1. (12 Points) Consider the demand for trading cards listed below. Year 2011 201
ID: 353711 • Letter: 1
Question
1. (12 Points) Consider the demand for trading cards listed below. Year 2011 2012 2013 2014 2015 Demand 50,000 40,000 54,000 62,000 86,000 Develop 2 year moving average forecasts for 2013,2014, and 2015. a. b. Develop exponential smoothing forecasts for 2012 through 2016 with a smoothing constant of .2. To initialize the process, you may assume that the forecast for 2011 was 50,000. c. Calculate the MAPE for both of your moving average forecasts and exponential smoothing forecasts covering 2013 through 2015 from part a and part b. 2. (13 points) (You can round all quantities to the nearest whole unit, and you can round all annual costs to the nearest whole dollar.) Suppose that your firm manufactures toy flying drones. Monthly demand for the drones is 46,000 units. Setup cost per order is $160, and the annual holding cost percentage is 22%. The drones cost $40 to produce and are sold for $89. a. If you have one warehouse, what is the economic order quantity for the drones? What is the total of the annual setup and holding costs of this quantity? b. Suppose that you have 81 warehouses instead of one, and total demand is equally distributed among the warehouses. If setup and holding costs are the same in the smaller warehouses as they would be for the single large warehouse, what is the EOQ for the dolls at each of the 81 warehouses? What is the total of the annual setup and holding costs at each warehouse? What is the total of the company's annual setup and holding costs? c. Using centralized warehousing as in part a means that products must be shipped over longer distances. Suppose that shipping costs $1.20 per unit when using one warehouse and $0.90 per unit when using 81 warehouses. Which option should the company choose? Support your answer. d. Based on your answers to a and b above, if total company demand is D, what is the general formula for the total company EOQ cost of using N warehouses instead of one (if the demand is spread evenly over those warehouses)?Explanation / Answer
PLEASE FIND BELOW ANSWER TO QUESTION NUMBER 1 :
Following formula for forecast values are to be noted :
Ft = ( Dt-1 + Dt-2 ) /2
Ft = Forecast for period t
Dt-1, Dt-2 = Demand for period t-1 and t-2 respectively
Ft = alphaxDt-1 + ( 1 – alpha)x Ft-1
= 0.2 x Dt-1 + 0.8 x Ft-1
Alpha = Exponential smoothing constant = 0.2
Dt-1 = Demand for period t-1
Ft = Forecast for period t
Ft-1 = Forecast for period t-1
And
Mean Absolute Percentage error ( MAPE ) = Sum of all APE / Number of observations
Based on above, please find below table for necessary data which have been asked for :
Year
Demand (Dt)
Forecast ( Ft) – 2 year moving average basis
Absolute Percentage Error ( APE )
Forecast ( Ft) – Exponential smoothing forecast basis
Absolute Percentage Error ( APE )
2011
54,000
50000
2012
40,000
50000
2013
54,000
45000
16.67
48000
11.11
2014
62,000
47000
24.19
49200
20.65
2015
86,000
58000
32.56
51760
39.81
Sum =
73.42
71.57
MAPE =
24.47
23.86
Year
Demand (Dt)
Forecast ( Ft) – 2 year moving average basis
Absolute Percentage Error ( APE )
Forecast ( Ft) – Exponential smoothing forecast basis
Absolute Percentage Error ( APE )
2011
54,000
50000
2012
40,000
50000
2013
54,000
45000
16.67
48000
11.11
2014
62,000
47000
24.19
49200
20.65
2015
86,000
58000
32.56
51760
39.81
Sum =
73.42
71.57
MAPE =
24.47
23.86
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