HAPTER MATERIALS OST PRATIAL PROBLEMS LEVELS OF INVENTORY Q1: P Ltd. uses three types of materials A, B and for production of 'X' the final product. The relevant monthly data for the components are as given below: Particulars A B Normal Usage (units) 00 150 180 Minimum Usage (units) 100 100 90 Maximum Usage (units) 300 50 70 Reorder Quantity (units) 750 900 70 Reorder Period (months) to 3 3 to 4 to 3 alculate for each component: (a) Reorder Level; (b) Minimum Level; (c) Maximum Level and (d) Average Stock Level. Solution: (a) Reorder Level = Maximum consumption x Maximum Delivery Period A = (300 x 3) = 900 units B = (50 x 4) = 1,000 units = (70 x 3) = 810 units (b) Minimum level = Reorder level (Normal onsumption x Normal Period) A = 900 (00 x.5) = 400 units B = 1000 (150 x 3.5) = 1,000 55 = 475 units = 810 (180 x.5) = 810-450 = 360 units (c) Maximum Level = Reorder Level + Reorder Quantity (Min. onsumption x Min Delivery Period) A = 900 + 750 (100 x ) = 1,650 00 = 1,450 units B = 1,000 + 900 (100 x 3) = 1,900 300 = 1,600 units = 810 + 70 (90 x ) = 1,530 180 = 1,350 units (d) Average Stock Level = (Minimum Level + Maximum Level)/ A = (400 + 1,450)/ = 95 units B = (475 + 1,600)/ = 1,037.5 units = (360 + 1,350)/ = 855 units Q: Re-Order Quantity of Material X is 5,000 kg.; Maximum Level 8,000 kg.; Minimum Usage 50 kg.
per hour; Minimum Re-Order Period 4 days; daily working hours in the factory is 8 hours. You are required to calculate the Re-Order Level of Material X. (A IP May 010) Solution: Re-Order Level = Maximum Level [Re-Order Quantity (Minimum Usage per day x Minimum Re-Order Period) = 8,000 kg. [5,000 kg. (400 kg* x 4 days)] = 8,000 kg. 3,400 kg. = 4,600 kg. Hence, Re-Order level is 4,600 kg. *Minimum Usage per day = 50 kg. x 8 hours = 400 kg. Q3: In a manufacturing company, a material is used as follows: Maximum onsumption-1,000 units per week. Minimum onsumption-4,000 units per week. Normal onsumption-8,000 units per week. Reorder Quantity-48,000 units. Time required for delivery: Minimum: 4 weeks; Maximum: 6 weeks. alculate: (a) Re-Order Level, (d) Danger Level and, (b) Minimum Level, (e) Average Stock Level. (c) Maximum Level, Solution: Normal Lead Time = Minimum Lead time + Maximum Lead time = 4 weeks + 6 weeks = 5 weeks (a) Reorder Level = Maximum onsumption x Maximum Lead Time = 1,000 units x 6 weeks = 7,000 units (b) Minimum Level = Reorder Level (Normal onsumption x Normal Lead time) = 7,000 units (8,000 units x 5 weeks) = 3,000 units (c) Maximum Level = Reorder Level + Reorder Quantity (Minimum Usage x Minimum Period) = 7,000 units + 48,000 units (4,000 units x 4 weeks) = 1,04,000 units (d) Danger Level = Normal onsumption x Delivery Period Emergency Purchase = 8,000 units x 3 weeks = 4,000 units Note: It is assumed that delivery period for emergency purchase is 3 weeks (less than minimum time of delivery). (e) Average Stock Level = Minimum Level + Maximum Level = 3,000 units + 1,04,000 units = 68,000 units Q4: Following details are related to a manufacturing concern: Re-order Level Economic Order Quantity Maximum Stock level Average Lead time Difference between Minimum lead time and Maximum lead time 1,60,000 units 90,000 units 1,90,000 units 6 days 4 days
alculate: (i) Maximum consumption per day (ii) Minimum consumption per day (A IP Nov 014) Solution: (a) Difference between Minimum lead time and Maximum lead time = 4 days Max. lead time = Min. lead time + 4 days..................... (i) Average lead time is given as 6 days i.e. Max. lead time + Min. lead time = 6 days........................ (ii) Putting the value of (i) in (ii), Min. lead time + 4 days + Min. lead time = 6 days Or, Minimum lead time = 8 days = 4 days Putting this Minimum lead time value in (i), we get Maximum lead time = 4 days + 4 days = 8 days (i) Maximum consumption per day: Re-order level = Max. onsumption x Max. Lead Time 1,60,000 units = Maximum onsumption per day x 8 days Maximum onsumption per day = 1,60,000 units = 0,000 units 8 days (ii) Minimum onsumption per day Maximum Stock Level = Re-order level + Re-order Quantity (Min. lead time Min. onsumption per day) 1,90,000 units = 1,60,000 units + 90,000 units (4 days Min. onsumption per day) 4 days Min. onsumption per day =,50,000 units 1,90,000 units Minimum onsumption per day = 60,000 units = 15,000 units 4 days LEVELS OF INVENTORY & REORDER QUANTITY Q5: The following information relating to a type of Raw material is available: Annual Demand,000 units Unit price `0.00 Ordering ost per order `0.00 Storage ost % p.a. Interest Rate 8% p.a. Lead Time Half-month alculate Economic Order Quantity and Total Annual Inventory ost of the Raw Material. (A IP Nov 009) Solution: EOQ = x A x O = x,000 units x `0 = 80,000 = 00 units ` A =,000 units O = `0 per order = `0 x (% + 8%) = ` Total Annual Inventory ost
Annual Purchase ost of,000 Units @ `0 `40,000 Add: Annual Ordering ost *10 orders x `0 `00 * No. of Orders,000 units = 10 00 units Add: Annual arrying cost of Average Inventory 00 units x `0 x `10 `00 100 Total Annual Inventory osts `40,400 Q6: (a) From the following information, find out the Economic Order Quantity. Annual onsumption 1,000 units (360 days) ost per unit `1 Ordering ost `1 per order Inventory arrying harge 4% Normal Lead Time 15 days Safety Stock 30 days consumption (b) Also find out: (i) When should the order be placed? and, (ii) What should be the ideal inventory level immediately before the order material is received? (A PE II May 005) Solution: (a) EOQ = x A x O = x 1,000 units x `1 = 1,095 units `0.4 A = 1,000 units O = `1 per order = 4% x `1 = `0.4 (b)(i) ROL = SSL + (Normal onsumption x Normal Lead Time) = 1,000 units + 1,000 units x 15 days = 1,500 units 360 days (ii) SSL = Safety Stock Time x Annual onsumption = 30 days x 1,000 units = 1,000 units 360 days 360 days Q7: ML Manufacturing Ltd. is required 1,000 units of material EX on an average for a week which is purchased at a price of `30 per unit. The ordering cost is `150 per purchase order and inventory carrying cost per unit amounted to `0.06 per week. The re-order period is 1 to 3 weeks and the weekly usage of material EX varies from 750 to 1,50 units. You are required to compute: (i) The Economic Order Quantity. (ii) Re-order Stock Level, Minimum Stock Level and Maximum Stock Level. (A PE II Nov 009) Solution: (i) EOQ = x A x O = x 5,000 units x `150 =,36 units `3.1 A = 1,000 units x 5 weeks = 5,000 units O = `150 per order = `0.06 x 5 weeks = `3.1 (ii) Stock Levels: Re-order Level = Maximum Re-Order Period x Maximum Usage = 3 weeks x 1,50 units = 3,750 units Minimum Level = Re-Order Level (Average Re-order Period x Average Usage)
= 3,750 units ( weeks x 1,000 units) = 1,750 units Maximum Level = Re-Order Level + Re-Order Quantity (Min. Re-Order Period x Min. Usage) = 3,750 units +,36 units (1 week x 750 units) = 5,36 units Q8: You are required to calculate the following levels for part No. 13456 from the information given there under: (a) Re-ordering level,(b) Maximum level,(c) Minimum level,(d) Danger level,(e) Average Stock level. The following data may be used to calculate the re-ordering quantity. 1 Total ost of purchasing relating to the order. `0. Number of units to be purchased during the year. 5,000 3 Purchase Price per unit including transportation. `50 4 Annual ost of Storage of one unit. `5 Lead Times Average 10 days Maximum 15 days Minimum 6 days Max. for emergency purchase 4 days Rate of onsumption Average 15 units per day Maximum 0 units per day (A Inter May 1996 & Nov 1987) Solution: (a) Re-Ordering Level = Maximum onsumption x Maximum Lead Time = 0 units per day x 15 days = 300 units (b) Maximum Level = Reorder Level + Reorder Qty. - (Min onsumption x Min Lead time) = 300 + 00 (10 x 6 days) = 440 units (c) Minimum Level = Reorder Level (Average onsumption x Average Reorder Period) = 300 (15 units x 10 days) = 150 units (d) Danger Level = Average onsumption x Lead time for emergency purchases = 15 units x 4 days = 60 units (e) Average Stock level = Maximum Level + Minimum Level = 440 units + 150 units = 95 units Working Notes: A = Annual Requirement = 5,000 units. O = Ordering ost Per order = `0 = arrying ost per unit per annum = `5 per unit (1) EOQ = x A x O = x 5,000 x 0 = 00 units 5 () Minimum onsumption = x Average onsumption Maximum onsumption = ( x 15) 0 = 10 units Q9: A company manufactures 5,000 units of a product per month. The cost of placing an order is `100. The purchase price of the raw material is `10 per kg. The re-order period is 4 to 8 weeks. The consumption of raw materials varies from 100 kg to 450 kg per week, the average consumption being 75 kg. The arrying ost of Inventory is 0% per annum. You are required to calculate: (i) Re-Order Quantity (ii) Re-Order Level (iii) Maximum Level (iv) Minimum Level (v) Average Stock Level (A PE II Nov 00)
Solution: A = Annual Requirement = (Average onsumption per week x 5 weeks) = (75 kgs x 5 weeks) = 14,300 kgs. O = Ordering ost per Order = `100 per order = arrying ost per unit per annum = `10 x 0% = ` (i) EOQ = x A x O = x 14,300kg x `100 = 1,196 kgs. (Approx) ` (ii) Re-order Level = (Maximum onsumption x Maximum Reorder Period) = 450 kgs per week x 8 weeks = 3,600 kgs (iii) Maximum Level = Reorder Level + Reorder Quantity (Minimum onsumption x Minimum Re- Order Period) = 3,600 kg + 1,196 kg - (100 kg per week x 4 weeks) = 1,196 + 3,600-400 kg. = 4,396 kg. (iv) Minimum Level = Reorder Level - (Average onsumption x Average Reorder Period) = 3,600 kg - 100kg + 450kg x 4 weeks + 8 weeks = 3,600 kg - (75kg x 6 weeks) = 1,950kgs. (v) Average Stock Level = Maximum Level + Minimum Level = 4,396 kg + 1,950 kg = 3,173 kg Q10: A company uses annually 48,000 units of raw material costing `1.0 per unit. Placing each order costs `45 and inventory carrying costs are 15 % per year of the average inventory values: (i) Find the EOQ. (ii) Suppose that the company follows the EOQ policy and its operates for 300 days a year, that the procurement time is 1 operating days and the safety stock is 500 units, find (a) Re-Ordering Level, (b) The Maximum Level, (c) The Minimum Level; (d) The Average Inventory. Solution: A = 48,000 units O = `45 per order = 15% x 1.0 = `0.18 per unit p.a. (i) EOQ = x A x O = x 48,000 units x `45 = 4,899 units `0.18 (ii) (a) Re-Order Level = Safety Stock + (Normal onsumption x Normal Delivery Time) = 500 units + 48,000 units x 1 Days 300 days = 500 units + 1,90 units =,40 units (b) Maximum Level = Re-order level + Re-order Quantity - (Min. onsumption x Min. Period) =,40 units + 4,899 units 48,000 units x 1 Days = 5,399 units 300 Days (c) Minimum Level = Re-order Level (Normal onsumption x Normal Period) =,40 units 48,000 units x 1 Days = 500 units 300 Days (d) Average Inventory = Minimum Level + ½ of EOQ
= 500 units + ½ (4,899) units =,950 units Q11: PQR Ltd. manufactures a special product, which requires ZED. The following particulars were collected for the year 005-06: (i) Monthly Demand of Zed 7,500 units (ii) ost of placing an order `500 (iii) Re-Order Period 5 to 8 weeks (iv) ost per unit `60 (v) arrying ost % p.a. 10% (vi) Normal Usage 500 units per week (vii) Minimum Usage 50 units per week (viii) Maximum Usage 750 units per week Required: (i) Re-Order Quantity. (ii) Re-Order Level. (ii) Minimum Stock Level. (iv) Maximum Stock Level. (v) Average Stock Level. (A PE II Nov 006) Solution: (i) Re Order Quantity = x A x O = x 90,000 units x `500 = 3,873 units `6 A = 7,500 units x 1 months = 90,000 units O = `500 per order = `60 x 10% = `6 (ii) Re-Order Level = Maximum re-order period Maximum usage = 8 weeks x 750 units = 6,000 units (iii) Minimum Stock Level = Re-Order Level {Normal Usage x Average Reorder Period} = 6,000 units (`500 x 6.5 weeks) =,750 units (iv) Maximum Stock Level = Re-Order Level + Re-Order Quantity (Minimum Usage x Minimum Period) = 6,000 units + 3,873 units (50 units x 5 weeks) = 8,63 units (v) Average Stock Level = ½ (Minimum Stock Level + Maximum Stock Level) = ½ (,750 units + 8,63 units) = 5,687 units Q1: R Tubes Ltd is the manufacturers of picture tubes for T.V. The following are the details of their operations during 1999-000: Ordering ost `100 per order Inventory arrying ost 0% p.a ost of Tubes `500 per tube Normal Usage 100 tubes per week Minimum Usage 50 tubes per week Maximum Usage 00 tubes per week Lead Time to Supply 6-8 weeks Required: (i) Economic Order Quantity. If the supplier is willing to supply quarterly 1,500 units at a discount of 5%, is it worth accepting?
(ii) Re-order Level. (iii) Maximum Level of stock if Re-Order Quantity is 1,500 units. (iv) Minimum Level of stock. (A Inter May 000 adapted) Solution: (i) EOQ = x A x O = x 5,00 tubes x 100 = 10 tubes `100 A = 100 tubes per week x 5 weeks = 5,00 tubes O = `100 per order = 0% x `500 = `100 per unit p.a. Statement showing Evaluation of Supplier s proposal Amount in (`) Particulars 10 tubes 1,500 tubes Annual Ordering ost 5,098 347 5,00 tubes x `100 ; 5,00 tubes x `100 10 tubes 1,500 tubes Annual arrying cost 5,100 71,50 10 tubes x `100 ; 1,500 tubes x `95 tubes tubes Annual Purchase ost [5,00 tubes x `500] 6,00,000 4,70,000 [5,00 tubes x `475] Total Annual Relevant osts 6,10,198 5,41,597 Yes, the supplier s offer for ordering 1,500 units should be accepted. (ii) Reorder Level = Maximum Usage x Maximum Lead Time = 00 tubes x 8 weeks = 1,600 tubes (iii) Maximum Level = Reorder Level + Reorder Quantity (Minimum Usage x Minimum Lead Time) = (1,600 tubes + 1,500 tubes) - (50 tubes x 6 tubes) =,800 tubes (iv) Minimum Level = Reorder Level (Normal Usage x Normal Lead Time) = 1,600 tubes (100 tubes x 7 weeks) = 900 tubes Q13: The quarterly production of a company's product which has a steady market is 0,000 units. Each unit of a product requires 0.5 kg of raw material. The cost of placing one order for raw material is `100 and the inventory carrying cost is ` per annum. The lead time for procurement of raw material is 36 days and a safety stock of 1,000 kg of raw materials is maintained by the company. The company has been able to negotiate the following discount structure with the raw material supplier: Order Quantity (Kgs.) Discount in (`) Upto 6,000 Nil 6,000-8,000 400 8,000-16,000,000 16,000-30,000 3,00 30,000-45,000 4,000 You are required to: (i) alculate the Re-Order Point taking 30 days in a month. (ii) Prepare a statement showing the total cost of procurement and storage of raw materials after considering the discount if the company elects to place one, two, four or six orders in the year. (iii) State the number of orders which the company should place to minimise the costs after taking EOQ also into consideration.
(A Inter May 00) Solution: (i) Annual Production = Quarterly Demand of Finished Product x 4 Quarters = 0,000 units x 4 quarters = 80,000 units A or Annual onsumption of Raw Material = Annual Production x Usage per unit of Finished Product = (80,000 units x 0.5 Kg) = 40,000 Kg O = `100 per order = ` per kg p.a. Reorder Point = Safety Stock Level + Normal Usage x Normal Lead Time = 1,000kg. + 40,000 kg x 36 days = 5,000 Kg 360 days (ii) Statement showing determination of EOQ Annual Requirement (Kg.) No. of Orders p.a. 40,000 1 4 6 Size of Order (Kg.) 40,000 0,000 10,000 6,666 Avg. Units (Kg.) 0,000 10,000 5,000 3,333 Annual Ordering ost (`) (A) 100 00 400 600 Annual arrying ost (`) (B) 40,000 0,000 10,000 6,666 Annual Discount (`) () 4,000 3,00,000 400 (iii) EOQ = x A x O = x 40,000 kg x `100 =,000 kg ` No discount on purchases, since the quantity is less than 6,000 Kg. Particulars Amount in (`) Annual Ordering & arrying ost of EOQ = x A x O x 4,000 = x 40,000kg x 100 x Less: Discount (0) Annual Ordering & arrying osts after discount 4,000 Advice: Optimal Order Size =,000 kg Optimal Number of Orders p.a. = Annual Requirement = 40,000 kg = 0 orders EOQ,000 kg Annual Ordering & arrying ost after Discount (`) (A)+(B)-() 36,100 17,000 8,400 6,866 Q14: Akash Udyog, a small scale manufacturer, produces a product X by using two raw materials A and B in the ratio of 3:. Material A is perishable in nature and if not used within 5 days of purchase it becomes obsolete. Material B is durable in nature and can be used even after one year. The company has estimated a sales volume of 30,000 kg. for the month of July 016 and expects that the trend will continue for the entire year. The ratio of input and output is 5:3. The purchase price per kilogram of raw material A and B is `15 and ` respectively exclusive of taxes. Material A can be purchased from the local market within days period. On the other hand Material B is purchased from neighbouring state and it takes 4 days to receive the material in the store. To place an order the company has to incur an administrative cost of `10. arrying cost for Material A and B is 15% and 5% respectively. At present Material A is purchased in a lot of 8,000 kg. to avail 10% discount on market price. GST applicable for material A is 4% (credit available) and GST on Material B is % (credit not available).
ompany works for 5 days in a month and production is carried out evenly. You are required to calculate: (i) Economic Order Quantity (EOQ) for each material; (ii) Maximum stock level for Material A; (iii) alculate saving/ loss in Material A if purchase quantity equals to EOQ. Solution: (i) alculation of EOQ: Monthly Production of X = 30,000 kgs. Raw Material Required = 30,000 x 5 = 50,000 kgs. 3 Particulars A B Annual Demand 3,60,000 kg.,40,000 kg. 50,000 x 3 x 1months 50,000 x x 1 months 5 5 Ordering ost per order `10 `10 arrying cost per unit p.a. (15% x `15) ; (5% x `.44) `.5 `1.1 EOQ = x A x O Material A = x (30,000 kg. x 1 months) x `10 (15% of `15) = 8,64,00,000 = 6,196.77 kg. or 6,197 kg..5 Material B = x (0,000 kg. x 1 months) x `10 (5% of.44*) = 5,76,00,000 = 7,164.97 or 7,165 kg 1.1 *Purchase price + % GST = ` + % of ` = `.44 (ii) alculation of Maximum Stock level: Since the Material A is perishable in nature and it is required to be used within 5 days, hence, the Maximum Stock Level shall be lower of two: (a) Stock equal to 5 days consumption = 30,000 kg. x 5 days = 6,000 kg. 5 days Or (b) Maximum Stock Level for Material A = Re-order Quantity + Re-order level (Normal consumption* Normal lead time) = 8,000 kg. + *,400 kg. - (30,000/5 days) = 8,000 kg. Stock required for 5 days consumption is lower than the maximum stock level. Therefore, Maximum Stock Level should never be more than 6,000 kg. (*Since, production is processed evenly throughout the month hence material consumption will also be even.) Re order Level = Normal onsumption x Normal Period = (1,00 kg x days) =,400 kg (iii) alculation of Savings/ loss in Material A if purchase quantity equals to EOQ Particulars Purchase Quantity = 8,000 kg. Purchase Quantity = EOQ (6,197 kg.)
Annual consumption 3,60,000 kg. 3,60,000 kg. (30,000 1 months) ; (30,000 1 months) No. of orders [Note- (i)] 60 60 (3,60,000 6,000) ; (3,60,000 6,000) Ordering ost (a) `7,00 `7,00 (`10 60) ; (`10 60) arrying ost (b) [Note- (ii)] `8,100 `6,97 (15% of `13.50 4,000) ; (15% of `15 3,098.5) Purchase ost (c) (for good portion) `48,60,000 `54,00,000 (`13.50 3,60,000) ; (`15 3,60,000) Loss due to obsolescence (d) [Note- (iii)] `16,0,000 `1,77,300 [`13.5 (60,000)] ; [`15 (60 197)] Total ost [(a) + (b) + (c) + (d)] `64,95,300 `55,91,47 If purchase quantity equals to EOQ, there will be a saving of `9,03,88 i.e. `64,95,300 - `55,91,47. Notes: (i) As after 5 days of purchase the Material A gets obsolete, the quantity in excess of 5 days consumption i.e. 6,000 kg. are wasted. Hence, after 6,000 kg. a fresh order needs to be given. (ii) arrying cost is incurred on average stock of materials purchased. (iii) The excess quantity of material gets obsolete and loss has to be incurred. (iv) Advice: Since the Material A is perishable in nature, the company should purchase Material A in lot of 6,000 kgs. Particulars ROQ -6,000 kgs Annual onsumption 3,60,000 kgs No. of Orders (3,60,000/6,000) 60 orders Ordering ost (`10 60) (A) `7,00 arrying ost (15% of `15 x 3,000kgs) (B) `6,750 Purchase ost (`15 x 3,60,000 kgs) () `54,00,000 Total ost (A + B + ) `54,13,950 Q15: ipla Ltd. has a monthly requirement for an item of raw material is 1,000 units. The purchase price per unit of material is 60. The cost of processing an order is `540 and the carrying cost is 0%. There is a single supplier for the material which offers quantity discounts as under: Order Quantity (in units) Price per unit (`) Less than,000 units 60.00,000 units and less than 4,000 units 59.80 4,000 units and less than 6,000 units 59.50 6,000 units and less than 8,000 units 58.90 8,000 units and above 58.40 The company uses the cash credit facility provided by the company s banker to finance its raw material purchase. The bank due to its own infrastructural constraint, can accommodate a maximum of five fund transfer (NEFT/ RTGS) requests for any single beneficiary per annum. The company in short term is unable to arrange any other source of finance. Required: (i) alculate the optimum purchase order size for the company ignoring discount;
(ii) onsidering discount, calculate the order level where the company could have minimised its total cost; (iii) The amount of loss that the company has to bear due to bank s inability to process fund transfer requests. Solution: (i) alculation of optimum purchase order size or Economic Order Quantity (EOQ): EOQ = x A x O Where, A = Annual requirement for inventory = 1,000 units 1 months = 1,000 units O = Ordering cost = `540 = arrying cost per unit per annum = 0% `60 = `1 EOQ = x 1,000 units x 540 = 1,9,60,000 = 1,039.3 or 1,039 units. `1 1 (ii) alculation of order level to minimise total cost: Annual require -ment (in units) Order size (in units) No. of orders ost per order (`) Ordering cost (`) (A) Average invento ry arrying cost per unit @ 0% (`) arrying cost (`) (B) Purch -ase cost per unit (`) Purchase cost (`) () Total ost (`) (A+B+) 1,000 1,500 8 540 4,30 750 1 9,000 60 7,0,000 7,33,30,000 6 540 3,40 1,000 11.96 11,960 59.80 7,17,600 7,3,800 4,000 3 540 1,60,000 11.90 3,800 59.50 7,14,000 7,39,40 6,000 540 1,080 3,000 11.78 35,340 58.90 7,06,800 7,43,0 8,000 1.5 540 810 4,000 11.68 46,70 58.40 7,00,800 7,48,330 At order level of,000 units, the total cost to the company is least. (iii) alculation of amount of loss due to bank s inability to process more than five fund transfer requests: No. of orders 5 Purchase quantity per order (1,000 units 5),400 units ost per unit `59.80 (a) Ordering ost (`540 5 orders) `,700 (b) arrying ost (0% of `59.80 1,00 units) `14,35 (c) Material ost (`59.80 1,000 units) `7,17,600 Total ost {(a) + (b) + (c)} Less: Minimum cost at,000 units order level `7,34,65 (`7,3,800) Loss `1,85 EONOMI ORDER QUANTITY Q16: Following information relating to a type of raw materials is available: Annual Demand,400 units Unit price `.40 Ordering ost per order `4.00 Storage ost % per annum. Interest Rate 10% per annum. Lead Time Half Month.
alculate EOQ and total annual inventory cost in respect of the particular raw material. Solution: (a) EOQ = x A x O = x,400 units x `4 = 58 units `0.88 A = Annual onsumption =,400 Kg O = Ordering ost = `4 per order = arrying cost per unit per annum = 1% x `.4 = `0.88 (b) Total ost = Annual Purchase ost + Annual Relevant osts (i.e. ordering & carrying costs) = 5,760 + 74.36 = `5,834.36 Working Note: (i) Annual Purchase ost =,400 units x `.40 = `5,760 (ii) Total Annual Relevant osts = x A x O x = x,400 units x 0.88 x `4 = `74.36 Q17: About 50 items are required every day for a machine. A fixed cost of `50 per order is incurred for placing an order. The Inventory arrying ost per item amounts to `0.0 per day. The Lead Period is 3 days. ompute: (a) Economic Order Quantity, (b) Re-Order Level. (A Inter Nov 1996) Solution: (a) EOQ = x A x O = x (50 items x 360 Days x `50) = 500 items `0.0 x 360 Days (b) Re-order Level = (Normal onsumption x Normal Delivery Period) + Safety Stock Level = (50 items x 3 days) + 0 = 1,600 units Q18: ZED ompany supplies plastic crockery to fast food restaurants in metropolitan city. One of its products is a special bowl, disposable after initial use, for service soups to its customers. Bowls are sold in pack of 10 pieces at a price of `50 per pack. The demand for plastic bowl has been forecasted at a fairly steady rate of 40,000 packs every year. The company purchases the bowl direct from manufacturer at `40 per pack within a three days lead time. The ordering and related cost is `8 per order. The storage cost is 10% per annum of average inventory investment. Required: (i) alculate Economic Order Quantity. (ii) alculate number of orders needed every year. (iii) alculate the total cost of ordering and storing bowls for the year. Determine when should the next order to be placed. (Assuming that the company does not maintain a safety stock and that the present inventory level is 333 packs with a year of 360 working days. (A P May 008) Solution: (i) Economic Order Quantity (EOQ) = x A x O = x 40,000 packs x `8 = 400 packs `4 A = 40,000 packs O = `8 per order = 10% x `40 = `4 (ii) Number of orders per year = Annual Requirements = 40,000 packs = 100 order per year Economic Order Quantity 400 packs (iii) Ordering and Storage osts Particulars Amount in (`) Ordering osts: 100 orders x `8.00 800 Storage ost: (400 packs/) x (10% of `40) 800
Total osts of Ordering & Storage 1,600 (iv) (a) Average Daily onsumption = Annual Requirement = 40,000 packs = 111 packs per day 360 days 360 days This implies that 111 packs are consumed everyday. (b) Number of Days the present inventory can be used = Present Inventory Held. Average Daily onsumption = 333 packs = 3 days requirement 111 packs (c) Time Interval for placing next order = Inventory left for day s requirement Lead Time of Delivery 3 Day s Requirements 3 Days Normal Lead Time = 0 This means that next order for the replenishment of supplies has to be placed immediately. Q19: The Average Annual onsumption of a material is 18,50 units at a price of `36.50 per unit. The Storage ost is 0% on an Average Inventory and the ost of placing an Order is `50. How much quantity is to be purchased at a time? (A P May 007) Solution: EOQ = x A x O = x 18,50 units x `50 = 500 units `7.3 A = 18,50 units O = `50 per order = 0% x `36.50 = `7.3 Q0: The complete Gardener is deciding on the economic order quantity for two brands of lawn fertilizer : Super Grow and Nature's Own. The following information is collected: Fertilizer Super Grow Nature's Own Annual Demand,000 Bags 1,80 Bags Relevant Ordering ost per purchase order `1,00 `1,400 Annual Relevant arrying ost per bag `480 `560 Required: (i) ompute EOQ for Super Grow and Nature's Own. (ii) For the EOQ, what is the sum of the Total Annual Relevant Ordering osts and Total Annual Relevant arrying osts for Super Grow and Nature's Own? (iii) For the EOQ compute the number of deliveries per year for Super Grow and Nature's Own. (A Inter Nov 1999) Solution: Particulars Super Grow Nature's Own (i) A = Annual Requirement O = Ordering ost per order = arrying ost per Bag per annum EOQ = x A x O (ii) Total Annual Ordering & arrying ost at EOQ: Total Relevant ost = x A x O x,000 Bags `1,00 `480 = x,000 Bags x 1,00 `480 = 100 Bags = x,000 Bags x `1,00 x `480 = `48,000 1,80 Bags `1,400 `560 = x 1,80 Bags x 1,400 `560 = 80 Bags. = x 1,80 Bags x `1,400 x `560 = `44,800
(iii) No. of Deliveries i.e.; No. of orders to be placed per year Annual Requirement.,000 Bags = 0 orders p a. 1,80 Bags = 16 orders p.a. Re order Quantity 100 80 Q1: The Annual arrying ost of Material X is `3.6 per unit and its total carrying cost is `9,000 per annum. What would be the Economic Order Quantity for material X, if there is no safety stock of material X? (A P Nov 008) Solution: Annual arrying ost = EOQ + Safety Stock Units x arrying cost per unit `9,000 = EOQ + 0 x `3.60 `9,000 x = EOQ `3.60 EOQ = 5,000 units Q: A wholesaler supplies 30 stuffed dolls each week day to various shops. Dolls are purchased from the manufacturer in lots of 10 each of `100 per lot. Every order incurs a handling charge of `60 plus a freight charge of `50. Multiple and fractional lots also can be ordered and all orders are filed the next day. The incremental cost is `0.60 per year to store a doll in inventory. The wholesaler finances inventory investment by paying its holding company % monthly for borrowed funds. Assume that there are 50 week days in a year. (a) How much dolls should be ordered at a time in order to minimise the Total Inventory ost? (b) How frequently should he order? Solution: A = (50 days x 30 dolls) = 7,500 dolls O = `60 + `50 = `310 = `0.60 + % x 1 months x `10 = `0.60 + 4% x `10 = `0.60 + `.40 = `3.00 (a) EOQ = x A x O = x 7,500 dolls x `310 = 1,45 dolls 3 (b) No. of orders p.a. = Annual Demand = 7,500 dolls = 6 orders EOQ 1,45 dolls Time between orders = 360 days = 60 days or 50 week days = 41.66 week days 6 orders 6 orders Q3: AB Plumbing Supply ompany stocks thousands of plumbing items sold to regional plumbers, contractors, and retailers. Mr. X, the firm's general manager, wonders how much money could be saved annually if EOQ were used instead of the firm's present rules of thumb. He instructs Mr. Y the ost Accountant of the company to conduct an analysis of one material only to examine if significant savings might result from using the EOQ. Mr. Y develops the following estimates from accounting information: Annual Demand = 10,000 units Present Order Quantity = 400 units per order (present order quantity) arrying ost = `4 per unit per year Ordering ost = `55 per order Solution: (a) EOQ = x A x O = x 10,000 units x `55 = 54.4 units `4
Determination of Annual ost Savings Particulars Order 54.4 units Order 400 units Annual Ordering ost 10,000 units x `55 10,000 units x `55 1048.80 1,375 54.4 units 400 units Annual arrying ost 54.4 units x 4 400 units x 4 1048.80 800 Total Annual Relevant ost,097.60,175 Annual ost Savings = `77.40