Assignment #

$3$

$$

$$Simulation

$($

$1$

$0$

$$marks

$)$

$$Topic: Balancing Process Capacity Objective: A car wash company wants to maximize its capacity utilization and total profits for the eight

$-$

hour workday

$($

$9$

:

$0$

$0$

$$am to

$5$

:

$0$

$0$

$$pm

$)$

$.$

$$The operations manager of this company should work on two scenarios

$($

challenges

$)$

:

$($

a

$)$

$$the no variation and

$($

b

$)$

$$the variation. In the former scenario, there is no variability in demand and process

$($

supply

$)$

$,$

$$while in the latter scenario, variability is present. Key concepts: Capacity utilization; Cycle time; Throughput: flow rate

$($

or throughput rate

$)$

$$and flow time

$($

or throughput time

$)$

; Inventory

$($

or work

$-$

in

$-$

process

$)$

; Little

$$

s law; Variability in demand and process Specifications: The customer arrival rate varies according to the time of day, with a peak in demand from

$1$

$2$

:

$0$

$0$

$$pm to

$1$

:

$0$

$0$

$$pm

$.$

$$Serving as the operations manager of the car wash company, you are responsible for allocating the company

$$

s entire budget of $

$3$

$$million to the three stages of the process

$($

i

$.$

e

$.$

$,$

$$the vacuum, the machine wash, and

$/$

or the hand dry stations

$)$

$$to maximize efficiency and thereby overall profitability. Questions

$1$

$.$

$$Please work on two scenarios

$/$

challenges

$($

i

$.$

e

$.$

$,$

$$no variation and variation

$)$

$$and run the simulations as many times as you want to identify the:

$($

a

$)$

$$maximum profit,

$($

b

$)$

$$optimal number of cars should be washed to maximize profits,

$($

c

$)$

$$optimal budget

$($

available budget: $

$3$

$$million

$)$

$$allocation to the three stages. Tip: the optimal budget allocation for Challenge

$1$

$($

i

$.$

e

$.$

$,$

$$no variation

$)$

$$is as follows: Vacuum: $

$1$

$,$

$0$

$0$

$0$

$,$

$0$

$0$

$0$

; Wash: $

$5$

$0$

$0$

$,$

$0$

$0$

$0$

; Hand Dry: $

$1$

$,$

$5$

$0$

$0$

$,$

$0$

$0$

$0$

; Profit: $

$8$

$2$

$5$

$.$

$$Challenge

$2$

:

Process information before investment:

Vacuum and Trash Removal: Min

$2$

$2$

$.$

$5$

$,$

$$Mode

$3$

$6$

$.$

$0$

$,$

$$Max

$4$

$0$

$.$

$5$

$,$

$$Upgrade: $

$1$

M buys

$+$

$1$

$.$

$5$

$$cars

$/$

$$hr

Machine Wash: Min

$1$

$8$

$.$

$8$

$,$

$$Mode

$3$

$0$

$.$

$0$

$,$

$$Max

$3$

$3$

$.$

$8$

$,$

$$Upgrade: $

$1$

M buys

$+$

$1$

$5$

$$cars

$/$

hr

Hand Dry and Windows: Min

$2$

$1$

$.$

$0$

$,$

$$Mode

$2$

$4$

$.$

$0$

$,$

$$Max

$3$

$3$

$.$

$0$

$,$

$$Upgrade: $

$1$

M buys

$+$

$9$

$$cars

$/$

$$hr$.$ run one: vacuum: $1,150,000,$ wash: $450,000,$ hand dry: $1,400,000$ resulted in profit of $635.$ run two: vacuum: $1,450,000,$ wash: $500,000,$ hand dry: $1,050,000$ resulted in profit of $660.$ run three: vacuum: $1,150,000,$ wash: $550,000,$ hand dry: $1,300,000$ resulted in profit of $675.$ run four: vacuum: $1,275,000,$ wash: $625,000,$ hand dry: $1,100,000$ resulted in profit of $685.$ taking these information into account how much money should i allocate to the three variables to get the optimal profit?