# An Integrated Capacity Allocation and Dynamic Pricing Model Designed for Air Cargo Transportation
## 2 Materials, Methods, and Models
### Dynamic Pricing  
Price is one of the most flexible marketing elements, with a direct and short-term impact on a company's profitability and cost effectiveness. To improve economic and financial performance, companies should define their pricing policies according to a basic systematic understanding of internal capacities and customer needs and wants, as well as market conditions, such as economic conditions and the degree of competition [27]. These multifaceted factors must be meticulously considered during the formulation of dynamic pricing models. In the context of air cargo transportation, a notable example of a dynamic pricing problem arises when attempting to optimize revenue by allocating predefined capacity during a designated planning period, a strategy that necessitates the implementation of dynamic pricing methodologies. In the field of transport, dynamic pricing practices have been shown to offer advantages to both shippers and carriers. These pricing strategies benefit carriers by reducing transport costs during off-peak periods and by influencing customers to make purchases during these times. This, in turn, contributes to the supply chain by increasing demand. Conversely, carriers are able to maximize their revenue by adapting to market changes and fluctuations in demand through dynamic pricing [28]. The presence of both fixed and variable costs within the sector is a key factor in the determination of pricing strategies. A variety of variable costs, including fuel charges, labor costs, storage costs, and the cost of alternative modes of transport (e.g., land transport, sea transport, etc.) utilized in addition to the flight route for cargo delivery to its final destination, contribute to the overall cost structure. Variable costs exhibit fluctuations in accordance with the volume of cargo, with an increase in cargo volume resulting in a corresponding rise in variable costs. [PERSON] and colleagues [5] incorporated weight and volume capacities, booking type, weight and volume distribution, and cargo type into their dynamic pricing study for air cargo revenue management. [PERSON] et al. [29] incorporated product weight and type, seasonality, distance, origin and destination countries, crude oil price, capacity, and demand inputs into their dynamic pricing model for air cargo transport. [PERSON] and [PERSON] [30] incorporated a comprehensive set of factors into their study, including demand, priority, cargo type, service quality (e.g., flight frequency, aircraft service reliability), fixed and variable cost of aircraft type, flight distance, flight frequency, capacity, and cargo volume. This study aimed to develop a model for pricing and scheduling strategies for air cargo carriers. The development of the model incorporated insights from sector experts and a thorough literature review. The route of the flight constitutes the most significant input variable in determining the price, with demand and market conditions along the route exerting an influence on the final price. The model incorporates a range of inputs to ensure comprehensive analysis, including the type of aircraft selected based on its impact on capacity, the date of the flight to account for seasonal variations, the product's tonnage, and the time remaining until the flight. The model inputs are listed below:  
Origin: The city where the sale is made. Destination: The destination city of the cargo shipped. Flight type: It is the type of aircraft in which the flight will take place, including passenger and cargo aircraft. Flight month: The flight was scheduled for the month of the year. Remaining time to flight: The remaining days indicator ranges from 0 to 30. A value of 0 signifies that the sale was executed on the day of the flight, while higher values indicate subsequent days. Tonnage: The weight in kilograms of the cargo sold (i.e., the priceable weight)  
Capacity: The capacity of the aircraft to perform the flight in terms of weight. Total tonnage of flight: Total weight of the flight.