1. a) WHAT DO YOU MEAN BY SIMULATION AND MODELING? WHAT ARE THE ADVANTAGES AND DISADVANTAGES OF SIMULATION?
Ans: Simulation is the imitation of the operation of a real-world process or system over time.
ADVANTAGES:
Ø New policies, operating procedures, decision rules, information flows, organisational procedures, and so on can be explored without disrupting ongoing operations of real system.
Ø New hardware designs, physical layouts, transportation system, and so on, can be tested without committing resources for their acquisition.
Ø Hypotheses about how or why certain phenomena occur can be tested for feasibility.
Ø Insight can be obtained about interaction of variables.
Ø Insight can be obtained about the importance of variables to the performance of the system
Ø Bottleneck analysis can be performed indicating where work-in-process, information, materials, and so on is being excessively delayed.
Ø A simulation study can help in understanding how the system operates rather than how individuals think the system operates.
Ø What-if questions can be answered. This is particular useful in the design of new system.
DISADVANTAGES:
Ø Model building requires special training. It is the art that is learned over time and through experience. Furthermore, if two models are constructed by two component individuals, they have similarities, but it is unlikely that they will be the same.
Ø Simulation results may be difficult to interpret. Since most simulation outputs are essentially random variables, it may be hard to determine whether an observation is a result of system interrelationships or randomness.
Ø Simulation modelling and analysis can be time consuming and expensive. Skimping on resources for modelling and analysis may result in a simulation model or analysis that is not sufficient for the task.
b) WHAT ARE THE TYPES OF SIMULATION MODEL?
Ans:
Static or dynamic simulation models
· Static simulation model ( Monte carlo ) represents a system at a particular point in time.
· Dynamic simulation model represents systems as they change over time.
Deterministic or stochastic simulation models
· Deterministic simulation models contain no random variables and have a known set of inputs which will result in a unique set of outputs.
· Stochastic simulation model has one or more random variables as inputs. Random inputs lead to random outputs.
Continuous vs. Discrete
· Discrete system is one in which the state variables change only at discrete points in time.
· Bank is an example of discrete system. State variable is the no of customers in the bank, which changes when the customer arrives or leaves the bank.
· Fig 1.1
· A continuous system is one in which the state variables change continuously over time.
· Example is the head of water behind the dam.
· Fig 1.2
2. EXPLAIN STEPS IN SIMULATION STUDY WITH A NEAT FLOW CHART.
ANS:
v PROBLEM FORMULATION
Every study begins with a statement of the problem, provided by policy makers. Analyst ensures it is clearly understood. If it is developed by analyst, policy makers should understand and agree with it.
v SETTING OF OBJECTIVES AND OVERALL PROJECT PLAN
o A determination must be made whether simulation is the appropriate methodology for the problem formulated.
o A statement of the alternative systems to be considered.
v MODEL CONCEPTUALIZATION
o The art of modelling is enhanced by an ability to abstract the essential features of a problem, to select and modify basic assumption that characterize the system, and then to enrich and elaborate the model until a useful approximate results.
o Model conceptualization enhance the quality of the resulting model and increase the confidence of the model user in the application of the model.
v DATA COLLECTION
o There is a constant interplay between the construction of model and the collection of needed input data. Done in the early stages. Objectives kinds of data are to be collected.
o As the complexity of the model changes, the required data elements may also change.
v MODEL TRANSLATION
o Real-world systems result in models that require a great deal of information storage and computation. It can be programmed by using simulation languages or special purpose simulation software. Simulation languages are powerful and flexible . Simulation software models development time can be reduced.
o GPSS or special-purpose simulation software.
v VERIFIED ?
o Is the computer program performing properly ?
o Debugging for correct input parameters and logical structure
v VALIDATED ?
o The determination that a model is a accurate representation of the real system.
o Validation is achieved through the collaboration the model.
v EXPERIMENTAL DESIGN
o The decision on the length of the initialization period , the length of simulation runs, and the number of replications to be made of each run.
v PRODUCTION RUNS AND ANALYSIS
o They are used to estimate measures of performance of the system designs that are being simulated.
v MORE RUNS?
o Based on the analysis of the runs that have been completed. The analyst determines if addition runs are needed and what design those additional experiments should follow.
v DOCUMENTATION AND REPORTING
There are two types of documentation:
o Program documentation: for the relationships between input parameters and output measures of performance, and for a modification
o Progress documentation: the history of a simulation, a chronology of work done and decision made.
v IMPLEMENTATION
o Success of the implementation phase depends on how well the previous 11 steps have been performed.
o If the model users has been thoroughly involved and understands the nature of the model and its outputs, likelihood of a vigorous implementation is enhanced
3. A Grocery store has one checkout counter. Customers arrive at random times from 1 to 8 minutes apart, with equal probability of occurrence. The service times vary from 1 to 6 minutes, with probabilities shown in table 1.1 . The random digits for interarrival and service times are given in table 1.2 . Analyze the system by simulating the arrival and service of 10 customers. Compute the average service time, average time b/w arrivals, and average time the customer spends in the system. TABLE 1.1
SERVICE TIME(in minutes) / PROBABILITY
1 / 0.1
2 / 0.2
3 / 0.3
4 / 0.25
5 / 0.10
6 / 0.05
IA
Time / - / 913 / 727 / 015 / 948 / 309 / 922 / 753 / 235 / 302 / 109 / 093 / 607 / 738 / 359
Service time / 84 / 10 / 74 / 53 / 17 / 79 / 91 / 67 / 89 / 38 / 32 / 94 / 79 / 05 / 79
Table 1.2
Solution:
TIME / PROBABILITY / CUMULATIVE PROBABILITY / RANDOM DIGIT ASSIGNMENT1 / 0.10 / 0.100 / 001 - 100
2 / 0.20 / 0.300 / 101 - 300
3 / 0.30 / 0.600 / 301 - 600
4 / 0.25 / 0.850 / 601 - 850
5 / 0.10 / 0.950 / 851 - 950
6 / 0.05 / 1.000 / 951 - 000
CUST / Inter arrival time / Arrival time / Service time / Time service begins / Waiting time in queue / Time service ends / Time customer spends in system / Idle time of server
1 / - / 0 / 4 / 0 / 0 / 4 / 4 / -
2 / 1 / 1 / 2 / 4 / 3 / 6 / 5 / 0
3 / 1 / 2 / 5 / 6 / 4 / 11 / 9 / 0
4 / 6 / 8 / 4 / 11 / 3 / 15 / 9 / 0
5 / 3 / 11 / 1 / 15 / 4 / 16 / 5 / 0
6 / 7 / 18 / 5 / 18 / 0 / 23 / 5 / 2
7 / 5 / 23 / 4 / 23 / 0 / 27 / 4 / 0
8 / 2 / 25 / 1 / 27 / 2 / 28 / 3 / 0
9 / 4 / 29 / 4 / 29 / 0 / 33 / 4 / 1
10 / 1 / 30 / 3 / 33 / 3 / 36 / 6 / 0
Average service time = total service time/ total no of customers
= 33/10
=3.3 mins
Average time b/w arrivals = sum of all times b/w arrivals / number of arrivals-1
= 30/9
= 3.33mins
Average time the customer spends in the system = total time customer spends in the system/total number of customers
=54/10
=5.4mins
4. A company sells refrigerators the system they use for maintaining an inventory is to review the situation after a fixed number of days(say N) and make a decision about how much is to be ordered to bring the inventory up-to-level(say M).simulate the system for 4 cycles with M=9, ending inventory=4, and N=4. Assume that an order of 6 refrigerators is placed on the 5th day and is expected to arrive after 2 days. The no refrigerators ordered and lead time for its arrival is given by the probability given in table 1.3 and 1.4 respectively. Random digits for demand and lead time is given in table 1.5
SOLUTION:
TABLE 1.3
Demand / Probability0 / 0.10
1 / 0.25
2 / 0.35
3 / 0.21
4 / 0.09
TABLE 1.4
LEAD TIME(DAYS) / PAOBABILITY1 / 0.60
2 / 0.30
3 / 0.10
DEMAND / 24 / 35 / 65 / 81 / 54 / 03 / 87 / 27 / 73 / 70 / 47 / 45 / 48 / 17 / 09 / 42
LEAD TIME / 8 / 7 / 2 / 3 / 1
DEMAND / PROBABILITY / CUMULATIVE PROBABILITY / RANDOM DIGIT ASSIGNMENT(DEMAND)
1 / 0.10 / 0.10 / 1-10
2 / 0.25 / 0.35 / 11-35
3 / 0.35 / 0.70 / 36-70
4 / 0.21 / 0.91 / 71-91
5 / 0.09 / 1.00 / 92-00
LEAD TIME / PROBABILITY / CUMULATIVE PROBABILITY / RANDOM DIGIT ASSIGNMENT(LEAD TIME)
1 / 0.6 / 0.6 / 1-6
2 / 0.3 / 0.9 / 7-9
3 / 0.1 / 1.00 / 00
Simulation table
DAY / CYCLE / DAY WITHIN CYCLE / BEGINNING INVENTORY / RANDOM DIGITS FOR DEMAND / DEMAND / ENDING INVENTORY / SHORTAGE QUANTITY / ORDER QUANTITY / RANDOM DIGITS FOR DEMAND / LEAD TIME / DAYS UNTILL ORDER ARRIVES1 / 1 / 1 / 4 / 24 / 1 / 3 / 0 / - / - / - / 1
2 / 1 / 2 / 3 / 35 / 1 / 2 / 0 / - / - / - / -
3 / 1 / 3 / 2 / 65 / 2 / 0 / 0 / - / - / - / -
4 / 1 / 4 / 0 / 81 / 3 / 0 / 3 / 12 / 8 / 2 / 2
5 / 2 / 1 / 0 / 54 / 2 / 0 / 5 / - / - / - / 1
6 / 2 / 2 / 0 / 03 / 0 / 0 / 5 / - / - / - / -
7 / 2 / 3 / 12 / 87 / 3 / 4 / 0 / - / - / - / -
8 / 2 / 4 / 4 / 27 / 1 / 3 / 0 / 6 / 7 / 2 / 2
9 / 3 / 1 / 3 / 73 / 3 / 0 / 0 / - / - / - / 1
10 / 3 / 2 / 0 / 70 / 2 / 0 / 0 / - / - / - / -
11 / 3 / 3 / 6 / 47 / 2 / 4 / 0 / - / - / - / -
12 / 3 / 4 / 4 / 45 / 2 / 2 / 0 / 7 / 2 / 1 / 1
13 / 4 / 1 / 2 / 48 / 2 / 0 / 0 / - / - / - / -
14 / 4 / 2 / 7 / 17 / 1 / 6 / 0 / - / - / - / -
15 / 4 / 3 / 6 / 09 / 1 / 5 / 0 / - / - / -
16 / 4 / 4 / 5 / 42 / 2 / 3 / 0 / 6 / 3 / 1 / 1
TOTAL 32 13
AVERAGE 1.875 2 0.8125
PART B
1. A. EXPLAIN THE EVENT SCHEDULING /TIME ADVANCE ALGORITH?
Ans:
Ø After the system snapshot at simulation time CLOCK=t has been updated, the clock is advanced to simulation time CLOCK = t1 the imminent event notice is removed from FEL, and the event is executed
Ø At time T1, new future events may or might not be generated, if any are, they are scheduled by creating event notices and putting them in to their proper position on the FEL.
Ø After the new system snapshot for TIME T1 has been updated, the clock is advanced to the new imminent event and that event is executed.
Ø This paper repeats until the simulation is over.
Ø The sequence of actions that a simulator is perform to advance the clock and build a new system snapshot is called the event-scheduling/ time-advance algorithm.
EVENT-scheduling/time-advance algorithm
Step 1: remove the eent notice for the imminent time from FEL.
Step 2: Advance CLOCK to imminent event time.
Step 3: execute imminent event, update system state. Change entity attributes and set membership as
Needed.
Step 4: generate future events and place their event notices on FEL ranked by event time.
Step 5: Update cumulative statistics and counters.
b. EXPLAIN THE TERMS/ CONCEPTS IN DISCREATE-EVENT SIMULATION.
Ans:
v SYSTEM : a collection of entities that interact together over time to accomplish one or more goals
v MODEL: an abstract representation of a system, usually containing structural, logical, or mathematical relationships which describe a system in terms of state, entities and their attributes, sets, processes, events, activities and delays.
v SYSTEM STATE: a collection of variables that contain all the information necessary to describe the system at any time.
v ENTITY: any object or component in the system which requires explicit representation in the model.
v ATTRIBUTES : the properties of the given entity
v LIST : a collection of the associated entities ordered in some logical fashion
v EVENT : an instantaneous occurrence that changes the state of a system as an arrival of a new customer
v EVENT NOTICE: a record of an event to occur at the current or some future time, along with any associated data necessary to execute the event; at a minimum the record includes the event type and the event time.
v EVENT LIST: a list of event notices for future events, ordered by time of occurrences also known as the future event list (FEL).
v ACTIVITY: duration of time of specified length, which is known when it begins.
v DELAY: Duration of time of unspecified in define length, which is not known until it ends.
v CLOCK: a variable representing simulated time.
2. For the grocery example mentioned in question 3, write the simulation table specifying the FEL, CHECKOUTLINE, and the cumulative statistics S, F and ND.
Solution:
Clock / LQ(t) / LS(t) / CHECKOUT LINE / FUTURE EVENT LIST / S / ND / F0 / 0 / 1 / (C1,0) / (A,1,C2)(D,4,C1)(E,60) / 0 / 0 / 0
1 / 1 / 1 / (C1,0)(C2,1) / (A,2,C3)(D,4,C1)(E,60) / 0 / 0 / 0
2 / 2 / 1 / (C1,0)(C2,1)(C3,2) / (D,4,C1)(A,8,C4)(E,60) / 0 / 0 / 0
4 / 1 / 1 / (C2,1)(C3,2) / (D,6,C2)(A,8,C4)(E,60) / 4 / 1 / 0
6 / 0 / 1 / (C3,2) / (A,8,C4)(D,11,C3)(E,60) / 9 / 2 / 1
8 / 1 / 1 / (C3,2)(C4,8) / (D,11,C3)(A,11,C5)(E,60) / 9 / 2 / 1
11 / 1 / 1 / (C4,8)(C5,1) / (D,15,C4)(A,18,C6)(E,60) / 18 / 3 / 2
15 / 0 / 1 / (C5,11) / (D,16,C5)(A,18,C6)(E,60) / 25 / 4 / 3
16 / 0 / 0 / (A,18,C6)(E,60) / 30 / 5 / 4
18 / 0 / 1 / (C6,18) / (D,23,C6)(A,23,C7) / 30 / 5 / 4
23 / 0 / 1 / (C7,23) / (A,25,C8)(D,27,C7)(E,60) / 35 / 6 / 5
3. Six dump trucks are used to haul coal from the entrance of a small mine to the railroad. Each truck is loaded by one of the 2 loaders. After loading, a truck immediately moves to the scale to be weighed as soon as possible. Both the loaders and the scale have a first come, first serve waiting line for trucks. Travel time from a loader to the scale is considered negligible. After being weighed a truck begins a travel time (during which time the truck unloads) and then afterwards returns to the loader queue. The distributions are given in tables 6.4, and 6.5, together with random digit assignment. Simulation to estimate the loader and scale utilizations (percentage of busy).