Question 2 (30 points) As the owner of IMSE MSDA Productions. You plan to sell y

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Question 2 (30 points) As the owner of IMSE MSDA Productions. You plan to sell your product during the Open House weekend which consists of 3 days (). You estimate the demand each day () to have a normal distribution with =4 and =2. Each product cost you $20 to make and each sells for $40. However, you cannot sell the product after the Open House weekend and each unsold product have to be discarded at an additional cost() of $10 due to the EPA regulation and the hazardous materials that you use. Moreover-you need to make all your products ahead of the three days event a) How many products shall you make? Is it an optimal solution? B) Belatedly you found out that the sales during the entire three days follow this specific discrete distribution: Probability 0.2 Demand per day 9 12 15 18 0.25 0.15 0.15 0.10 0.10 0.05 b1) How many products should you make now? b2) If you decided to make 12 products, exactly i) Find your Service Level Type I. i) Find your Service Level Type II

Explanation / Answer

Average demand over three days, = 4*3 = 12

Std dev of demand over 3 days, = 23 = 3.5

Shortage or Underage cost, Cu = selling price - cost = 40-20 = 20

Excess or Overage cost, Co = 20+10 = 30

Critical ratio = Cu/(Cu+Co) = 20/(20+30) = 0.40

z value corresponding to critical ratio = -0.2533

a) Optimal number of products to make = + z = 12 - 0.2533*3.5 = 11

B) Prepare cumulative probability distribution table

b1) Look for cumulative probability greater than or equal to critical ratio in the discrete demand distribution table. That value is 4. Therefore optimal number of products to make = 4*3 = 12

b2) i) If you make 12 products, that will satisfy average daily demand of 4 per day. Therefore service level type I = 0.45   (refer cumulative prob. distribution table)

ii) Expected backorders per day = (6-4)*0.15 + (9-4)*0.15 + (12-4)*0.1 + (15-4)*0.1 + (18-4)*0.05 = 3.65

Average demand = 1*0.2+4*0.25+6*0.15+9*0.15+12*0.1+15*0.1+18*.05 = 7.05

Service level type II = 1 - expected backorders per day / expected daily demand = 1 - 3.65/7.05 = 0.4823

Demand per day Probability Cumulative Probability 0 1 0.20 0.20 4 0.25 0.45 6 0.15 0.60 9 0.15 0.75 12 0.10 0.85 15 0.10 0.95 18 0.05 1.00

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