Operations Management: Balancing Process Capacity – Simulation Exercise Approach for the recommended budget allocation The three stages of the car wash operation: vacuum, machine wash, and hand dry stations need an allocation of the budget of total $3M. Given the constraint and operational efficiency of each stage, the allocation of $1M, $0.5M and $1.5M in the respective stages will improve operations and maximize the overall profitability to $825 with 100% capacity utilization at each stage. The above solution is calculated taking the flow rate as the main parameter for optimizing the entire process. Hence the flow rate is considered the most relevant metric. Given we must meet the constant demand of the car wash at each station, the number of blocked cars in between any stations needs to minimize, which can be achieved when the capacity flow rate of the all the machines processed at each stage is same and maximum. The total time per unit car at each stage are: Machine Initial Capacity The time required for each car Vacuum and Trash Control 36 Cars per hour 1.67 Minutes Machine Wash 30 Cars per hour 2 Minutes Hand dry 24 Cars per hour 2.5 Minutes “Hand Dry” has an initial capacity of 24 cars per hour hence contributing to the maximum time per car, leading hand dry to a bottleneck. Thus, to improve efficiency and profitability, a larger proportion of investment is required in this step of the process. Simulation output: The above graph has been created based on different combination of budget allocation and their respective profit generated. Exploring various alternate options and their profit trend, we could say that the budget that provided the optimal maximum profit of $825 was $1M in Vacuum, $0.5M in Wash and $1.5M in Dry. Rest any other combination led to a lower profit than $825. The same can also be derived from mathematical calculation discussed below Calculations for budget allocation As mentioned above, for maximizing the efficiency, the capacity should be maximized and equal at each stage. Let this final capacity at which each stage is operating be “x”. Since the rate at which capacity can be increased is different at each stage, the detailed working for the budget allocation is summarized below : Machine Capacity rate from Change in capacity The budget needed for $1M investment from the initial set up the increased capacity Vacuum and Trash 1.5 cars per hour x-36 (x-36)/1.5 Machine Wash 15 cars per hour x-30 (x-30/15 Hand dry 9 cars per hour x-24 (x-24)/9 Now, the sum of the budget needed for the increased capacity at each stage should amount to $3M. Hence, ( x−36) (x−30) (x −24) =3 + + 9 1.5 15 Solving this equation gives x = 37.5 cars per hour. The allocated budget for hand dry can be calculated by substituting the value of x in the table, hence (37.5-24)/9 = $1.5 M. Similarly, the budget required for the other steps in the process also get calculated: Vacuum machine gets $1M and Machine wash gets $0.5 M. The profit from this budget distribution gives the optimal profit of $825