Simulation: Caiib Paper 1 (Module B), Unit 8
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So, here we are providing “Unit 8: Simulation” of “Module B: Business Mathematics” from “Paper 1: Advanced Bank Management (ABM)”.
The Article is Caiib Unit 8: Simulation
Simulation is appropriate to situations where size and/or complexity of the problem make the use of other techniques difficult or impossible. For example, queuing problems have been extensively studied through simulation. Some types of inventory problems, layout and maintenance problems also can be studied through simulation. Simulation can be used with traditional statistical and management techniques.
Simulation is useful in training managers and workers in how the real system operates, in demonstrating the effects of changes in system variables and real-time control. Simulation is extensively used in driving lessons. The person who learns driving is made to face the real road situations (traffic jams and other problems) during learning, so that serious accidents can be avoided. Simulation is commonly used in financial world such forex, investment and risk management areas.
Application of simulation methods:
- Air Traffic control queuing
- Aircraft maintenance scheduling
- Assembly line scheduling
- Inventory reorder design
- Railroad operations
- Facility layout
- Risk modeling in finance area.
- Foreign exchange market
- Stock market
The owner of an outlet wishes to evaluate his daily ordering policy. His current rule is order the demand of the previous day. But he has started thinking recently that he should follow better methods to decide the quantum of order.
He purchases milk at Rs 12 and sells at Rs 16. He orders his requirement at the end of the day and gets the milk in the morning. From past experience, the vendor assessed that his demand is between 30 and 80 liters per day.
He also kept a record of relative frequency of the quantity demanded during the last 10 days. Now he thinks of a new ordering rule — mean of quantity sold in the last 10 days.
He maintained the sales in a tabular form. The table has two columns. The first column shows the Demand and the second one shows the Relative frequency, that is, in the selected period of 10 days, how many times such demand occurred.
|Demand per day in Litres||Relative Frequency|
|35||1/ 10, that is, only one day, out of ten
days, demand of 35 litres occured
|45||3/10, that is, only three days, out of
ten days, demand of 45 litres occured
|55||2 /10, that is, only two days, out of
ten days, demand of 55 litres occured
|65||3/10, that is, only three days, out of
ten days, demand of 65 litres occured
|75||1/10, that is, only one day, out of ten
days, demand of 75 litres occured
He settles for the ordering rule[(35 × 0.1) + (45 × 0.3) + (55 × 0.2) + (65 × 0.3) + (75 × 0.1)] = 55 litres.
So we have 2 rules: Old rule and New rule. Representing mathematically,
Old rule = quantity demanded on previous day is equal to D (n – 1).
New rule = Mean of the past 10 days is equal to 55
Now let us compare these orders in terms of profits.
Profit ‘P’ is equal to (Sold Quantity × selling price (p)) – (Ordered quantity × cost price (c)).
Assume that the unsold milk packets are thrown away as they are perishable. Now to prepare for simulation, we have to develop a method for demand generation. Let us use the probability distribution of demand and random numbers to generate a demand for the next 20 days.
Now arrange the chance process to generate occurrences in the system.
|Demand Per Day||Relative
|35||1/ 10||0.1||00 to 09|
|45||3/10||0.3||10 to 39|
|55||2/10||0.2||40 to 59|
|65||3/ 10||0.3||60 to 89|
|75||1/ 10||0.1||90 to 99|
With the above table and random numbers, we develop the demand for 20 days.
Step 1: Choose a random number.
Step 2: Find the random number interval associated with the random number.
Step 3: Read the daily demand corresponding to the random number interval.
Step 4: Assume D = 55 litres for day 0
Step 5: Calculate the quantity sold. Quantity sold will be lesser of the demand D or Quantity ordered Q1 (or Q2)
Step 6: Profit = (Sold quantity × selling price) – (Ordered quantity × cost price).
Selling Price is Rs 16 per litre and cost price is Rs 12 per litre
Step 7: Do all steps for 20 days to simulate.
(demand related to respective random number interval)
(quantity ordered based on demand of previous day)
(quantity sold under old method) (lesser of D and Q1)
(rupees) profit under old method (16 into S1)- (12 into
(quantity ordered) (mean of quantity sold in last ten days)
(quantity sold under new method) (lesser of D and Q2)
(rupees) profit under old method (16 into S1)- (12 into
We now see that the average demand according to simulation is 56 litres, Average sales is 50 litres, according to old method; and 50.5 litre according to new method. Average order is 55.50 litres under old method, whereas 55 hires under new method.
Thus you would find that profitability improves under the new method.
|DEFINE PROBLEM||Define objectives and variables|
|CONSTRUCT THE SIMULATION MODEL||Specification of variables, parameters, decision rules, probability distribution and time incrementing procedure — (fixed or variable)|
|SPECIFY VALUES OF PARAMETERS & VARIABLES RUN THE SIMULATION||Determine starting conditions and run length|
|EVALUATE RESULTS||Determine statistical tests|
|PROPOSE NEW EXPERIMENT||Compare with other information|
Simulation is desirable when experiments on the real system
- Would disrupt ongoing activities;
- Would be too costly to undertake;
- Require many observations over an extended period of time;
- Do not permit exact replication of events; and
- Do not permit control over key variables.
Simulation is preferable when a mathematical model
- is not available to handle the problem;
- is too complex and arduous to solve;
- is beyond the capability of available personnel; and
- is not robust enough to provide information on all factors of interest.
- Time consuming.
- Requires computer experience and expertise on the part of the user.
- Impossibility of quantifying and difficulty of casting complex problems in a format may cause difficulties; but simulations can be made to run under any type of assumption and these flaws can be overlooked.
- In spite of widespread applications, there are very few principles to guide the user in making decisions on what to include in the model and the length and number of simulation runs. This will be more like an art than science. The user has to use his intuitive judgments.
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