Essay About G1 And G2

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Chapter 4 Part 1 ExercisesExercise 1) EOQ with limited Production CapacityCost under EOQ model ; h’ = h(1-λ’/P’) = 2.4*(1-5000/10000) = 1.2Q* =  =  = 86,603[pic 1][pic 2]G(Q*) =  =  = 103,923[pic 3][pic 4]T1 = Q*/P’ = 86,603/10,000 = 8.66 daysT2 = T-T1 = Q*/ λ’ – T1 =(86,603/5,000)- 8.66 = 8.66 daysH = T1 * (P’- λ’) = 8.66 * 5000 = 43,300Cost under Q=20,000  : G(Q) =  =  = 225,000+12,000 = 237,000[pic 5][pic 6]We are saving approx 133,000 or 56% by using the adapted EOQ model Exercise 2) Mixed SKUsIndependent: k = 2000,  λ1 = 50,000, k1 = 800, h1 = 100       G1*= [pic 7]λ2 = 32,000, k2 = 1100, h2 = 150       G2*= [pic 8]If Independent, Total Cost G = G1 + G2 = $339,843If we switch to Mixed SKUs :K0 = K + K1 + K2 = 3900N =   =  = √ 1256.4 = 35.45[pic 9][pic 10]Q1*=1410.4[pic 11]Q2*=902.7[pic 12]G*MIX = K0.n+ h1.Q1/2 + h1.Q2/2        = 138255 + 70522 + 67701 = 276,478 Δ  = (G1* + G2*) – G*MIX = $63365 or 18.65%Exercise 3) Planned ShortageCost under EOQ model ; G(Q*) =  =  = 67,082[pic 13][pic 14]Cost under Planned Shortage : G(Q, θ) = [pic 15]Q* =  *  =  *  = 1785[pic 16][pic 17][pic 18][pic 19] = 50*1785 / 50+65 = 776[pic 20]G(Q,θ) = 50 *(1785-776)2/2*1785 + 65*7762/2*1785 + 3000*15000/1785= 14259+10964 + 25210 = 50433Planned Shortage method leads to a $ 16649 or approx 25% reduction in overall cost Exercise 4) DiscountsFor c1=5Q1*=  =  = 1565[pic 21][pic 22]Closest order quantity within the c=5 range is 999G1=  =  + 5*49000= 2,452+999+245000= 248,451[pic 23][pic 24]For c2=4.95Q2*=  =  = 1573 (within range)[pic 25][pic 26]