EXTRA PROBLEMS WITH SOLUTIONS Example 10: The ABC Co. is planning to stock a new product. The Co.Has developed the following information: Annual usage = 5400 units Cost of the product = 365 MU/unit Ordering cost = 55 MU/order Carrying cost = 28% /year of inventory value held. a Determine the optimal number of units per order b. Find the optimal number of orders/year c. Find the annual total inventory cost Solution: a. X0 = √2CB/zp = √2*5400*55/365*0.28 = ~76 units/order b. N0 = C/X0 =5400 / 76 = ~71 orders/year c. Ke= √2CBzp = √2*5400*55*365*0.28 = 7791.46 MU/year. Example 11: Holding costs are 35 MU/unit/year. The ordering cost is 120 MU/order and sales are relatively constant at 400 month. a. What is the optimal order quantity? b. What is the annual total inventory cost? Solution: a. X0 = √2CB/E= √2*(400*12)*120/35 = 181.42 units/order b. Ke= √2CBE= √2*(400*12)*120*35 = 6349.80 MU/year This cost includes wages. t0 = X0/C * 365 = 16 /200 *365 = 29. N0 *B = 12. Ke= √2CBZp = √2*200*10*0. Show and verify that the annual holding cost is equal to the annual ordering cost (due to rounding.18*87 = 15.5 % per month (or 18% per year) to hold items in stock.01 MU.18*87 = 125. X0 = √2CB/Zp = √2*200*10 /0. and it costs him about 1.28 MU/year e. she estimates that the cost of carrying are screw in inventory for a year is one-half of 0. has decided to determine by use of the EOQ model the best quantity to obtain in each order. . estimates that it costs 10 MU every time when an order is placed. Farmerson has determined from past invoices that he has sold about 200 chair during each of the past five years at a fairly uniform rate and he expects to continue at that rate.Example 12: Azim furniture company handles several lines of furniture. How many layback chairs should be ordered each time? b. the cost of the forms used in placing the order and so on. a. show these costs are approximately equal) Solution: a.18*87 = 250. How many orders would there be? c. one of which is the popular Layback Model TT chair. Leyla. He has estimated that preparation of an order and other variable costs associated with each order are about 10 MU. Farmerson. Assume that the demand is constant throughout the year.5 orders/year c.5 * 10 = 125 MU X0/2*Zp = 15. His cost for the chair is 87 MU. The manager.2 days d.98/2 * 0.98 =~16 chairs/order b. Leyla Tas has determined that the annual demand for #6 screws is 100000 screws. Calculate the minimum total inventory cost e. N0 = C/X0 =200 /16= 12. Furthermore. Determine the approximate lenght of a supply order in days? d.1 MU Example 13: A. Mr. Mr. It takes approximately 8 working days for an order of #6 screws to arrive once the order has been placed. how much more would this cost every year over the ordering policy that she developed. The demand is fairly constant.005 = 20 + 125 = 145 5 times a year = Ke= √2CBE = √2*100000*10*0. and on the average the store sells 500 screws each day. C. He believes that an order should be placed only twice/year. N0 = C/X0 = 100000/20000= 5 orders/year Total ordering cost = N*B = 5*10 = 50 MU/year c.01/2 = 0. How many #6 screws should Leyla order at a time to minimize total inventory cost? b. How many orders per year would be placed? What would the annual ordering cost be? c.005 = 50 MU/year B. if only two orders were placed each year. .a. Average inventory = x/2 = 20000/2 = 10000 units Total holding cost = x/2*E= 10000 * 0. The manager believes that Leyla places too many orders for screws /year.005 = 20000 screws/order b.005 = 100 MU Extra cost for manager’s offer = 45 MU No effect on ROP. If Leyla follows her manager`s policy. what effect would this have on the ROP? Solution: Twice a year = Ke= NB + X/2*E = 2*10 + 50000/2*0.005 X0 = √2CB/E X0 = √2*100000*10 / 0. What would the average inventory be? What would the annual holding cost be? Solution: a. What is the ROP? Solution: ROP = Ro= use rate * lead time = c*tlt = 500 screws/day * 8 days = 4 000 screws. E= 0. 18) 2( 30 ) = 25. What are the optimal MU per order? Solution: X0 = 2CpB = Z 2( 28 000 )( 48) = 3418. How many months’ supply should the purchasing department order at on time to minimize total annual cost of inventory? Solution: t 0 = 12 2B = 12 CpZ 2( 45) = 0. Ayşe has estimated order costs to be 48 MU per order.23 Example 16: EMU uses 96 000 MU annually of a particular reagent in the chemistry department of the EMU estimates the ordering cost at 45 MU and thinks that the university can hold this type of inventory at an annual storage cost of 22% of the purchase price.22) .69orders/year Example 15: Ayşe Çalışkan.annual demand for the computers is 28 000 MU and carrying cost is 23 percent. It cost Ahmet 30 MU to place an order and his carrying cost is 18%.owner of Computer Village.784 month' ssupply ( 96 000)( 0. How many orders per year should Ahmet place for the balls? Solution: N0 = CpZ = 2B ( 220 000 )( 0.62 mu/order 0.Example 14: Ahmet Uslu experiences an annual demand of 220 000 MU for pro quality tennis balls at the İzmir Tennis Supply Company. needs to determine an optimal ordering policy for Porto-Pro computers. Minimization of inventory cost is her objective. from the files of the credit firm. The owner believes the assumptions of the EOQ model are met reasonably well. a) How many should she order at one time? b) How many times per year will she replenish its inventory of this material? c) What will be the total inventory costs associated with this material? .is planning to stock new product. Relevant data.46mu/year Example 18: A local artisan uses supplies purchased from an overseas supplier.has developed the following information: Annual usage = 5400 units Cost of the product = 365 MU/unit Ordering cost = 55 MU/order Carrying cost = 28%/year of inventory value held a) Determine the optimal number of units per order? b) Find the optimal number of orders/year? c) Find the annual total inventory cost? Solution: a) X 0 = 2CB = Zp 2( 5400 )( 55) ≅ 76 units/order 365( 0. are annual demand (C) = 240 units. The ABC co.Example 17: The ABC co.28) b) N o = C 5400 = ≅ 71 orders/year X0 76 c) K e = 2CBZp = 2( 5 400 )( 55)( 365)( 0. and holding cost = 4 MU/unit/year.28) = 60 706 800 = 7 791. ordering cost (B) = 42 MU/order. d) If she discovered that the carrying cost has been overstated.38 Times/year X0 71 K e = 2CBE = 2( 240)( 42 )(1) = 142 MU/yr.06 c) N 0 = .97 MU/year d) X 0 = 2CB = E 2( 240 )( 42 ) = 141. Assume 52 weeks/year.58 kgs/order E 2 b) K e = 2CBE = 2( 3)( 7 )( 2) = 9. a) How many kgs should Ground to order at a time? b) What is total annual inventory cost? c) How many orders should ground place annually? d) How many days will there be between orders(assume 310 operating days)? Solution: 2CB 2( 3)( 7 ) = = 4.1 ≅ 9 days d) t = × 310 = N 34. Example 19: Ground Coffee shop uses 3 kgs of a specialty tea weekly.165 MU/week a) X 0 = K e = 9.99 ≅ 142 Units 1 C 240 = = 3. what is the corrected value of EOQ? Solution: C = 240 units/year B = 42 MU/order E = 4MU/unit/year a) X o = b) N 0 = 2CB = E 2( 240)( 42) = 70.59 MU/year C 3 × 52 = = 34. each kg.99 = 71 Units/order 4 c) K e 2CBE = 2( 240 )( 42)( 4 ) = 283.06 Times/year X0 4. costs 16 MU. Assume the basic EOQ model with no shortages applies.165 ×52 = 476. Carrying costs are 2 MU/kg/week because space is very scarce. It costs the firm 7 MU to prepare an order. and was in reality only 1 MU/unit-year.58 1 1 × 310 = 9. Solution: . and the average carrying cost per unit per year is 0.20 yr = 73days C 1000 X0 = Example 22: Lemar Supermarket sells about 200 000 kilos of milk annually. Holding costs are 1.50 C X 1 000 200 Ke = ⋅B + E= ⋅10 + ⋅ 0. The milk is purchased for 4 MU/kg. The annual demand is 1 000 units.80 MU/year Example 21: ABC. Calculate EOQ . Each order costs 35 MU. would like to reduce its inventory cost by determining the optimal number of pump housings to obtain per order. the ordering cost is 10 MU/order.42 Units/order 35 K e = 2CBE = 2( 400 ×12 )(120 )( 35) = 6 349.(i. a) What is the optimal order quantity? b) What is the annual total inventory cost? Solution: X0 = 2CB = E 2( 400 ×12 )(120 ) = 181.40 MU/kg/yr.the optimal number of units per order). If the shelf life of the milk is only 5 days. The ordering cost is 120 MU/order.5 = 100MU X 2 200 2 C 1000 N0 = = = 5times / yr Q 200 Q 200 T = = = 0. a company that sells pump housings to other manufacturers.Example 20: Holding costs are 35 MU/unit/year.50 MU. Solution: 2(1 000 )(10 ) 2CB = = 40 000 = 200units E 0. and sales are reletively constant at 400/month.e. how many kilos should be ordered at a time. 454 MU X 2 91.77 days. why not a order convenient 100 tonnes? Solution: a) EOQ for cement = 2CB = Zp 2( 25)( 2 000 ) = 91.287 ( 0. .454 MU or we can calculate K e by Ke = C X 2000 ⋅ B + ⋅ Zp = ( 25) + 91. K e = 2CBZp = 2( 25)( 2000 )( 0. 365 Example 23: A building materials stockist obtains its cement from a single supplier.73 kilos should be ordered every 5 days. Last year the company sold 2 000 tonnes of cement. a) How much cement should the company order at a time? b) Instead of ordering EOQ.40 X 3 162.287 tonnes 0. But the shelf life is 5 days so some milk will start to go sour.28 t 0 = 0 × 365 = × 365 = 5.2 )( 60 ) = 1095. It estimates the costs of placing an order at around 25 MU each time an order is placed and charges inventory holding at 20% of purchase cost.287 2 Total cost of ordering plan for X 0 = 100 tonnes.C = 200 000kg/yr P = 4 MU/kg E = 1.77 days C 200 000 With an EOQ of 3 162.28 kilos an order must be placed every 5.2)( 60) = 1095.28 kilos E 1.2( 60 ) b) Total cost of ordering plan for X 0 = 91.287 tonnes. Demand for cement is reasonably constant throughout the year.40 MU/kg/yr B = 35 MU/order Shelf Life = 5 days EOQ = 2CB 2( 200 000 ×35) = = 3 162. The company purchases cement at 60 MU per tonne. Therefore 200 000 ⋅ ( 5) = 2 739. 25( 0. The purchase cost of each item is 6 MU and the holding cost for this item is estimated to be 20% of the stock value per annum.02 ) = 0.02 MU each and sell for 0.15 MU each. Determine the optimal number of pencils for the bookstore to purchase and the time between placement of orders.005 = 9.675 MU 2 2 C 3 120 Average Ordering Cost = ⋅ B = ×12 = 9.24 yr. It costs the bookstore 12 MU to initiate an order and holding costs are based on an annual interet rate of 25%.55 MU. The production/operations manager therefore should feel confident in using the more convenient order quantity.2)( 60) = 1100 MU 100 2 Result: The extra cost of ordering 100 tonnes at a time is 1 100 MU-1095. C 3 120 X 3 870 Average Holding Cost = ⋅ E = ⋅ 0. Every order placed by the wholesaler cost 10 MU in administration charges regardless of the number ordered? Solution: C = annual demand = 50x12 = 600 items p = price unit = 6 MU .675 MU X 3 870 X0 = E = 0.454 MU= 4.005 MU/unit/yr Example 25: A wholesaler has a steady demand for 50 items of a given product each month. Example 24: # 2 pencils at the EMU bookstore are sold at a fairly steady rate of 60 per week. What are the holding and setup costs for this item? Solution: C = 60 × 52 = 3 210 Units Zp = E 2CB 2( 3120 )(12 ) = = 3 780 Units E 0.Ke = 2 000 100 ⋅ 25 + ( 0.005 X 3 870 T = = = 1. The pencil cost the bookstore 0. The manager found that the demand is constant and 2 000 cases/week.” and “when to order” decisions for Segio Beer that will result in the lowest possible cost.The cost of holding for the TT beer inventory is 25% of the value of the inventory. (Note that definding the holding cost as a % of the value of the product is convenient. the # 1 selling TT beer.8 ≅ 693items 2 / 100 An order size of 693 items is recommended Example 27: TT Beverage Co. averages approximately 50 000 cases.20x6 X0 = 2CB = Zp 2 ×10 ×600 =100items 0. TT supplies nearly 1000 retail stores with beverage products. wine and soft drinks product. The purpose of the study is to establish the “how-much to order. P =Purchase price = 3 MU/unit E = Holding cost = 2 MU/100 items/week B = Order cost =12 MU/order X0 =? C 600 = = 6times / year X 0 100 Solution: X0 = 2CB = E 2( 400)(12 ) = 692. is a distributor of beer.2 ×6 An order size of 100 is used at an order frequency of N 0 = Example 26: C = Demand/week = 400 unit. With an average cost per case of approximately 8MU. which constitutes about 40% of the company’s total inventory. TT estimates the value of its beer inventory to be 400 000 MU. TRNC. because it is easily transferable to other products) . From a main warehouse located in Magusa. The warehouse manager has decided to do a detailed study of inventory costs associated with Sergio Beer.B = order cost = 10 MU E = holding cost of one item per year = Zp= 0. The beer inventory. c) How frequently theorder will be placed? d) Find the cycle time? e) Calculate minimum total inventory cost. Solution: a) Find EOQ X0 = 2CB = Zp 2( 2000 × 52 )( 32 ) = 1824cases 0. and the manufacturer of Sergio Beer guarantees 2-day delivery on any order placed.6 working days. K e = 2CBEZp = 2(104000 )( 32 )( 0. b) Find the reorder point R0 = c ⋅ t Lt c= 2000 = 400 5 R0 = 400units × 2days = 800cases c) How frequently the order will be placed? N= C 104000 = = 57order / year X 1824 d) Find the cycle time.25 )( 8) K e = 13312000 ≅ 3648MU 1824 Total order cost ( 57 × 32) 1824 Total holding cost ( 1824 ⋅ 2 ≅ 1824) 2 .6days N 57 The cycle time is 4. b) Find reorder point.TT is paying 32 MU/order regardless of the quantity requested in the order. Suppose TT is open 5 days each week.25 × 8 The use of an order quantity of 1824 cases will yield the minimum-cost inventory policy for TT beer. a) Find Economic Order Quantity. e) Calculate minimum total inventory cost. T = 1 1 = × 260 = 4.