Probability- 3 Way Branch

Example 5: Probability- 3 Way Branch

Extra Credit IE 429

Professor: Sima Parisay

Vanessa Condie Richard Quach Valeria Ramirez

January 25, 2011 Probability 3Way-Branch Concepts:

The probability 3 way feature used in Arena is applicable after the “Decide” branch. This illustrates the three possible outcomes with each having a different set probability. The total of all three outcomes must equal one hundred percent. This feature is widely used in situations in which we want to know the amount or number of parts, components, units, etc that would be distributed to three different locations. For example, a company makes TV’s, radios, and VCR’s and would like to know how many of each unit will be sent to the three different electronics stores that they distribute to, depending on the demand that each product has at the various locations. Another situation would be when distributing the number of frozen pizzas to Costco, SAMS Club and WINCO, we would want to know how much each store would need. The importance of the probability lies in the fact that it tells the program what percentage of each item (TV’s, radios, VCR’s, pizzas) should be allocated to the designated location. If we were not to take this into account, we would not be able to meet the demand of each store, and also would not be able to run the program properly.

Steps Used to Create a Probability-3 Way in Arena:

1. Create- Here we choose as many entities as specified in the problem statement.

2. Process- This is where all the entities meet in order to go through the process that they are subject to. When the entities go through a process they each have a specific distribution. 3. Decide- This is where the probabilities are being accounted for. It must consist of three branches with their respective percentages. At this point only two percentages will suffice, given that the third percentage will be automatically accounted for.

4. Record- This feature represents the count for each of the entities that have gone through the process given their assigned percentages. The count represents the amount that is leaving the system to its specified location.

5. Dispose- This is where each of the entities gets released or leaves the system.

Our Example:

Problem Statement-

A beverage company produces three different types of beverages: juice, energy drinks, and soda. There are three locations that the beverage company distributes to: grocery store, gas station, and restaurants. However, the demand at grocery stores is 45% and 30% at gas stations. The beverages arrive to the packing station with an exponential distribution with an average of 5 hrs for the juice, 8 hrs for the energy drinks, and 10 hrs for the sodas. The beverages leave the packing station with a mean of 2 hrs. Then the beverages go through inspection and then distributed to their specific locations. The company would like to know how many of each beverage will be distributed to their respective locations. Run the simulation for 10,000 hours. Logical Model-

Snapshots from Arena-

Model designed in Arena “Decide” branch displaying probabilities Results from Running Our Model Verification-

Item Arrival Simulation Simulation/Arriva Arena Time Time l Output of Items Juice 5 hrs 10,000 hrs 2,000 2,003 Energy 8 hrs 10,000 hrs 1,250 1,255 Drink Soda 10 hrs 10,000 hrs 1,000 981

Report to Manager- Dear Manager,

Your company approached us asking us to find the number of beverages distributed to each specific location. This is important to your company because you would like to know how much of your production is being focused on each beverage. From historical data we found the demand of the three beverages for each location. Grocery stores have the highest demand and restaurants have the lowest. Therefore, for our simulation we assigned probabilities to match the demand from the locations. Since, grocery stores have the highest demand we gave it a probability of 45% and restaurants have the lowest priority so we assigned it a probability of 25%.

For this simulation we looked at time period of 10,000 hours. From the 10,000 hours of production time we observed 4,239 total beverages are being distributed. A total of 2,003 juices produced, 981 sodas produced, and 1,255 energy drinks produced. Grocery stores received the highest amount of beverages, 1,871. Restaurants received the lowest amount of 1,050 beverages and gas stations received 1,318 beverages.

We hope that our analysis of your production of beverages helped you understand the total amount of beverages produced and how many are being distributed to your three locations.