# USC BUAD 311 – Homework 3 Forecasting and Inventory Systems

Homework #3Forecasting and Inventory SystemsBUAD311- Operations ManagementFall 2016 1. (10 pts)You give your friend some demand data, and she performs an exponentialsmoothing forecasting analysis with ? =0.5?? =0.2 . She plots the originaldemand and forecasts with different alphas. The below graph is a portion of thisplot. Unfortunately, she was not careful to label the plot! Which series do you thinkcorresponds to actual demand, forecast with alpha 0.2 and forecast with 0.5respectively? Briefly explain. Forecast using Exponential Smoothing555045403530252015 1 2. (30 pts, 6 pts per part) Trojan Plastic (TP) produces various high quality BPA-free plastictoys. The production process requires a special industrial chemical. Currently, annualdemand for this chemical is normally distributed with mean 2000 pound andstandard deviation 80. The cost per pound from supplier is $10. Shipping andhandling cost is $100 per order. It takes 4 weeks to receive the chemical from thesupplier after placing an order. TP also pays for special storage at 15% of thepurchasing cost. The annual interest rate is 10% and TP would like to maintain aservice 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 thecorresponding inventory turns? About how many orders would TP need to place in ayear?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% thischemical is lost. In other words, process has a yield of 95%–100 pounds of inputwill have only 95 pounds of output. Should TP increase or decrease the EOQcalculated 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 howmuch 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 thefollowing table. You started the forecast process at the end of week 1, when youused the week 1’s demand as the forecast of week 2’s demand.WeekDemand for silverDemand for red metallic119032009221111808318051999420101778522221567624351799721131665823481438925551589a. Calculate the simple exponential smoothing forecast for the demand forsilver cameras in Week 10 with =0.5. What is value of the MAD? 2 b. Calculate the simple exponential smoothing forecast for the demand forred 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 ofnot meeting the demand for silver cameras in week 10 is 0.1? How manyred metallic cameras must you stock in order that the probability of notmeeting 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 metalliccamera is an outside shell (which can be bought very cheaply). Henceyou can forecast the combined demand for silver and red metalliccameras, and stock enough basic cameras (without the colored outsideshell) to ensure that the probability of not meeting the combined demandfor silver or red metallic cameras is 0.1. How many basic cameras(without the colored outside shell) must you stock? Is this numbergreater 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 theUS. He wants to purchase a cell phone and a plan for the duration of his stay. Beingstudents of Operations Management and experts at decision making you decide to helphim find the cheapest plan, i.e., with the lowest expected payment. You narrow thingsdown 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 perminute. 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 pay400x$0.15=$60 at the beginning of the month. If you end up using 410minutes during the month, you will have to pay (410-400)*0.50=$5 in additionto the $60.Your friend is quite chatty and forecasts his requirements for the phone for this month tobe distributed as follows (he does not modify his usage based on his bill!):Minutes250350600800 Probability0.150.20.40.25 a. (8pts) What is the optimal number of minutes that should be contracted at thebeginning of the month under Plan B?.b. (8pts) What is the expected payment for the month under Plan B if you contractfor the minutes you computed in part a)?c. (4pts) Which plan do you recommend to your friend and why? 3