Sql Education Tool

Chapter 4 Part 1 Exercises

Exercise 1) EOQ with limited Production Capacity

Cost under EOQ model ;

h’ = h(1-λ’/P’) = 2.4*(1-5000/10000) = 1.2

Q* =  =  = 86,603[pic 1][pic 2]

G(Q*) =  =  = 103,923[pic 3][pic 4]

T1 = Q*/P’ = 86,603/10,000 = 8.66 days

T2 = T-T1 = Q*/ λ’ – T1 =(86,603/5,000)- 8.66 = 8.66 days

H = T1 * (P’- λ’) = 8.66 * 5000 = 43,300

Cost 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 SKUs

Independent:

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 = $339,843

If we switch to Mixed SKUs :

K0 = K + K1 + K2 = 3900

N =   =  = √ 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 Shortage

Cost 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 = 50433

Planned Shortage method leads to a $ 16649 or approx 25% reduction in overall cost

Exercise 4) Discounts

For c1=5

Q1*=  =  = 1565[pic 21][pic 22]

Closest order quantity within the c=5 range is 999

G1=  =  + 5*49000= 2,452+999+245000= 248,451[pic 23][pic 24]

For c2=4.95

Q2*=  =  = 1573 (within range)[pic 25][pic 26]

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