Simulation
Simulation is a common management science technique. It is typically used to model random processes that are too complex to be solved with analytical formulas. One disadvantage of simulation is that there is no guarantee that you preformed enough trials so your conclusions are accurate.

One begins a simulation by developing a mathematical statement of the problem.
The model should be realistic yet solvable within the speed and storage constraints of the computer system being used. Input values for the model as well as probability estimates for the random variables must then be determined.

Simulation and Inventory Analysis
Probability and Random Number Interval (RNI) for Daily Ingredients Demand Demand for Ingredients (Boxes) | Frequency (Days) | Probability | Cumulative Probability | RNI | 0 | 5 | 0.04 | 0.04 | 01 to 04 | 10 | 20 | 0.14 | 0.18 | 05 to 18 | 20 | 15 | 0.11 | 0.29 | 19 to 29 | 30 | 25 | 0.18 | 0.46 | 30 to 46 | 40 | 30 | 0.21 | 0.68 | 47 to 68 | 50 | 45 | 0.32 | 1.00 | 69 to 00 | Total | 140 | 1.00 | | |

Probability and Random Number Interval (RNI) for Reorder Lead Time Lead Time (Days) | Frequency (Orders) | Probability | Cumulative Probability | RNI | 1 | 10 | 0.17 | 0.17 | 01 to 17 | 2 | 20 | 0.33 | 0.50 | 18 to 50 | 3 | 30 | 0.50 | 1.00 | 51 to 00 | Total | 60 | 1.00 | | |

The probability for a given variable is normally obtained through the historical outcomes of the organization. But, it is difficult to gain such kind of data which are private and confidential to every organization. Thus, we will assume that the probabilities is distributed normally. Gong Cha has decided to place an order of 100 boxes of ingredients when there are only left 15 boxes of ingredients. Gong Cha stimulate 10 days of operation whereas assuming that there are 50 boxes of ingredients left in the current inventory.
Gong Cha’s First Inventory Stimulation

Order Quantity = 100

Reorder Point = 15

Random Number = 56, 74, 54, 31, 62, 37, 33, 33, 82, 68, 50, 22, 27

Day | Boxes Received | Beginning Inventory | RN | Demand | Ending Inventory | Lost Sales | Order? | RN | Lead Time | 1 | 0 | 50 | 56 | 40 | 10 | 0 | Yes | 74 | 3 | 2 | 0 | 10 | 54 | 40 | 0 | 30 | No | | | 3 | 0 | 0 | 31 | 30 | 0 | 30 | No | | | 4 | 0 | 0 | 62 | 40 | 0 | 40 | No | | | 5 | 100 | 100 | 37 | 30 | 70 | 0 | No | | | 6 | 0 | 70 | 33 | 30 | 40 | 0 | No | | | 7 | 0 | 40 | 33 | 30 | 10 | 0 | Yes | 82 | 3 | 8 | 0 | 10 | 68 | 40 | 0 | 30 | No | | | 9 | 0 | 0 | 50 | 40 | 0 | 40 | No | | | 10 | 0 | 0 | 22 | 20 | 0 | 20 | No | | | Total | | | | | 130 | 190 | | | |

Analyzing Gong Cha’s Inventory Costs
Average Ending Inventory = Total Ending Inventory / Operation Time = 130 / 10 = 13 boxes per day

Average Lost Sales = Total Lost Sales / Operation Time = 190 / 10 = 19 boxes per day

Average Number of Orders Placed = Number of Orders Place / Operation Time = 2 / 10 = 0.2 orders per day

The above calculations show that how the average Ending Inventory, Lost Sales and Number of Orders Placed being calculate. We can conclude that the average Lost Sales has a higher value that Average Ending Inventory. Whereas, Gong Cha is having a lost sales of 19 boxes of ingredients and an average inventory of 13 boxes per day. This occurs due to insufficient of ingredients to produce a number of beverage to fulfill the demands of the customers. Even though Gong Cha is ordering 100 boxes of ingredients each time when it reach its reorder point of 15 boxes, the quantity still do not meet the wants of the customers.

In order to solve this issue, Gong Cha can increase the order quantity each time to 150 boxes of ingredients and will also increase the sales of Gong Cha. Also, increasing the reorder point to 20 boxes will also help to solve this situation.

New Adjustment of Gong Cha’s First Inventory Stimulation

Adjusted Order Quantity = 150

Adjusted Reorder Point = 20

Day | Boxes Received | Beginning Inventory | RN | Demand | Ending Inventory | Lost Sales | Order? | RN | Lead Time | 1 | 0 | 50 | 56 | 40 | 10 | 0 | Yes | 74 | 3 | 2 | 0 | 10 | 54 | 40 | 0 | 30 | No | | | 3 | 0 | 0 | 31 | 30 | 0 | 30 | No | | | 4 | 0 | 0 | 62 | 40 | 0 | 40 | No | | | 5 | 150 | 150 | 37 | 30 | 120 | 0 | No | | | 6 | 0 | 120 | 33 | 30 | 90 | 0 | No | | | 7 | 0 | 90 | 33 | 30 | 60 | 0 | No | | | 8 | 0 | 60 | 82 | 50 | 10 | 0 | Yes | 68 | 3 | 9 | 0 | 10 | 50 | 40 | 0 | 30 | No | | | 10 | 0 | 0 | 22 | 20 | 0 | 20 | No | | | Total | | | | | 290 | 150 | | | |

Average Ending Inventory = 290 / 10 = 29 boxes per day

Average Lost Sales = 150 / 10 = 15 boxes per day

When the Order Quantity is increased to 150 boxes of ingredients and the reorder point increase to 20 boxes, then Gong Cha can have a lower lost sales which is 15 boxes per day and a higher inventory of 29 boxes per day.

From this situation we can see that simulation helps to resolve the management’s concern by providing the quantitative data to provide an aid in the process decision making. Moreover, Gong Cha will be more confirmed with their decision to expand their business throughout the Asia when they base on the simulation result.

‘What-if’ Problem:
Simulation also allow to solve the ‘what-if’ question.
“What if the Gong Cha is going to open an outlet nearby Chatime and Ding Tea?”
By using the simulation software, management team will be able to try out a few of new policy decisions and view the results. In addition, simulation will also bring benefit like complementing with the actual information that gained from other resources.

Simulation of Gong Cha Queuing Problem
Data for Gong Cha’s Customer Arrivals Inter Arrival Time (Minutes) | Frequency | Probability | Cumulative Probability | RNI | 0 | 10 | 0.06 | 0.06 | 01 to 06 | 1 | 20 | 0.12 | 0.18 | 07 to 18 | 2 | 25 | 0.15 | 0.32 | 19 to 32 | 3 | 50 | 0.29 | 0.62 | 33 to 62 | 4 | 30 | 0.18 | 0.79 | 63 to 79 | 5 | 35 | 0.21 | 1.00 | 80 to 00 | Total | 170 | 1.00 | | |

Data for Gong Cha’s Service Time Service Time (Minutes) | Frequency | Probability | Cumulative Probability | RNI | 1 | 5 | 0.04 | 0.04 | 01 to 04 | 2 | 10 | 0.08 | 0.13 | 05 to 13 | 3 | 20 | 0.17 | 0.29 | 14 to 29 | 4 | 30 | 0.25 | 0.54 | 30 to 54 | 5 | 35 | 0.29 | 0.83 | 55 to 83 | 6 | 20 | 0.17 | 1.00 | 84 to 00 | Total | 120 | 1.00 | | |

Queuing Simulation of Gong Cha Customer Arrivals and Service Time Customer Number | RN | Inter Arrival Time | Arrival Time | RN | Service Time | Start Service | End Service | Wait Time | Idle Time | 1 | 52 | 3 | 3 | 99 | 6 | 3 | 9 | 0 | 3 | 2 | 37 | 3 | 6 | 78 | 5 | 9 | 14 | 3 | 0 | 3 | 82 | 5 | 11 | 56 | 5 | 14 | 19 | 3 | 0 | 4 | 69 | 4 | 15 | 60 | 5 | 19 | 24 | 4 | 0 | 5 | 98 | 5 | 20 | 44 | 4 | 24 | 28 | 4 | 0 | 6 | 96 | 5 | 25 | 57 | 5 | 28 | 33 | 3 | 0 | 7 | 33 | 3 | 28 | 82 | 5 | 33 | 38 | 5 | 0 | 8 | 50 | 3 | 31 | 23 | 3 | 38 | 41 | 7 | 0 | 9 | 88 | 5 | 36 | 64 | 5 | 41 | 46 | 5 | 0 | 10 | 90 | 5 | 41 | 49 | 4 | 46 | 50 | 5 | 0 | Total | | 41 | | | | | | 39 | 3 |

Based on the above table, Gong Cha starts time is at 0, but the staffs start to provide service at the time of 3. Thus, within the time of 0 to 3 it can be classified as the idle time. Inter Arrival Time is the time between the successive customers arrivals. So, by adding in the Inter Arrival Time, we will know when the customers will arrive. Service time is the time taken for the staff to make the beverages and we will get the end of service time by adding in service time to the start of service time. Waiting time is the time that the customers need to wait till their turn. We can get it by deducting the arrival time from the start service time.

Average of Inter Arrival Time = Total Inter Arrival Time / Number of Customers = 41 / 10 = 4.1 inter arrival time per customer

Average Wait Time = Total Wait Time / Number of Customers = 39 / 10 = 3.9 wait time per customer

Average Idle Time = Total Idle Time / Number of Customers = 3 / 10 = 0.3 idle time per customer