Pareto analysis-simplified J.Skorkovský, KPH What is it ? •tool to specify priorities •which job have to be done earlier than the others •which rejects must be solved firstly •which product gives us the biggest revenues •80|20 rule How to construct Lorenz Curve and Pareto chart •list of causes (type of rejects) in % •table where the most frequent cause is always on the left side of the graph • • Reject Type Importance Importance (%) Accumulative (%) 1 Bad size 10 71% 71 %=71% 2 Bad material 3 21 % 92%=71%+21% 3 Rust 1 8% 100 %=92%+8% Pareto chart Lorenz curve High priorities Use of PA in Inventory Management Statements I. •ABC analysis divides an inventory into three categories : –"A items" with very tight control and accurate records –"B items" with less tightly controlled and good records –"C items" with the simplest controls possible and minimal records. Statements II. •The ABC analysis suggests, that inventories of an organization are not of equal value •The inventory is grouped into three categories (A, B, and C) in order of their estimated importance. Example of possible allocation into categories •A’ items – 20% of the items accounts for 70% of the annual consumption value of the items. •‘B’ items - 30% of the items accounts for 25% of the annual consumption value of the items. •‘C’ items - 50% of the items accounts for 5% of the annual consumption value of the items • Beware that 20+30+50=100 and 70+25+5=100 !! Example of possible categories allocation-graphical representation (4051 items in the stock) ABC Distribution ABC class Number of items Total amount required A 10％ 70％ B 20％ 20％ C 70％ 10％ Total 100％ 100％ Minor difference from distribution mentioned before !! Objective of ABC analysis •Rationalization of ordering policies –Equal treatment – OR –Preferential treatment See next slide Equal treatment Item code Annual consumption (value) Number of orders Value per order Average inventory 1 60000 4 15000 7500 2 4000 4 1000 500 3 1000 4 250 125 TOTAL INVENTORY (EQT) 8125 1. Value per order= Annual consumption/Numer of orders 2. Average inventory = Value per order/2 see next slide which is taken from EOQ simplified presentation Carrying cost (will be presented next slide) 13 •Resource- Taylor- Wikipedia To verify this relationship, we can specify any number of points values of Q over the entire time period, t , and divide by the number of points. For example, if Q = 5,000, the six points designated from 5,000 to 0, as shown in shown figure, are summed and divided by 6: Preferential treatment Item code Annual consumption (value) Number of orders Value per order Average inventory 1 60000 8 7500 3750 2 4000 3 1333 666 3 1000 1 1000 500 TOTAL INVENTORY (PT) = 4916 TOTAL INVENTORY (EQT)= 8125 Determination of the Reorder Point (ROP) •ROP=expected demand during lead time + safety stock 20 50=ROP 50-20=30 Determination of the Reorder Point (ROP) (home study) •ROP = expected demand during lead time + z* σdLT • where z = number of standard deviations and • σdLT = the standard deviation of lead time demand and z* σdLT =Safety Stock • aan Example (home study) •The manager of a construction supply house determined knows that demand for sand during lead time averages is 50 tons. •The manager knows, that demand during lead time could be described by a normal distribution that has a mean of 50 tons and a standard deviation of 5 tons •The manager is willing to accept a stock out risk of no more than 3 percent Example-data (home study) •Expected lead time averages = 50 tons. •σdLT = 5 tons •Risk = 3 % max •Questions : • –What value of z (number of standard deviation)is appropriate? –How much safety stock should be held? –What reorder point should be used? – Example-solution (home study) •Service level =1,00-0,03 (risk) =0,97 and from probability tables you will get z= +1,88 – – See next slide with probability table Probability table Example-solution (home study) •Service level =1,00-0,03 =0,97 and from probability tables we have got : z= +1,88 •Safety stock = z * σdLT = 1,88 * 5 =9,40 tons •ROP = expected lead time demand + safety stock = 50 + 9.40 = 59.40 tons •For z=1 service level =84,13 % •For z=2 service level= 97,72 % •For z=3 service level = 99,87% (see six sigma) – ABC and VED and service levels A items should have low level of service level (0,8 or so ) B items should have low level of service level (0,95 or so) C items should have low level of service level (0,95 to 0,98 or so) D items should have low level of service level (0,8 or so ) E items should have low level of service level (0,95 or so) V items should have low level of service level (0,95 to 0,98 or so) Matrix Resource : https://www.youtube.com/watch?v=tO5MmOBdkxk Prof. Arun Kanda (IIT), 2003