Operations Analysis Final Exam Review Problems

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Feb 20, 2024

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Page 1 of 9 Problem1: Decision Trees Reliable is a cell phone seller serving the Asian markets. Current annual demand of its product is 2 million. The seller has a choice between two manufacturers. The first manufacturer, company A, produces the cell phone with the wholesale price $23 but it asks for a two-year agreement with a 5 million dollars upfront payment. The other manufacturer, company B, asks for an annual agreement with no upfront payment but the wholesale price is equal to $25. The current sale price of this phone brand in the market is $40, and Reliable incurs $10 per phone for the distribution, marketing, etc. costs. The estimated rate of return is 10% per year. a) Compute the net present value of profit for 2-year period with company A. [Answer: NPV = $21.73 million] b) Compute the net present value of profit for 2-year period with company B. [Answer: NPV = $19.09 million] c) Based on the NPV calculations above, which manufacturer would you choose? [Answer: Company A] Demand from year 0 to year 1 remains same with no change, but from year 1 to year 2 it is expected to go up by 10 percent, with a probability of 0.7, or go down by 30 percent, with a probability of 0.3. d) If Reliable picks company A, what is the NPV of profit over 2-year agreement? Based on the agreement, company A should produce more cellphone if the demand goes up. Upfront Cost remains same as in (a). Year 1 Profit remains the same as in (a). To calculate Year 2 profit we need to use the decision tree. - Demand = 2 [Ans: Profit = $14MM] d Demand = 2.2 [Ans: Profit = $15.4MM] Demand = 1.4 [Ans: Profit = $9.8MM] 0.7 0.3 Period 0 Period 1 Upfront cost = $5
Page 2 of 9 [ Answer: Year 2 Profit = $13.72 million] [Answer: NPV = 21.47 million] e) Company B agrees if the demand goes up by “A % ” , it reduces the wholesale price correspondingly by “A % ” up to a maximum of 10%. If Reliable picks company B, what is the NPV of profit over 2-year collaboration? Upfront Cost remains same as in (b). Year 1 Profit remains the same as in (b). To calculate Year 2 Profit we need to use the decision tree. [Answer: Year 2 Profit = $13.65 million] [Answer: NPV = $22.41 million] f) Based on the NPV calculations above, which manufacturer would you now choose? [Answer: Company B] Demand = 2 [Ans: Profit = $10MM] Demand = 2.2 [Ans: Profit = $16.5MM] Demand = 1.4 [Ans: Profit = $7MM] 0.7 0.3 Period 0 Period 1 Upfront cost = $0
Page 3 of 9 Problem 2: All Units Quantity Discount The Weighty Trash Bag Company has the following price schedule for its large trash can liners. For orders of less than 500 bags, the company charges 30 cents per bag; for orders of 500 or more but fewer than 1,000 bags, it charges 29 cents per bag; and for orders of 1,000 or more, it charges 28 cents per bag. In this case the breakpoints occur at 500 and 1,000. The discount schedule is all-units because the discount is applied to all of the units in an order. The order cost function C (is defined as 𝐶 = { 0.3 𝑖𝑓 0 ≤ 𝑄 < 500 0.29 𝑖𝑓 500 ≤ 𝑄 < 1000 0.28 𝑖𝑓 1000 ≤ 𝑄 Find the Optimal Policy for All-Units Discount Schedule when the demand is 600 units per year, ordering cost is $8 per order, and the holding cost is 20 percent of unit cost per year. Here D = 600 units/year; S = $8/per order, h = 0.20 times unit cost per year; C varies depending on the order quantity. [Answer: The optimal order quantities for second and third price points are not in the range, i.e. 𝑄 2 ∗ is not between 500 and 1000 units and 𝑄 3 ∗ is not more than 1000 units. Therefore, the total annual cost for 𝑄 1 ∗ = 400 and the break points, 500 and 1000 units should be computed. The lowest total cost comes out to be with Q=500. Therefore, the optimal ordering quantity is 500 units]
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Page 4 of 9 Problem 3: Project Scheduling, Critical Path Method Oliver has managed to obtain funding for a project. For accomplishing this project, the list of tasks, the times required, and the precedence relationships are provided below. The network diagram associated with this project is drawn below:
Page 5 of 9 Based on the forward and backward pass, the Early Start/Early Finish and Latest Start/Latest Finish times have been provided in the diagram above. You will notice that Activities A, C, E, G, I have zero slack and therefore are critical activities. Answers to the questions below can be gathered from the network diagram. a) The latest finish time for C will be 5 (The lower right number in the activity C box) b) The expected completion time for the project is 25 (Shown on the Finish Node) c) The critical path for the project will be A-C-E-G-I (A, C, E, G, I are critical activities) d) The earliest start time of activity H is 10 (The upper left number in the activity H box)
Page 6 of 9 Problem 4: Forecasting Observations of the demand for a component part stocked at a parts supply depot during the calendar year 2013 are provided in the following table. Monthly forecast using 3-month moving average is also provided in the table. Month Demand Forecast Error MAD Bias TS Jan 89 Feb 57 Mar 144 Apr 221 96.67 -124.33 124.33 -124.33 -1.00 May 177 140.67 -36.33 80.33 -160.67 -2.00 Jun 280 180.67 -99.33 86.67 -260.00 -3.00 Jul 223 226.00 3.00 65.75 -257.00 -3.91 Aug 286 226.67 -59.33 64.47 -316.33 -4.91 Sep 212 263.00 51.00 62.22 -265.33 -4.26 Oct 275 240.33 -34.67 58.29 -300.00 -5.15 Nov 188 257.67 69.67 59.71 -230.33 -3.86 Dec 312 F E M -317.33 T What are the values of F, E, M and T? Answer [F=225; E= - 87, M = 62.74; T = -5.06]
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Page 7 of 9 Monthly forecast using simple exponential smoothing with 𝛼 = 0.2 is provided in the table below: Month Demand Level Forecast Error MAD Bias TS Jan 89 Feb 57 Mar 144 205.33 Apr 221 208.47 205.33 -15.67 15.67 -15.67 -1.00 May 177 202.17 208.47 31.47 23.57 15.80 0.67 Jun 280 217.74 202.17 -77.83 41.65 -62.03 -1.49 Jul 223 218.79 217.74 -5.26 32.56 -67.29 -2.07 Aug 286 232.23 218.79 -67.21 39.49 -134.50 -3.41 Sep 212 228.19 232.23 20.23 36.28 -114.26 -3.15 Oct 275 237.55 228.19 -46.81 37.78 -161.08 -4.26 Nov 188 L 237.55 49.55 39.25 -111.53 -2.84 Dec 312 244.51 L E2 M2 -195.89 T2 What are the value of L, E2, M2 and T2? [Answer: L=227.64; E2 = -84.36; M2 = 44.27; T2 = -4.43]
Page 8 of 9 Problem 5: Economic Ordering Quantity The Rahway, New Jersey, plant of Metalcase, a manufacturer of office furniture, produces metal desks at a rate of 200 per month. Each desk requires 40 Phillips head metal screws purchased from a supplier in North Carolina. The screws cost 3 cents each. Fixed delivery charges and costs of receiving and storing shipments of the screws amount to about $100 per shipment, independent of the size of the shipment. The firm uses a 25 percent annual interest rate to determine holding costs. Metalcase would like to establish the ordering policy with the supplier. What order size should they use that would minimize the total cost? D=200*12*40=96,000/year C=$0.03/item S=$100/order h=0.25 times item cost/year [Ans: Optimal Order Quantity = 50,597; Annual Holding Cost = Annual Ordering Cost =189.74]
Page 9 of 9 Problem 6: Safety Inventory Weekly demand for smartphones at the Apple store is normally distributed, with a mean of 500 and a standard deviation of 300. The Apple store continuously monitors inventory and currently orders 2,500 smartphones each time the inventory drops to 1000. Foxconn, the assembler, takes two weeks to supply an order to the Apple store. How much safety inventory does the Apple store carry? [Answer: SS=0] With the same problem as above what is the safety stock level if the lead-time is equal to 1 week instead of 2 weeks? [Answer: SS= 500]
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