Question

Consider the following information about an end-product item:

Ordering cost =$45/order

Average usage =12 units/week

Inventory carrying cost =$1/unit/week

(a) How many orders should we place per year (52 weeks) to replenish inventory of the item based on average weekly demand?

(b) Given the following time-phased net requirements from an MRP record for this item, determine the sequence of planned orders using economic order quantity (EOQ) and periodic order quantity (POQ) procedures. Assume lead time equals zero and current on-hand inventory equals zero. Calculate the inventory carrying cost on the basis of weekly ending inventory values. Which procedure produces the lowest total cost for the eight-week period?

	Week
	1	2	3	4	5	6	7	8
Requirements	15	2	10	12	6	0	14	9

Answer 1

STEP 1: The material Requirement planning (MRP) estimates the amount of material and components required to manufacture a Product by converting the master Production schedule into a time. Phased Schedule. From the time. Phased schedules, the sequence of planned order is determined using Procedures such as economic order quantity and Periodic order quantity. STEP 2: Consider the following information to determine the number of orders per year to replenish the inventory based on average weekly demand: Ordering cost = $45 / order Average usage = $12 units/week Inventory carrying cost = $1/unit/week Number of weeks Per year = 52. following formula: STEP 3: (a) Calculate the economic lot size using the Economic lot size (2000 - ean. The ordering cost is cp The average usage is D. The inventory carrying cost is (n. Economic bot size - 2X45X12 11080 = 32.363 = 33 units

year to replenish Calculate the number of orders per the inventory using following formula Number ol Orders peut year. Average usage * humber of weet Year Economic lot size en Number of onders per year 12852 33 = 624 33 = 19 orders Therefore, the number of orders per year to replenish the - inventory are [19 Orders " STEP 4 (6) Consider the following time-phased net requirements to determine the sequence of planned ouders using economic Order quantity and Periodic order quantity Procedures: Week 14 Requirements 15/2 110 112 610 Lead time to Ton-hand Inverstory o Table 1: Time phased net requirements STEP 5:- The order quantity required to produce for each week! is the economic lot Sze hat is 33 units. The ending inventory is calculated using the following tomula! Ending inventory Beginning Inventory - Requirement of a week! The ending inventory of a week is considered to be the beginning inventory of next week

'If the ending inventory of Preceding weer exceeds the requirement of a week, then the Order quantity needs to be placed in that particular week. STEP 6 : The Ordering cost is calculated by considering the number of onders placed in all the weeks. Calculate the Ordering cost using the following formula: Total ordering cost - Ordening cast Per order & number of ouders calculate the inventory carrying and cost considering the a ending inventory of each weet using the following formula: Total inventory carrying coste Sum of ending inventory O Inventory carrying cost Calculate the total cost of the eight-week period using the following formula: I Total cost = Total ordering cost & Total carrying costo Determine the sequence of planned economic order quantity using the above in a Spreadsheet as shown below: orders using formulae Cie, 3, 4,5,6). 6 7 8 12 33 DO Week 4 13 Requirements 15 TO 14. Onder quantity 33 Beginning Inventory 34 - 141 DG Ending Inventory FB5-B3/65-03 =D5 D3 15-13 Total ordering 45 dira 9-37*C7 Cost Is Total Inventory SUMCBGD-BS* (8. Carrying cost Total cost SUM(P7:16) =16 5 83 56 56 14 16 95-63H5.43 -15 13. Onders using Table 2: Formulae economic for sequence of Planned Onder quantity

23 33 BEDE Ele le - Week T I 2 3 4 5 6 7 8 3 Requirements 15 2 110 112 60 149 4 Order quantity 5 Beginning Inventory 16 6 Ending Inventory I 18 6 6 27 21 21 7 311 7 Total ordering cost $45 I 3 $135 8 Total Inventory careying ost $1 | 147 $1.47 a Total cost $282 33 18 Table 3: Sequene of Planned Order quantity orders using economic :. The total cost Onder for the eight-weet Period using economic quantity is $282

STEP 7 Periodic order Calculate the time between orders in quantity using the following formula - © Time between Ordens - Economic lot sizge Average usage where, The economic lot size is 33 units The average wage is units /week. - Time between orders 33 12- = 2.75 & The Time between orders is 3 weeks) The orders are placed meeting the exact requirements for a three weet interval Cakulate the sequence of planned Orders using Periodic Order quantity in a spreadsheet as shown below! Week 1 2 3 4 5 6 7 8 3 Requirements 15 12 10 12 16 10 14 19 a order quantity -B3103103 #3473163 = 43413 s Beginning inverstory =B4 =B6 =CG LE4+D6 E6 =FG = H4+G646 6 Ending inventory = BS+B3-05-03 =D5 D3 = 45.63 = FS-F3 -6563 = 45-413 / 1513 7 Total Ondering cost 45 3 =B7(71 8 Total Inventory carryingust I SUM(B61) - BBY C8 ! 9 Hotal cost surilor De Table 4. Formulae Periodic for sequence of planned Onder quantity Orders using

STEP 8: To Week G 6 15 27 ~ 12 10 8 6 3 Requirements 4 Order quantity 127 Beginning Inventory 6 Ending Inventory 7 Total ordering cost 45 8 Total Inventory carrying cost | 9 Total cost 13 1135 132 / 2 - 172 Periodic Table 5. Sequence of planned Orders using Order quantity. total cost for the eight-weet Period using Order quantity is $172/ Periodic 2 . The STEP 9 The economic order quantity Procedure Produces with the total cost of $282 and the Periodic oder quantity Produces with the total cost of $172 Hence, the Periodic order quantity Procedure Produces with the - bwest total cost for the eight-weet Period.