Modelling

Question 1

Irreducable

Answer 1

A chain is irreducible if every state can be reached by every other state

Question 2

Closed state

Answer 2

If the system once in one of the states of the set will then remain there indefinitely

Question 3

Absorbing state

Answer 3

Closed set with only one state

Question 4

N from fundamental matrix

Answer 4

N = ( I - Q )^-1
The expected number of times the process is in the transient

Question 5

Balking

Answer 5

Behaviour where potential customers or clients decide not to join the queue because it is too long or moving too slowly

Question 6

Renegading

Answer 6

Behaviour where customers who have already joined a queue decide to leave it before receiving the service

Question 7

Jockeying

Answer 7

For where there are more than one channels,
where a customer switches from one line to another in attempt to find a faster queue

Question 8

Waiting lines total costs

Answer 8

Waiting costs - Decrease as speed of service rises
Service cost - Increase as speed of service rises

Question 9

How to recognise Poisson distribution? (2 crude rules)

Answer 9

1. Random arrivals
2. Sample mean and variance will be approximately equal

Question 10

Assumptions of waiting line models (7)

Answer 10

1. First in, first out
2. All customers wait regardless of queue length
3. arrivals independent of preceding arrivals, but avg arrivals dont change over time
4. Infinite population arrive by poisson dist
5. Service times vary and are independent, but Avg is known
6. Service times are negative exponential probability distribution
7. Average service rate is greater than average arrival rate

Question 11

Total costs model for waiting lines

Answer 11

CwLs + CsK

Question 12

Arbitrary service times

Answer 12

Service times that do not follow a specific distribution pattern.
Reflective of reality

Question 13

Reasons for simulation (4)

Answer 13

1. Actual environment too hard to observe
2. not possible to develop analytical solution
3. not sufficient time to allow time to operate extensively
4. actual operation and observation is too disruptive

Question 14

2 Types of simulation model

Answer 14

1. Deterministic - all data known with certainty
2. Probabilistic - Some data described by probability distributions

Question 15

Shortcomings of simulation (5)

Answer 15

1. Not precise
2. Expensive, and timely to develop
3. Not available for all situations. Without random component, all experiments would produce same answer
4. Evaluates, does not generate solution techniques
5. Changing too many parameters at same time

Question 16

5 steps of Monte Carlo simulation

Answer 16

For RANDOM NUMBERs.
1. Setting up probability distribution for variables
2. Building a cumulative probability distribution for a variable
3. Establish an interval of random numbers for a variable
4. Generate random numbers
5. Simulate a series of trials

Question 17

Midsquare technique for random numbers

Answer 17

1. Start with 4 digit number
2. Square it to get 8 digit (add 0 to front if 7)
   take middle 4 (digit 3, 4, 5, and 6) and /1000 for random number
3. The middle 4 digits is the next base number

Question 18

Congruential random number generator

Answer 18

Random number is a function of seed mod m.
eg. seed Z0 =1, f(Z)=aZ0 mod m
a = 6, m=13
Z1 = (1*6)/13 = 0 remain 6.
6/m-1= 6/12=0.5
0.5 is the random number.

Question 19

Why use inventory management models

Answer 19

Help managers face problems of maintaining sufficient inventories to meet demand as well as incurring lowest inventory holding costs

Question 20

Inventory management costs to consider

Answer 20

• Ordering costs
• Holding costs
• (Backorder cost)

Question 21

What is Simulation?

Answer 21

The process of building a mathematical or logical model of a system or a decision problem and experimenting with the model to obtain insights into the system’s behaviour or to assist in solving the decision problem.

Question 22

Steps in Simulation Process (7)

Answer 22

1. Define the problem/system, identifying the basis entities.
2. Formulate the model (i.e., process and flows).
3. Identify/collect data to test the model.
4. Test the model: compare the behaviour of the model with actual problem.
5. Run the simulation.
6. Analyse the results of the simulation.
7. Validate the simulation.

Question 23

Formula to calculate x for a Uniform Probability Distribution

Simulation - Random Numbers

Answer 23

x = a + R(b - a)

Question 24

Formula to calculate x for a Normal Probability Distribution

Answer 24

x = mu +/- SD(z)
From the fomula: z = (x - mu)/SD

Question 25

Alternative Approaches to Inventory Management

Answer 25

- Deterministic Inventory Models - rate of demand is constant or near constant. - Probabilistic Inventory Models - demand for items fluctuates. - Material Requirement Planning (MRP) - where demand is directly dependent on demand of final products in inventory system. - Just-in-time (JIT) - eliminating waste, including unnecessary inventory.

Question 26

What is the Economic Order Quantity (EOQ)?

Answer 26

The number of units that a company should add to inventory with each order to minimise the total costs of inventory. Model for calculating the appropriate reorder point, and optimal reorder quantity.

Question 27

Constraints to EOQ model | In terms of Demand and Quantity.

Answer 27

- Demand (D) for an item is constant per time period. - Quantity (Q) ordered arrives at one point in time - inventory level then decreases until the next re-order point.

Question 28

What is the equation for adjusted reorder point for Safety Stock?

Answer 28

rss = (d x m) + SS

Question 29

EOQ model Assumptions | (Economic Order Quantity)

Answer 29

- Demand is deterministic and occurs at a constant rate. - The order quantity is the same for every order, and it all turns up at once. - The cost per order is constant, does not depend on the quantity ordered. - The purchase cost per unit is constant and does not depend on quantity ordered. - The inventory holding cost per unit per time period is constant. - Shortages, such as stockouts or backorders are not permitted. - The lead time for an order is constant. - The inventory position is reviewed continuously. As a result, an order is placed as soon as the inventory positioon reaches the reorder point.

Question 30

What is the Economic Production Lot Size Model?

Answer 30

Goods arrive at a constant rate (p) over a full period of time.

Question 31

Disadvantages of Quantity Discounts for the EOQ Model

Answer 31

- higher ordering costs - older stock - becomes unhealthy to eat, but also the volatility of prices of component parts of technology. - more money upfront

Question 32

What are the 3 levels of Management Science?

Answer 32

1. Fundamental Level - Probability, Optimisation and Dynamical systems. 2. Modelling Level - building models, analysing them mathematically, gathering and interpreting data. 3. Application Level - make a practical impact and be a driver for change in the real world.