two question on General Principles of Discrete Event Simulation

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ISE 405 - 161

Assignment 2

This assignment is due on Wednesday 2nd of November 2016 at 2:00 PM.

Late submission is not acceptable

Instructions

Use random numbers from the attached table. Each students group is assigned a different start, in

each of the following problems start using random numbers form your indicated start.

Group Start Group Start Group Start Group Start

1A Line 1/Col. 1 1F Line 1/Col. 6 2A Line 11/Col. 1 2F Line 11/Col. 6

1B Line 1/Col. 2 1G Line 1/Col. 7 2B Line 11/Col. 2 2G Line 11/Col. 7

1C Line 1/Col. 3 1H Line 1/Col. 8 2C Line 11/Col. 3 2H Line 11/Col. 8

1D Line 1/Col. 4 1I Line 1/Col. 9 2D Line 11/Col. 4 2I Line 11/Col. 9

1E Line 1/Col. 5 1J Line 1/Col. 10 2E Line 11/Col. 5 2J Line 11/Col. 10

1- A baker is trying to determine the profit of selling dozens of bagels each day. The probability distribution of the number of customers asking for bagels is as follows:

Customers order 1, 2, 3, or 4 dozen bagels according to the following probability distribution.

Bagels sell for $6 per dozen. They cost $4 per dozen to make. All bagels not sold at the end of the

day are sold at half-price to a local grocery store. Based on 5 days of simulation, and Q = 25 dozens

baked every day, what is the average profit per day?

2- An elevator in a manufacturing plant carries exactly 400 kilograms of material. There are three kinds of material packaged in boxes that arrive for a ride on the elevator. These materials and their

distributions of time between arrivals are as follows:

Material Weight (kg) Interarrival Time (minutes)

A 200 4 ± 2 (uniform)

B 100 8 (constant)

C 50 P(2) = 0.33, P(3) = 0.67

It takes the elevator 1 minute to go up to the second floor, 2 minutes to unload, and 1 minute to

return to the first floor. The elevator does not leave the first floor unless it has a full load. Simulate

1 hour of operation of the system. What is the average transit time for a box of material A (time

from its arrival until it is unloaded)? What is the average waiting time for a box of material B?

How many boxes of material C made the trip in 1 hour?

Number of Customers/Day 3 4 5 6 Probability 0.35 0.30 0.25 0.10

Number of Dozen Ordered/Customer 1 2 3 4 Probability 0.4 0.3 0.2 0.1

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3- Consider a single-product (s, S) inventory system, where the inventory level is

checked at the beginning of every week. An order up to level S is placed if the

inventory level I is less than s, while no order is placed if I is greater than or equal to

s. Demand occurs with inter-demand time following a discrete uniform distribution

with probabilities given by p(b) = 1/3 with b = 2, 3, 4 days. Demand size = 5, 6, 7, 8

with respective probability 1/6, 2/6, 2/6, 1/6. If the current policy parameters s, and S

equals 10, 40 respectively and the delivery lag (lead time) is fixed at 3 days, calculate

the total inventory cost of 4 weeks given the following cost information;

Ordering cost is $32+ $3 × Q, where Q is the order size.

Holding cost is $0.1 per item per day.

Shortage cost is $1 per item per day

Note that at time 0, there is 40 items on hand.

4- Given A, B, and C, three independent random variables: Variable A is normally

distributed with µ = 100 and σ2 = 400. Variable B is exponentially distributed with mean equals 0.4, and variable C is distributed in accordance with the following table.

Value of C Probability

10 .05 20 .25 30 .50 40 .20

Use a sample of size 6 trials to estimate the mean of a new variable D, defined as;

D = (A − 25B)/(2C)

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