Question

T YSON Data Table for Problems 14.17 through 14.19* Period 1 2 3 4 5 6 7 8 9 10 11 12 Gross requirements 30 40 30 70 20 10 80 50 "Holding cost = $2.50/unit week; setup cost = $150; lead ume = 1 week; beginning inventory = 40. mem • 14,17 Develop a lot-for-lot solution and calculate total rele- vant costs for the data in the preceding table, PX . 14.18 Develop an EOQ solution and calculate total relevant costs for the data in the preceding table. Stockout costs equal $10 per unit. Px

Answer 1

Answer:

14.17

B C E I L M 2 4 8 11 4 5 Period 1 2 Gross requirements 30 3 Beginning inventory 40 4 Ending inventory =83-B2 5 Net requirements 6 Order receipts Order releases D 3 0 4 -03+06-D2 =02-03 30 = 84 =C3-C2 12 0 L4 =D4 =E3+E6-E2 F 5 30 =E4 =F3+F6-F2 =F2- F3 30 170 G 6 70 =F4 =G3+G6-G2 G 2-G3 70 20 H 7 20 =G4 =H3-H6-H2 =H2-H3 20 H4 =13+16-12 J 9 10 =14 =13+16-12 -12-13 10 BO K 10 80 =14 =K3+K6-K2 =K2-K3 80 =K4 L.3+L6-L2 =L2-L3 =M2-M3 SO 30 30 10 50 8 9 Holding cost Setip cost -2.5*(83-84)/2) -2.5*(C3-C4)/2) =2.5°(D3-D4/2) =2.5°(E3-E4/2) =2.5*((F3+F4)/2) -2.5||G3+G4/2) =2.5*((H3+H4)/2) =2.5*(13-14)/2) =2.5903-14/2) =2.5*((K3+4)/2) =2.5*((L3-L4)/2) =2.5*((M3-M4)/ FIF[B7>0,150,0) FIF(C7>0.150,0) FIF(D7>0,150,0) FIF[E7>0,150,0) FIF(F7>0,150,0) FIF[G7>0,150,0) FIF(H7>0,150,0) FIF(17>0,150,0) FIF07>0,150,0) FIF(K7>0,150,0) - FL7>0,150,0) FIF/M7>0,150,0) Total cost ESUM(B9:M10)

C E F к - 2 D 3 40 4 5 G 6 70 00 10 | В 1 30 40 10 11 ДА 1 Period 2 Gross requirements 3 Beginning inventory 4 Ending inventory 5 Net requirements 6 Order receipts 7 Order releases 0 H 7 20 0 0 20 20 10 10 0 0 10 0 0 10 0 0 70 80 0 0 80 80 50 0 0 50 50 0 30 30 70 0 30 30 70 10 30 30 20 10 80 50 12.5 0 0 0 Holding cost Setip cost 62.5 0 25 1500 0 150 0 150 0 1500 0 150 0 1500 0 1500 9 10 11 12 Total cost 1150

14.18

5013-14-18P AID: 1825 17/08/2013 It is given that the stock out cost is $10 per unit, holding cost is $2.50 per unit or week, set up cost is $ 150, lead time is 1 week, and beginning inventory is 40 Wallets Period 1 2 3 4 5 6 7 8 9 10 11 12 Gross requirements 30 40 30 70 20 10 80 10 1 1020 10 80 501 Now, calculate the demand for the economic order quantity Demand = Sum of gross requirement = 30+40+30+70+ 20+10+80+50 ...... (1) = 330 The demand for the economic order quantity is 330 units The information given that the demand is 330, number of periods is 12, set up cost is $150, and holding cost is $2.50 per unit Now, calculate the economic order quantity:

QH Q=2DS Where D Demand S Set up or ordercost H Holding cost 2DS Economic order quantity=Q=; VH 2x330x150 V 2.50x12 ...... (2) 99,000 V 30 = 57.44 or 57 units The economic order quantity for the given information is 57 units. . It is given that demand is 330 units, lead time is 1 week, and number of periods is 12. Now, calculate the reorder point: Demand Reorder point = Number of periods * Lead time 330 .....(3) = xlweek 12 = 27.5 or 28units

The reorder point of the demand is 28 units. It is given the beginning inventory is 40 and the economic order quantity, that is, number of orders is 57. Now, explain the terms in material requirement planning: • Planned order release: Given the order release is for every alternate week and it is released in the 2, 4, 6, 8, 11, and 12 periods. • Planned order receipts The receipt for the released order will be given in the next period of releases. In this economic order quantity [from Equation (2)], 57 is constant. • The project on hand or beginning inventory: Addition of planned order receipt in the present period and ending inventory in the previous period. The given beginning inventory is 40 • Ending inventory Subtraction of beginning inventory and gross requirement.

Now calculate the lot to lot size method using economic order quantity Periods 2 3 4 5 6 7 8 9 10 11 12 Gross requirements 30 40 30 | 20 | 1080 Beginning inventory 400 67 278454 -16|2178|68 -12-12 Ending inventory 10|10|27|27|54|16|21|21|68|–12 –12| -5 Planned order receipts Planned order release Note: If gross requirement is greater than the beginning inventory, then the ending inventory will have negative values. In this case, these negative values are termed as stock out values. Now, calculate stock out cost and total inventory cost:

Stock out cost: The cost in the ending inventory is where the negative variables occur, i.e., with negative sign (-). Need to add the all stock out cost to obtain the actual cost Stock out cost = 16+12+5 .....(4) = 33 Total inventory: The sum of all the ending inventory excluding stock out costs; these sums are the total units used in the material requirement scheduling. sum of all ending inventories Total inventory = (excluding the stock out cost ...... (5) = 10+10+27 +27 +54 +21+21+68 = 238 It is given that the total inventory is 238 [from Equation (3)], stock at cost is 33 [from Equation (2)], 6 orders with order cost of $ 150 per order, holding cost is $2.50, and $10 per stock out in its cost. Now, calculate the actual total cost:

Cost = Order cost + Holding cost+stock out cost (6 orders $150 per order +238 units x $2.50+33 units $10 perunit or stock) ...... (6) = 900+595 +333 = $1,825.00 It is given that the demand is 330 [from Equation (1)], the economic order quantity is 57 [from the Equation (2)], set up cost is $150, holding cost is $2.50, and the number of periods is 12. Now, calculate the theoretical total cost: Theoreticalcost = Order cost + holding cost DS QH q* 2 Where D Demand S set up cost Q→ Economic order quantity H Holding cost _DS QH O2 330x150 57(12x2.50) ..() 572 = 862.42 +855.00

Hence, the actual cost of the economic order quantity is $1,825.00 [from Equation (6)] is more than the theoretical cost of $1,721.42 [from Equation (7)] that shows the poor performance. Note: Since backorder is used because of stock out, the company results in poor performance and to eradicate the poor performance use double size method. It is given [from the Equation (2)] that the economic order quantity is 57 and the beginning inventory is 40. Now, explain the terms in material requirement planning: • Planned order release The given order release is for every alternate week and it is released in 2, 4, 5, 9 and 11 periods. The period 8 has not been used because of no gross requirement and the order is doubled for the 10th period • Planned order receipts: The receipt for the released order will be given in the next period of releases. In this economic order quantity [from Equation (2)], 57 is constant. • The project at hand or beginning inventory The beginning inventory is 40. Subtraction of planned order receipt in the present period and net requirement in the present period gives the project on hand for the next period

• Ending inventory or net requirements: Subtraction of gross requirement and project on hand. Now, calculate the double size method for appropriate results Periods Initial values 1 2 3 4 5 6 7 8 9 10 11 12 Gross requirements 40 30 70 20 10 80 Project on Hand 40 40 10 10 27 27 54 41 21 21 11 45 45 52 Net requirements 3 1600 Tot Planned order receipt Planned order release 57 57 57

Note: If the gross requirement is less than project on hand, the net requirement is quoted "0" and the difference is carry forwarded to the project on hand of the next period Now, calculate the total number of units involved in the double size of the economic order quantity sum of all project on hand Total units = (excluding begining inventory) (10+10+27+27 +54 +41+21+21) ...... (8) +11+45 +45+52 = 364 The total units in the project on hand are 364 It is calculated that total units are 364 [from Equation (8) and given information holding cost is $2.50 per order, set up cost is $150 per order, and the planned order receipts used is 5. Now, calculate the total set up cost and total holding cost: Total set up cost * = Number of orders x Set up cost per order of all orders ...... (9) = 5x150 = $750

Total holding } = Holding Cost Number of Units cost of units = 2.50x364 = $910 ...... (10) It is given the total setup cost is $750 [from Equation (9)] and total holding cost of units is $910 [from Equation (10)] Now, calculate the total cost of the economic order quantity for double size; Total cost = Total set up cost of orders + Total holding cost of the units = $750+$910 = $1,660.00 Hence, the total ordering cost of the economic order quantity is $1,666.00 -