HW04-F08_Key

# HW04-F08_Key - MGMT 46000 HW 04 40 Points(Due November 3...

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HW04 F08_Key.doc 1 MGMT 46000: HW 04 40 Points (Due: November 3, 2008) Question 1: Part A: Solve problem 25 / 253. In part (b), round off ROP value to 2 decimal places. (a) Lot Size [gallons] 1-399 400-799 > 800 C [\$/pulley] 2 1.70 1.62 H [\$/pulley/year] 3 3 3 Q 0 = (2*D*S/H) 300 feasible 300 (infeasible) 300 (infeasible) Lot Size, Q* 300 400 800 Purchase Cost [\$/yr] 2*4500=9000 1.70*4500=7650 1.62*4500 =7290 Ordering cost [\$/yr] 30*4500/300=450 30*4500/400 =337.5 30*4500/800=168.75 Holding Cost [\$/yr] 300/2*3=450 400/2*3=600 800/2*3=1200 Total Annual Costs 9900 8587.50 8658.75 So order quantity is 400 units (b) Service level=98.5% Z SL =2.17. So, μ LT =4500/360*4*3/4=37.5 g. σ LT =2 3 ROP = μ LT + Z 0.985 * σ LT = 37.5 + 2.17* 2 3 45.02 gallons Part B: Solve problem 21 parts “a” and “b” only from page 253. a. Weekly demand ~ N[21, 3.5]. SL = 90%, LT = 2 days =2/7 weeks. Z 0.90 = 1.29 ROP = 21 * 2/7 + 1.29 * ( 2/7) * 3.5 = 8.41 gallons. Average daily demand is 3 gal. This supply ( = ROP ) will last for 8.41 / 3 2.8 days. b. Calculate order size Q for OI = 10 days and SL = 90%. OI = 10 days. IP = 8 gallons. OUL = (OI+LT) * μ + Z SL * { (OI+LT) } * σ = [(10 + 2)/7] * 21 + 1.29 * { (10 + 2) /7)} * 3.5 = 36 + 5.91 42 gallons. Q = OUL – IP = 42 – 8 = 34 gallons. What is the probability of stock-out before this order arrives. This was not covered in the class and will not be graded. However, here is how we could solve this. LT = 2 days. Average demand during LT = 21 * 2/7 = 6. Std. dev = 3.5 * (2/7). What we want to find is Prob (X 8), with mean and std. deviation [6, 3.5 * (2/7)]. The answer will work out to be 0.1423.

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HW04-F08_Key - MGMT 46000 HW 04 40 Points(Due November 3...

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