Optimizing Inventory Decisions in LittleField Technologies Game

Order Quantity Inventory Decisions in LittleField Technologies Ardavan Asef Ardavan Asef- -Vaziri Vaziri

Inventory Decisions in LittleField Technologies EOQ & ROP in LittleField Technologies Game, Ardavan Asef-Vaziri 2

Inventory Decisions in LittleField Technologies In our EOQ (Economic Order Quantity) models, R and D are used interchangeably. D is demand, R is throughput. We assume R=D Everything produced is sold. Assume that the average demand in a LittleField Technology game is 16 contracts per day, and assume it is relatively stable; it is stationary. Assume that you have enough capacity to fulfill the demand. We need 60 kits for each contract at the rate of $10 per kit. While the demand is probabilistic, and moves up and down around the average, in order to be able to use the EOQ model, we need to assume that the demand is deterministic. Therebefore, the kits are used at a steady rate per day and a year is 365 days. The game assumes no storage and no obsolescence cost during the period that we have access to the game. Holding cost is 10% of the purchase price. Ordering cost is $1000 per order. How much should we order each time to minimize our total costs (total ordering and carrying costs)? EOQ & ROP in LittleField Technologies Game, Ardavan Asef-Vaziri 3

Inventory Decisions in in LittleField Technologies D = R = 60(16)(365)= 350400 kits per year or D = R = 16(365)= 5840 contracts per year. H = $10*0.10 = $1 per kit per year, or H = $10*0.10(60) = $60 per contract per year. S = $1000 per order. Ordering Quantity = Q # of orders per year = D/Q = 5840/Q Ordering Cost per year = 1000(5840)/Q Q # of Orders=R/Q 58.4 29.2 19.5 14.6 11.7 9.7 8.3 7.3 6.5 5.8 5.3 4.9 4.5 4.2 3.9 OC D=R Dy/Yr S H EOQ 5840 365 1000 60 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 $58,400 $29,200 $19,467 $14,600 $11,680 $9,733 $8,343 $7,300 $6,489 $5,840 $5,309 $4,867 $4,492 $4,171 $3,893 $70,000 $60,000 $50,000 $40,000 Axis Title $30,000 $20,000 $10,000 $0 0 200 400 600 800 1000 1200 1400 1600 Axis Title EOQ & ROP in LittleField Technologies Game, Ardavan Asef-Vaziri 4

Average Inventory & Carrying Cost At the start of cycle, we have the order size Q units, at the end of the cycle we have 0. Average inventory = (Q+0)/2 = Q/2 units Q/2 is also called cycle inventory. Quantity Time In each cycle we have Q/2 inventory In all cycles we have Q/2 inventory. Throughout the year we have Q/2 inventory. Cost of carrying (holding) one unit of inventory for one year = H $ per unit per year. Total Holding Costs (Total Carrying Costs) = CC = HQ/2 $ per year EOQ & ROP in LittleField Technologies Game, Ardavan Asef-Vaziri 5

Carrying Cost & Ordering Cost Q Carrying Q/2 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 CC $3,000 $6,000 $9,000 $12,000 $15,000 $18,000 $21,000 $24,000 $27,000 $30,000 $33,000 $36,000 $39,000 $42,000 $45,000 D=R Dy/Yr S H EOQ 5840 365 1000 60 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 $50,000 $45,000 $40,000 $35,000 $30,000 $25,000 $20,000 $15,000 $10,000 $5,000 $0 0 200 400 600 800 1000 1200 1400 1600 CC EOQ & ROP in LittleField Technologies Game, Ardavan Asef-Vaziri 6

EOQ: When Carrying Cost Equates Ordering Cost Q # of Orders=R/Q 58.4 29.2 19.5 14.6 11.7 9.7 8.3 7.3 6.5 5.8 5.3 4.9 4.5 4.2 3.9 OC Carrying Q/2 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 CC $3,000 $6,000 $9,000 $12,000 $15,000 $18,000 $21,000 $24,000 $27,000 $30,000 $33,000 $36,000 $39,000 $42,000 $45,000 TC=OC+CC $61,400 $35,200 $28,467 $26,600 $26,680 $27,733 $29,343 $31,300 $33,489 $35,840 $38,309 $40,867 $43,492 $46,171 $48,893 D=R Dy/Yr S H EOQ 5840 365 1000 60 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 $58,400 $29,200 $19,467 $14,600 $11,680 $9,733 $8,343 $7,300 $6,489 $5,840 $5,309 $4,867 $4,492 $4,171 $3,893 $70,000 $60,000 $50,000 OC $40,000 CC $30,000 TC=OC+CC $20,000 $10,000 $0 0 200 400 600 800 1000 1200 1400 1600 EOQ & ROP in LittleField Technologies Game, Ardavan Asef-Vaziri 7

Economic Order Quantity At EOQ (Economic Order Quantity), OC=CC SD/Q = HQ/2 1000(5840)/Q= 60Q/2 Q2= 194667 Q = 441.2 contracts SD/Q = HQ/2 Q2 = 2DS/H 2?? ? 2(5840)(1000) 60 ??? = ??? = = 441.2 That is one way to compute EOQ and not to memorize it. 441.2(60)= 26472 kits is enough for how long? Demand per day = 16 contracts or 16(60)= 960 kits 26472/960 = 27.58 28 days In order to find D, we did 16(365)= 5840, but the game only runs for 50+7(24)+50= 50+168+50 days. It does not matter. If instead of 365 we put 268, then instead of H=60 we should put $60 multiplied by (268/365). To clarify, let us instead of year, do our computations for month. EOQ & ROP in LittleField Technologies Game, Ardavan Asef-Vaziri 8

Economic Order Quantity If yearly demand is 5840, then monthly demand is 5840/12 = 486.6667 Order cost remains $1000 per order. Carrying cost for kits of one contract is $60 per year. Therefore, it is $60/12= $5 per month. Now plug these numbers into the formula 2?? ? 2(486.67)(1000) 5 ??? = = = 441.2 As long as D and H are defined over the same period, year, month, week, day, they all result in the same EOQ. Ordering cost is still S(D/Q), and carrying cost is still H(Q/2). But note that throughout the game, based on the volume of demand, and how you manage the capacity, each time you may use a different value as your yearly or monthly demand (and throughput) estimate changes. Therefore, it is not a bad idea to always forecast for the next 30 days and assume it as D or R and then S=$1000 and H=$5 EOQ & ROP in LittleField Technologies Game, Ardavan Asef-Vaziri 9

ROP - When We have Access to the Game Now suppose the standard deviation of daily demand is 5 (again this will change throughout the game). Furthermore, suppose we are on $1000 contract. What service level should we choose? What is the underage cost (Cu)? If a contract is available but we cannot deliver it, we don t earn $1000. We would have spent $600 on the 60 kits required for each contract. Cu=$1000-$600=$400. However, we do not loose this profit because we earn it in the next cycle. Since each cycle is 28 days and interest rate is 10% for 365 days, therefore, underage cost Cu = 0.1(28/365)(400)= 0.0077($400)=3.08. What is the overage cost (Co)? If we order kits for one extra contract, and we do not use it in this cycle, we use it in the next cycle. But we lose the interest rate that we could have earned on the $600 spent on kits. Therefore, overerage cost Co = 0.1(28/365)(600)= 0.0077($600)=4.62. Since 0.0077 appears in both Co and Cu, for the sake of simplicity, we drop it from both. EOQ & ROP in LittleField Technologies Game, Ardavan Asef-Vaziri 10

Service Level - For the Last Order for the Last 50 Days SL*=3.08/(3.08+4.62) = 0.4 NORM.S.INV(0.4) = -0.253standard deviation of lead time demand to the right. That is -0.253 to the left Standard deviation of the demand during the lead time during the game differs from that of the end of the game. During the game, we have a lead time of 4 days. Therefore, LTD=SQRT(4)*5=10 Is = -0.253 (10)=-2.53 -3 Demand per day R=16 Lead time demand =LTD = L*R=4(16)=64 LTD ~ N(64, 10) ROP=94-3 = 91 = 91 orders ROP = 91 orders x 60 kits / order = 5460 kits. We place an order Q= 26472 kits when inventory reaches ROP=5460 kits. EOQ & ROP in LittleField Technologies Game, Ardavan Asef-Vaziri 11

Service Level - For the Last Order for the Last 50 Days But there is one component of Cu that we did not discussed since it needs a knowledge beyond the mathematical content of our course. What if shortage of kits lead to delay in the delivery of contract. A delay may reduce the revenue of a contract from 1000 to 0. That is a huge increase in Cu. Therefore, throughout the game, but not in the very last 50 days of the game, apply a large service level, say 3 standard deviations to the right- which is about %99.9 service level. Then monitor the inventory level, if you think you carry extra inventory, instead of three standard deviations, you may chose two or even one standard deviation. But the situation is entirely different in the very last 50 days of the game. EOQ & ROP in LittleField Technologies Game, Ardavan Asef-Vaziri 12

Service Level - For the Last Order for the Last 50 Days What is L and what is LTD a few hours before when we will be disabled of making any changes. Suppose it is a little before 11 AM in the last day, and the 218 days of the game ends at 1 PM. The game then runs for 50 more days, but it takes a second for computer to do all the computations. Therefore, at 1:01 PM you can see your final standing. Now it is a little before 11, and therefore, the game has 50+2 days to run. L=52. Demand per day = R=16 Demand in 52 days =LTD = 52R = 832 Standard deviation of daily demand = R=5 Standard deviation of demand for 52 days of demand = LTD= SQRT(52)*5 = 36 LTD=N~(832, $36) What are Cu and Co? EOQ & ROP in LittleField Technologies Game, Ardavan Asef-Vaziri 13

Service Level - For the Last Order for the Last 50 Days If a contract is there but the kits are not, you could have spent $600 and have earned $1000. Cu = $400. If kits for a contract are there but contract is not, you have no use for them, and at the end of the game their value is 0. Cu = $600. SL*=$400/($400+600) = 0.4 NORM.S.INV(0.396739) = -0.253standard deviation of lead time demand to the right. That is -0.253347103 to the left Is = -0.253347103 (36)=-9.21 -9 LTD=N~(832, 36) Q= 832-9 = 823 EOQ & ROP in LittleField Technologies Game, Ardavan Asef-Vaziri 14

Service Level - For the Last Order for the Last 50 Days Should we order the kits required for 823 contracts? Should we order 49380 kits? No. Why We need to check how much inventory we have. Suppose we have 6000 kits which is enough for 100 contracts. Set your new order quantity 49380-6000= 43380 kits, then quickly set your ROP to more than 6000 kits to make sure that you trigger that materials order immediately. EOQ & ROP in LittleField Technologies Game, Ardavan Asef-Vaziri 15