
(Madras,)
[Ans: EOQ = 600 units]
Hint: Carrying cost of Rs 2 per unit can be directly used in the formula without any reference to cost per unit.
Annual usage | 8,000 units |
Cost per unit | Re 0.30 |
Buying cost | Rs 7 per order |
Storage and carrying costs as percentage of average inventory holding 15%.
[Ans: 1,578 units]
Annual usage | Rs 1,20,000 |
Cost of placing and receiving one order | Rs 60 |
Annual carrying cost | 10% of inventory value |
(Madras, 1995)
[Ans: EOQ = Rs 12,000]
Material usage per month | Rs 1,600 |
Buying cost per order | Rs 40 |
Storage and carrying cost | 15% of inventory value |
[Ans: EOQ = Rs 3,200]
Reorder quantity | 4,000 units | |
Minimum stock level to allow for emergencies | 5 weeks | |
Average delivery time from suppliers | 4 weeks | |
Maximum stock level allowed by management | 20 weeks | |
Average rate of consumption per week | 250 units | |
Minimum consumption in 4 weeks | 800 units |
(B.Com., Madras)
[Ans: (a) 2,250; (b) 1,250]
Minimum consumption | 240 units per day | |
Maximum consumption | 420 units per day | |
Normal consumption | 300 units per day | |
Reorder quantity | 3,600 units | |
Reorder period | 10–15 days | |
Normal reorder period | 12 days |
(Madras, 1995)
[Ans: (a) 7,500 units; (b) 2,700 units; (c) 6,300 units; (d) 5,100 units or 4,500 units]
Normal consumption per day | 500 kg | |
Minimum consumption per day | 200 kg | |
Maximum consumption per day | 800 kg | |
Lead time | 10–16 days | |
Reorder quantity | 3,000 kg |
(Madras, 1990)
[Ans: maximum stock level = 13,800 units; minimum stock level = 6,300 units;
average stock level = 10,050 units or 7,800 units]
Normal consumption per day | 500 kg | |
Minimum consumption per day | 200 kg | |
Maximum consumption per day | 800 kg | |
Lead time | 10–16 days | |
Reorder quantity | 3,000 kg |
(B.Com., Calicut)
[Ans: 13,800 kg; 6,300 kg; 7,800 kg]
In a manufacturing firm, a material is used as follows:
Maximum consumption | 12,000 units per week | |
Minimum consumption | 4,000 units per week | |
Normal consumption | 8,000 units per week | |
Reorder quantity | 48,000 units | |
Minimum | 4 weeks | |
Maximum | 6 weeks |
Calculate (a) reorder level, (b) minimum level, (c) maximum level and (d) average stock level.
(B.Com., Bangalore)
[Ans: (a) 72,000; (b) 32,000; (c) 1,04,000; (d) 56,000 or 38,000]
Maximum usage in a month | 300 kg |
Minimum usage in a month | 200 kg |
Average usage in a month | 225 kg |
Time lag in the procurement of materials | maximum—6 months, minimum—2 months |
Reordering quantity | 750 kg |
(Madras, 1998)
[Ans: reorder level = 1,800 units; minimum level = 900 units;
average stock level = 1,275 units (900 + 375)]
Maximum consumption | 9,000 units per week | |
Minimum consumption | 3,000 units per week | |
Normal consumption | 6,000 units per week | |
Reorder quantity | 36,000 units | |
Time required for delivery | 4–6 weeks | |
Time required for emergent supplies | 1 week |
Calculate (a) reorder level, (b) minimum level, (c) maximum level, (d) danger level and (e) average stock level.
(B.Com., Madurai)
[Ans: (a) 54,000 units; (b) 24,000 units; (c) 78,000 units; (d) 6,000 units; (e) 42,000 units]
Minimum consumption | 100 units per day | |
Maximum consumption | 150 units per day | |
Normal consumption | 120 units per day | |
Reorder period | 10–15 days | |
Reorder quantity | 1,500 units | |
Normal reorder period | 12 days |
(Madras, 1998)
[Ans: minimum stock level = 810 units; maximum stock level = 2,750 units;
reordering level = 2,250 units]
Reorder quantity | 1,500 units | |
Reorder period | 4–6 weeks | |
Maximum consumption | 400 units per week | |
Normal consumption | 300 units per week | |
Minimum consumption | 250 units per week |
(ICWA)
[Ans: maximum level = 2,900 units; minimum level = 900 units; reorder level = 2,400 units]
Normal usage | 300 units per week | |
Maximum usage | 450 units per week | |
Minimum usage | 150 units per week | |
Reorder period | 4–6 weeks | |
Reorder quantity | 2,400 units |
(Madras, 1997)
[Ans: reorder level = 2,700 units; minimum stock level = 1,200 units; maximum stock level =
4,500 units; average stock level = 2,850 units or 2,400 units]
Reorder quantity | 4,000 units |
Minimum stock level to allow for emergencies | 4 weeks |
Average delivery time from suppliers | 4 weeks |
Maximum stock level allowed by management | 20 weeks |
Average rate of consumption per week | 250 units |
Minimum consumption in 4 weeks | 800 units |
(Madras, 1992)
[Ans: reorder level = 2,000 units (250 × (4 + 4)); maximum stock level = 5,200 units;
minimum stock level = 1,000 units]
Maximum usage in a month | 300 numbers |
Minimum usage in a month | 200 numbers |
Average usage in a month | 225 numbers |
Time lag in the procurement of materials: | |
Maximum | 6 months |
Minimum | 2 months |
Reorder quantity | 760 numbers |
(Madras, 1991)
Normal usage | 4,500 units each per week | |
Minimum usage | 2,250 units each per week | |
Maximum usage | 6,750 units each per week | |
Reorder quantity | ||
X | 19,500 units | |
Y | 21,000 units | |
Reorder period | ||
X | 3–5 weeks | |
Y | 2–4 weeks |
Calculate for each of the components (a) reorder level, (b) minimum level and (c) maximum level.
(Madras, B.A., 1995)
[Ans: (a) X—33,750 units; (b) X—15,750 units; (c) A—46,400 units, X—27,000 units,
Y—13,500 units, B—43,500 units]
Annual consumption | 12,000 units (360 days) |
Cost per unit | Re 1 |
Cost per order | Rs 12 |
Inventory carrying cost | 20% per annum |
Lead time (maximum, normal and minimum): | 30—15—5 (days) |
Daily consumption (maximum, normal and minimum) | 45—33—15 (units) |
Calculate inventory levels.
(Madras, 1999)
[Ans: reorder level = 1,350 units; EOQ = 1,200 units; maximum level = 2,475 units;
minimum level = 855 units]
Maximum stock level | 8,400 units |
Budgeted consumption: | |
Maximum | 1,500 units per month |
Minimum | 800 units per month |
Estimated delivery period: | |
Maximum | 4 months |
Minimum | 2 months |
You are required to calculate | |
(a) reorder level and | |
(b) reorder quantity |
(Madras, 1989)
[Ans: (a) 6,000 units; (b) 4,000 units]
Maximum stock level | 16,800 units |
Budgeted consumption | |
Maximum | 3,000 units per month |
Minimum | 1,600 units per month |
Estimated delivery period | |
Maximum | 4 months |
Minimum | 2 months |
[Ans: (a) 12,000 units; (b) 8,000 units]
Annual requirement | 1,600 units |
Cost of material per unit | Rs 40 |
Cost of placing and receiving one order | Rs 50 |
Annual carrying cost of inventory is 10% of inventory value. |
(Madras, 1986)
[Ans: EOQ = 200 units]
Annual consumption | 600 units |
Ordering cost | Rs 12 per order |
Carrying cost | 20% |
Price per unit | Rs 20 |
(B.Com., Punjab)
[Ans: 60 units]
Consumption of material per annum | 10,000 kg | |
Ordering cost per order | Rs 50 | |
Cost per kilogram of raw material | Rs 2 | |
Store cost | 8% on inventory |
(Madras, 1988)
[Ans: EOQ = 2,500 kg]
Annual return on investment | 10% |
Rent, insurance, taxes per unit per year | Rs 13 |
Cost of placing an order | Rs 100 |
Determine EOQ.
(Bharathidasan, 1992)
Return on investment is 8% | 11.20 |
Rent, taxes, insurances, handling charges, etc. | Rs 2.80. |
Calculate the EOQ.
Annual return on investment | 10% |
Rent, insurance, taxes per unit per year | Re 1 |
Cost of placing an order | Rs 100 |
Determine the EOQ.
(Madras, 1994)
Interest | Re 0.06 per unit per year |
Deterioration cost | Re 0.004 per unit per annum |
Storage cost | Rs 1,000 per annum for 5,000 units |
Calculate the EOQ.
(Madras, 1996)
Consumption of material per annum | 10,000 kg |
Cost of material per kilogram Rs | 2 |
Order placing costs per order Rs | 50 |
Storage costs 8% on average inventory.
(Madras, 1991)
[Ans: EOQ = 2,500 kg, number of orders to be placed = 4]
Annual requirement | 1,600 units | |
Cost of materials per unit | Rs 40 | |
Cost of placing and receiving one order | Rs 50 | |
Annual carrying cost of inventory | 10% of the inventory value |
(Madras, 1987)
[Ans: EOQ = 200 units, number of orders per annum = 8]
(Bharathidasan, B.Com.)
[Ans: EOQ = 600 kg, number of orders = 10 per annum, frequency =
one order per 36.5 or 37 days, or one order per 1.2 months]
10a. Find EOQ, given the following:
Monthly usage | 150 units |
Buying cost | Rs 2 per order |
Cost per unit | Re 0.32 paise |
Storage cost | 25% per annum |
(Osmania, B.Com.)
[Ans: EOQ = 300 units]
Normal usage | 50 units each per week | |
Minimum usage | 25 units each per week | |
Maximum usage | 75 units each per week | |
Reorder quantity | X—400 units, Y—600 units | |
Reorder period | X—4–6 weeks, Y—2–4 weeks |
Calculate for each component (a) reorder level, (b) minimum level, (c) maximum level and (d) average level.
(M.Com., Calicut)
[Ans: (a) reorder level X = 450 units, Y = 300 units; (b) minimum level X = 200 units,
Y = 150 units; (c) maximum level X = 750 units, Y = 850 units;
(d) average stock X = 400 units, Y = 450 units]
Normal usage | 600 units each per week | |
Maximum usage | 900 units each per week | |
Minimum usage | 300 units each per week | |
Reorder quantity | X—4,800 units, Y—7,200 units | |
Reorder period | X—4–6 weeks, Y—2–4 weeks |
Calculate for each component (a) reorder level, (b) minimum level, (c) maximum level and (d) average stock level.
(B.Com., Andhra)
Normal usage | 100 units per week each |
Minimum usage | 50 units per week each |
Maximum usage | 150 units per week each |
Reorder quantity | A—400 units, B—600 units |
Reorder period | A—6–8 weeks, B—3–5 weeks |
Calculate for each component (a) minimum level, (b) maximum level and (c) average stock level.
(B. Com., Madurai)
Normal usage | 100 units per day | |
Minimum usage | 60 units per day | |
Maximum usage | 130 units per day | |
EOQ | 5,000 units | |
Reorder period | 25–30 days |
(B. Com., Kerala)
[Ans: (a) 3,900 units; (b) 1,150 units; (c) 7,400 units]
Reorder period | 4–6 weeks | |
Maximum consumption | 100 units per week | |
Minimum consumption | 50 units per week | |
Normal consumption | 75 units per week | |
Annual consumption | 36,000 units | |
Cost per unit | Re 1 | |
Ordering cost | Rs 25 |
Inventory carrying cost is 20% of unit value.
[Ans: (a) 3,000 units; (b) 3,400 units; (c) 225 units; (d) 600 units]
15a. In a manufacturing firm, a material is used as follows:
Maximum consumption | 12,000 units per week | |
Minimum consumption | 4,000 units per week | |
Normal consumption | 8,000 units per week | |
Reorder quantity | 48,000 units | |
Minimum | 4 weeks | |
Maximum | 6 weeks |
Calculate (a) reorder level, (b) minimum level, (c) maximum level and (d) average stock level.
(B. Com., Bangalore)
[Ans: (a) 72,000; (b) 32,000; (c) 1,04,000; (d) 56,000 or 38,000]
Calculate the material turnover ratio of the two materials X and Y and express in number of days the average inventory held. Also, determine which of the two materials is fast moving.
X is fast moving.
3.133.134.58