USC BUAD 311 - Homework 3 Forecasting and Inventory Systems

Homework #3
Forecasting and Inventory Systems
BUAD311- Operations Management
Fall 2016 1. (10 pts)You give your friend some demand data, and she performs an exponential
smoothing forecasting analysis with ? =0.5?? =0.2 . She plots the original
demand and forecasts with different alphas. The below graph is a portion of this
plot. Unfortunately, she was not careful to label the plot! Which series do you think
corresponds to actual demand, forecast with alpha 0.2 and forecast with 0.5
respectively? Briefly explain. Forecast using Exponential Smoothing
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15 1 2. (30 pts, 6 pts per part) Trojan Plastic (TP) produces various high quality BPA-free plastic
toys. The production process requires a special industrial chemical. Currently, annual
demand for this chemical is normally distributed with mean 2000 pound and
standard deviation 80. The cost per pound from supplier is $10. Shipping and
handling cost is $100 per order. It takes 4 weeks to receive the chemical from the
supplier after placing an order. TP also pays for special storage at 15% of the
purchasing cost. The annual interest rate is 10% and TP would like to maintain a
service level of 97.5%. There are 52 weeks in every year.
a) How many pounds (EOQ) of this chemical should TP order each time?
b) At what level of on-hand inventory should TP place an order for this chemical?
c) What is the average inventory of this special chemical in TP? What are the
corresponding inventory turns? About how many orders would TP need to place in a
year?
d) What is the annual inventory related cost for this chemical (setup plus holding)?
e) After a detailed study, TP found that during the production process, 5% this
chemical is lost. In other words, process has a yield of 95%--100 pounds of input
will have only 95 pounds of output. Should TP increase or decrease the EOQ
calculated in part a) to account for this loss? What about the ROP and Safety Stock?
Explain. (No need to run calculations.) 3. (40 points, 10 points each part) You are a camera retailer and are deciding how
much to stock of a particular digital camera. The camera comes in two colors:
silver and red metallic. Demand in the first 9 weeks for the camera is shown in the
following table. You started the forecast process at the end of week 1, when you
used the week 1’s demand as the forecast of week 2’s demand.
Week
Demand for silver
Demand for red metallic
1
1903
2009
2
2111
1808
3
1805
1999
4
2010
1778
5
2222
1567
6
2435
1799
7
2113
1665
8
2348
1438
9
2555
1589
a. Calculate the simple exponential smoothing forecast for the demand for
silver cameras in Week 10 with =0.5. What is value of the MAD? 2 b. Calculate the simple exponential smoothing forecast for the demand for
red metallic cameras in Week 10 with =0.5. What is value of the MAD?
c. How many silver cameras must you stock in order that the probability of
not meeting the demand for silver cameras in week 10 is 0.1? How many
red metallic cameras must you stock in order that the probability of not
meeting the demand for red metallic cameras in week 10 is 0.1?
d. You realize that the only thing that differentiates a silver and red metallic
camera is an outside shell (which can be bought very cheaply). Hence
you can forecast the combined demand for silver and red metallic
cameras, and stock enough basic cameras (without the colored outside
shell) to ensure that the probability of not meeting the combined demand
for silver or red metallic cameras is 0.1. How many basic cameras
(without the colored outside shell) must you stock? Is this number
greater than or less than the sum of your answers to part c)?
4. (20 pts) Your friend has just arrived from abroad and will be spending a month in the
US. He wants to purchase a cell phone and a plan for the duration of his stay. Being
students of Operations Management and experts at decision making you decide to help
him find the cheapest plan, i.e., with the lowest expected payment. You narrow things
down to two plans:
Plan A: Has a flat rate of $0.20 per minute used.
Plan B: You can purchase talk time at the beginning of the month at the rate of $0.15 per
minute. For each additional minute (beyond the purchased talk time) the rate is
$0.50 per minute. For example, if you contract for 400 minutes, you first pay
400x$0.15=$60 at the beginning of the month. If you end up using 410
minutes during the month, you will have to pay (410-400)*0.50=$5 in addition
to the $60.
Your friend is quite chatty and forecasts his requirements for the phone for this month to
be distributed as follows (he does not modify his usage based on his bill!):
Minutes
250
350
600
800 Probability
0.15
0.2
0.4
0.25 a. (8pts) What is the optimal number of minutes that should be contracted at the
beginning of the month under Plan B?
.
b. (8pts) What is the expected payment for the month under Plan B if you contract
for the minutes you computed in part a)?
c. (4pts) Which plan do you recommend to your friend and why? 3