SIMULATION OF DEMAND FORECASTING PROBLEM - Quantitative Techniques for management

Simulation Problems and Solutions in Operations Research

The simulation problems and solutions in operations research are mentioned below

Example : An ice-cream parlor's record of previous month’s sale of a particular variety of ice cream as follows (see Table).

Simulation of Demand Problem

Simulation of Demand Problem

Simulate the demand for first 10 days of the month

Solution: Find the probability distribution of demand by expressing the frequencies in terms of proportion. Divide each value by 30. The demand per day has the following distribution as shown in table.

Probability Distribution of Demand

Probability Distribution of Demand

Find the cumulative probability and assign a set of random number intervals to various demand levels. The probability figures are in two digits, hence we use two digit random numbers taken from a random number table. The random numbers are selected from the table from any row or column, but in a consecutive manner and random intervals are set using the cumulative probability distribution as shown in Table.

Cumulative Probability Distribution

Cumulative Probability Distribution

To simulate the demand for ten days, select ten random numbers from random number tables. The random numbers selected are, 17, 46, 85, 09, 50, 58, 04, 77, 69 and 74 The first random number selected, 7 lies between the random number interval 17-49 corresponding to a demand of 5 ice-creams per day. Hence, the demand for day one is 5. Similarly, the demand for the remaining days is simulated as shown in Table.

Demand Simulation

Demand Simulation

Example : A dealer sells a particular model of washing machine for which the probability distribution of daily demand is as given in Table.

Probability Distribution of Daily Demand

Probability Distribution of Daily Demand

Simulation Problems using Random numbers

The simulation problems using random numbers are given below

Find the average demand of washing machines per day.

Solution: Assign sets of two digit random numbers to demand levels as shown in Table.

Random Numbers Assigned to Demand

Random Numbers Assigned to Demand

Ten random numbers that have been selected from random number tables are 68, 47, 92, 76, 86, 46, 16, 28, 35, 54. To find the demand for ten days see the Table below.

Table 15.7: Ten Random Numbers Selected

Ten Random Numbers Selected

Average demand =28/10 =2.8 washing machines per day. The expected demand /day can be computed as,
Expected demand per day

Expected demand per day

where, pi = probability and xi = demand

= (0.05 × 0) + (0.25 × 1) + (0.20 × 2) + (0.25 × 3) + (0.1 × 4) + (0.15 × 5)
= 2.55 washing machines.

The average demand of 2.8 washing machines using ten-day simulation differs significantly when compared to the expected daily demand. If the simulation is repeated number of times, the answer would get closer to the expected daily demand.

Example : A farmer has 10 acres of agricultural land and is cultivating tomatoes on the entire land. Due to fluctuation in water availability, the yield per acre differs. The probability distribution yields are given below:

a. The farmer is interested to know the yield for the next 12 months if the same water availability exists. Simulate the average yield using the following random numbers 50, 28, 68, 36, 90, 62, 27, 50, 18, 36, 61 and 21, given in table.

Simulation Problem

Simulation Problem

b. Due to fluctuating market price, the price per kg of tomatoes varies from Rs. 5.00 to Rs. 10.00 per kg. The probability of price variations is given in the Table below. Simulate the price for next 12 months to determine the revenue per acre. Also find the average revenue per acre. Use the following random numbers 53, 74, 05, 71, 06, 49, 11, 13, 62, 69, 85 and 69.

Simulation Problem

Simulation Problem

Solution:

Table for Random Number Interval for Yield

Table for Random Number Interval for Yield

Table for Random Number Interval for Price

Table for Random Number Interval for Price

Simulation for 12 months period

Simulation for 12 months period

Average revenue per acre = 21330 / 12
= Rs. 1777.50

Example : J.M Bakers has to supply only 200 pizzas every day to their outlet situated in city bazaar. The production of pizzas varies due to the availability of raw materials and labor for which the probability distribution of production by observation made is as follows:

Simulation Problem

Simulation Problem

Simulate and find the average number of pizzas produced more than the requirement and the average number of shortage of pizzas supplied to the outlet.

Solution: Assign two digit random numbers to the demand levels as shown in table

Random Numbers Assigned to the Demand Levels

Random Numbers Assigned to the Demand Levels

Selecting 15 random numbers from random numbers table and simulate the production per day as shown in table below.

Simulation of Production Per Day

Simulation of Production Per Day

The average number of pizzas produced more than requirement
= 12/15
= 0.8 per day
The average number of shortage of pizzas supplied
= 4/15
= 0.26 per day


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