MSCI 333 (F23) Assignment 1

MSCI 333 (F23) Simulation Analysis and Design Assignment 1 Deadline: 11:30 pm, Sep 29, 2023 Total Points: 100 Instruction: The assignment should be uploaded in Crowdmark as a pdf file . Any question required modeling in Excel or Arena you should take a screenshot of all pages and include in the pdf file uploaded in Crowdmark. Then the Excel/Arena files needs to be uploaded in Learn Dropbox . Question 1: 10 Points Name several entities (differentiate the resources from the entities), attributes, activities, events and state variables for the following systems: 1. Driver Test center 2. A gym check-in counter 3. A café-bakery in town 4. Terry Fox run event 2023 5. Accessibility center in UW Example: Bank Teller Model • Entities: o Customers o Tellers (Resource) • Attributes: o Customers ▪ Account type – Saving, Chequing, credit or combination of three ▪ Bank balances ▪ Profession o Tellers (Resource) ▪ Break times ▪ Availability • Activities: o Customers banking – (deposits, withdraws, etc.,) • Events: o Customer – Arrival o Customer – Departure • State Variables: o Teller Status – Busy with customer, Available or Not available (in break or away) o Number of customers waiting in Queue for service Tip: Refer to Table 1.1 of the textbook for more examples.

Question 2: 15 points Canadian Superstore customers load their carts with goods totaling between $50 and $300, uniformly (and continuously) distributed; call this the raw order amount. Assume that customers purchase independently of each other. At checkout, 60% of customers have PC Optimum loyalty card that gives them 3% off their raw order amount. Also, 30% of customers have coupons to match prices that give them 5% off their raw order amount. These two discounts occur independently of each other, and a given customer could have one or both of them, or neither of them, to get to their net order amount (what they actually pay). Also, the customers who don’t have the PC Optimum loyalty card are asked to have one and usually 50% of customers accept to get the loyalty card and if they do then will get the 3% discount immediately. Construct a spreadsheet simulation to simulate 100 customers with 1000 replications and collect statistics on the net order amount; these statistics should include the average, standard deviation, minimum, maximum, and a histogram to describe the distribution of the net order amounts between $50 and $300. Question 3: 20 points Consider a shop with three machines where machines A and B are in parallel and do same process, but machine C does a finishing process if needed. Items arrive at the system with a mean time between arrivals of 5 minutes, with the first arrival at time 0. They are immediately sent to machine A or B, if they are not busy otherwise will join the line for process on either machine A or B. The process time on either machine A or B has a mean time of 7 minutes. Upon completion, they are sent to machine C for a finishing process with a probability of 0.6 or leave the shop without the finishing process with the probability of 0.4. The mean time of finishing process on machine C is 2 minutes. Items sent to finishing process depart the shop upon completion of the process. Performance measures of interest are the average waiting time for machines A or B and machine C, and the average total time in system of items. Construct a spreadsheet simulation to simulate 100 parts arriving the system with 1000 replications.

Question 5: 15 points Lead-time demand may occur in an inventory system when the lead-time is other than instantaneous. The lead-time is the time from the placement of an order until the order is received. The lead-time is a random variable. During the lead-time, demand also occurs at random. Lead-time demand is thus a random variable defined as the sum of the demands during the lead-time, or 𝐿𝑇𝐷 = ∑ 𝐷 𝑖 𝑇 𝑖=1 where i is the time period (day) of the lead-time and T is the lead-time length. The distribution of lead-time demand is determined by simulating many cycles of lead-time and the demands that occur during the lead-time to get many realizations of the random variable LTD. Notice that LTD is the convolution of a random number of random demands. Suppose that the daily demand for the item is given by Normal distribution with the mean of 5 items and standard deviation of 2. The lead-time is random variable with the following distribution: Lead time (in days) 4 5 6 7 8 Probability 0.1 0.3 0.35 0.1 0.15 Use a spreadsheet to simulate 1000 instances of LTD. Report the mean of LTD for the 1000 observations. Estimate the chance that LTD is greater than or equal to 35.

Question 6: 15 points Consider a newsvendor who requires to buy the same, fixed number q of copies at the cost of 𝑐 = 65 cents each, selling for ? = $1.2 each through the day. In case of any left over at the end of the day, the excess newspapers can be sold as scrap to the recycler for ? = 8 cents each. The problem is to find the value of q that maximizes the newsboy’s expected profit. Demands from day to day are independent of each other. The days have different pattern of demands. Days can be weak, medium, or strong in terms of demand with probabilities 0.25, 0.5, and 0.25 respectively. Assume the following distributions for the daily demands: • Weak demand day: Uniform between 30 and 50 newspapers per day • Medium demand day: Normal with the mean of 120 and standard deviation of 30 (round down the number to have it as an integer) • Strong demand day: 160, 200, or 240 newspapers per day with probabilities of 0.3, 0.45, and 0.25 respectively. Simulate the problem in Excel for 30 days with 100 replications to obtain the order quantity that maximizes the profit with the possible order quantities ( q ) of 50, 100, 150, 200, and 220. Question 7 (Arena): 15 points Modify the simple machine processing system (introduced in lab 1) with the following changes: • Add a second machine for fixing the parts with quality issues. Immediately after the first machine, there’s a pass/fail inspection that takes a mean time of 5 minutes to carry out and has a 70% chance of a passing result; queueing is possible for the single inspector, and the queue is first-in, first-out. The passed parts depart the system, but the failed parts will go to machine 2 to be fixed. Processing time at machine 2 has a mean time of 10 minutes. If machine 2 is busy, then arriving parts for this machine will join the queue. Gather all the statistics as before, plus the time in queue, queue length, and utilization at the second machine. • Include plots to track the queue length at all stations; put all queue lengths together in the same plot (you’ll need to turn on the plot Legends to identify the curves). Configure them as needed. • Run the simulation for 1440 minutes (three 8-hour shift) instead of 20 minutes.