Effective Strategies for Wait Line Management and Revenue Optimization
Effective Strategies for Wait Line Management
Variability in inter-arrival and processing times can cause confusion in managing wait lines. However, understanding and controlling this variability can be turned into a competitive advantage. The net profit can be calculated as the expected profit minus the cost of variability. Raising the cost of waiting increases the optimal service capacity, while increasing the cost of service lowers it. Pooling resources is a more efficient approach.
- Capacity Utilization: (R x P) / m
- CVa: Standard Deviation / Average Inter-arrival Time
- CVp: Standard Deviation / Average Processing Time
Reducing Queue Length (Iq)
To reduce queue length, consider the following:
- Decrease U:
- Reduce demand rate
- Reduce processing time
- Increase the number of servers
- Increase m
- Decrease CVa and CVp
T = (Iq / R) + p
Excessive wait times can lead to customer abandonment or corner-cutting. To mitigate this, focus on reducing process time through:
- Worker specialization
- Process redesign
- Engaging customers (simplification, pre-processing)
- Technology implementation
Customer Experience Effects
Customer assessments are based on:
- Sequence Effect: The trend in the sequence of pain or pleasure, high and low points, and the ending.
- Duration Effect: People often don’t notice how long a task takes, but they get increasingly irritated as time passes.
- Rationalization Effect: People want things to make sense (e.g., queue numbers).
Linear Programming
Linear Programming (LP) is a modeling technique for optimally allocating limited resources among competing activities. It was developed by George B. Dantzig (1914-2005).
Steps in Linear Programming
- Identify:
- Input parameters
- Decision variables
- Objective function
- Resources & constraints
- Write down the mathematical model
- Solve the LP problem
- Interpret the solution
- Perform sensitivity analysis
Assumptions in Linear Programming
- Resources are limited
- Linearity: The objective function and constraints are linear
- Certainty: Values of parameters are known and constant
- Divisibility of products and resources
Sensitivity Analysis
The sensitivity report allows us to quantify the value of our resources. A shadow price of 0 means adding extra resources will have no impact. The change in the final value can be calculated as: Change in Resource x Shadow Price.
The objective coefficient represents the profit margins on a product. Reduced costs indicate how much we need to alter the objective coefficient to become profitable.
Interpretation for Range
- How much we can change the Right-Hand Side (RHS) without the shadow price changing.
- How much we can change each objective coefficient without changing the optimal solution.
Sensitivity analysis corresponds to the impact of perturbing some of the input parameters of the model. The focus is on the RHS of the constraints and the coefficients of the objective function. Consider one-at-a-time changes.
Revenue Management
Revenue Management is the science of selling the right item to the right person at the right price, especially with limited capacity and uncertain demand. Price is used as a lever. Ideally, you would charge every person their individual reservation price, but this is unrealistic.
Conditions Favoring Revenue Management
- Customer heterogeneity
- Demand variability and uncertainty
- Fixed selling horizon/perishable goods
- Production inflexibility
- Price is not a signal for quality
- Data and Information Systems (IS) infrastructure exist
Airline Example
Capacity: 100 seats
Two Classes:
- Business: $499 / Demand = Normal(25, 5)
- Leisure: $99 / Demand = Normal(120, 20)
How to decide how many business seats to reserve:
- Overstocking Cost: $99
- Understocking Cost: $400
- Probability (Business demand < reserved seats): Under Cost / (Under Cost + Over Cost)
- Answer: NORMINV(400/499, 25, 5) = 29.24 seats