Standard RM Systems

E

Bases: RmSys

A standard RM system of type "E".

This RM system uses leg-level seat allocation controls with EMSR-B optimization, along with EM untruncation and standard leg forecasting.

Parameters:

emsr_variant ((b, a), default: 'b' ) –

Specifies which variant of the EMSR algorithm to use, either 'b' for EMSR-B, or 'a' for EMSR-A. At this time only 'b' is supported.
forecast_algorithm ((additive_pickup, exp_smoothing, multiplicative_pickup), default: 'additive_pickup' ) –

Specifies which leg-level forecasting algorithm to use for generating leg demand forecasts. Options are 'additive_pickup', 'exp_smoothing', or 'multiplicative_pickup'. The default is 'additive_pickup'.

Notes

This RM system consists of the following actions executed in order:

EM Untruncation of Leg Demands This step applies the EM algorithm to untruncate observed leg sales into inferred true demand levels. It runs only once at the beginning of each sample day, and detruncates demand for all timeframes.
Standard Leg Forecasting This step generates leg-level demand forecasts using a standard class-based forecasting algorithm (additive pickup by default). It runs full computations to produce leg forecasts for the entire booking horizon in one pass at the beginning of each sample day, and on later DCPs it simply moves a pointer forward through that array of forecasts to provide the correct forecast values at that time.
EMSR-B Optimization Optimizes leg-level seat availability using the Expected Marginal Seat Revenue Version B (EMSR-B) algorithm. This step runs on each DCP to update the seat availability controls based on the current leg forecasts, current sales, and the EMSR optimization logic.

availability_control `class-attribute` `instance-attribute`

availability_control = 'leg'

This RM system uses leg-level class allocation availability controls.

P

Bases: RmSys

A standard RM system of type "P".

This RM system uses path-level bid price controls with Pro-BP optimization, along with EM untruncation and standard leg forecasting.

Parameters:

forecast_algorithm ((additive_pickup, exp_smoothing, multiplicative_pickup), default: 'additive_pickup' ) –

Specifies which leg-level forecasting algorithm to use for generating leg demand forecasts. Options are 'additive_pickup', 'exp_smoothing', or 'multiplicative_pickup'. The default is 'additive_pickup'.
bid_price_vector (bool, default: True ) –

If True, enables bid price vector optimization in ProBP. If False, uses scalar bid prices.

Notes

This RM system consists of the following actions executed in order:

EM Untruncation of Path Demands This step applies the EM algorithm to untruncate observed path sales into inferred true demand levels. It runs only once at the beginning of each sample day, and detruncates demand for all timeframes.
Standard Path Forecasting This step generates path-level demand forecasts using a standard class-based forecasting algorithm (additive pickup by default). It runs full computations to produce path forecasts for the entire booking horizon in one pass at the beginning of each sample day, and on later DCPs it simply moves a pointer forward through that array of forecasts to provide the correct forecast values at that time.
Path Forecast Daily Decay Adjustment This step applies a daily decay adjustment to the path-level forecasts, to account for the changes in expected demand to come in between DCPs. It runs every day that isn't a DCP, to adjust the path forecasts accordingly.
ProBP Optimization Optimizes path-level bid prices using the Probabilistic Bid Price (ProBP) algorithm. This step runs every day, to update the bid price controls based on the current path forecasts, current sales, and the ProBP optimization logic.

availability_control `class-attribute` `instance-attribute`

availability_control = 'bp'

This RM system uses bid price availability controls.

U

Bases: RmSys

A standard RM system of type "U".

This RM system uses path-level bid price controls with UDP optimization, along with EM untruncation and standard leg forecasting.

Parameters:

forecast_algorithm ((additive_pickup, exp_smoothing, multiplicative_pickup), default: 'additive_pickup' ) –

Specifies which leg-level forecasting algorithm to use for generating leg demand forecasts. Options are 'additive_pickup', 'exp_smoothing', or 'multiplicative_pickup'. The default is 'additive_pickup'.
arrivals_per_time_slice (float, default: 0.5 ) –

Specifies the expected number of customer arrivals per time slice used in the dynamic program optimization. This value affects the granularity of the discrete time approximation of the Poisson arrivals process; smaller values lead to finer granularity and a closer match to the theoretical continuous-time model, but increased computational time. Note that achieving a closer match to the continuous-time model may not always lead to better RM performance, as the actual customer arrival process may deviate from the Poisson assumption in practice (and in PassengerSim simulations). The default value is 0.5, which provides reasonably fast computational speed, while still capturing all forecast demand in the dynamic program.

Notes

This RM system consists of the following actions executed in order:

EM Untruncation of Path Demands This step applies the EM algorithm to untruncate observed path sales into inferred true demand levels. It runs only once at the beginning of each sample day, and detruncates demand for all timeframes.
Standard Path Forecasting This step generates path-level demand forecasts using a standard class-based forecasting algorithm (additive pickup by default). It runs full computations to produce path forecasts for the entire booking horizon in one pass at the beginning of each sample day, and on later DCPs it simply moves a pointer forward through that array of forecasts to provide the correct forecast values at that time.
UDP Optimization Optimizes path-level bid prices using the Unbucketed Dynamic Program (UDP) algorithm. This step re-solves the dynamic program with updated displacement values based on actual sales and current forecasts only on the DCPs; however, it still updates the bid prices every day, using daily average bid price vectors taken from the most recent DP solution..

availability_control `class-attribute` `instance-attribute`

availability_control = 'bp'

This RM system uses bid price availability controls.

L

Bases: RmSys

A standard RM system of type "L".

This RM system uses leg-level seat allocation controls with EMSR-B optimization, along with EM untruncation of yieldable demand and hybrid conditional leg forecasting.

Parameters:

emsr_variant ((b, a), default: 'b' ) –

Specifies which variant of the EMSR algorithm to use, either 'b' for EMSR-B, or 'a' for EMSR-A. At this time only 'b' is supported.
forecast_algorithm ((additive_pickup, exp_smoothing, multiplicative_pickup), default: 'additive_pickup' ) –

Specifies which leg-level forecasting algorithm to use for generating leg demand forecasts. Options are 'additive_pickup', 'exp_smoothing', or 'multiplicative_pickup'. The default is 'additive_pickup'.
fare_adjustment ((mr, ki, None), default: 'mr' ) –

Specifies the type of fare adjustment to apply in the conditional path forecasting algorithm. The first option is 'mr' for marginal revenue adjustment, inspired by the work of Fiig, Isler, Hopperstad, and Belobaba (2010), which assumes a continuous pricing curve with a negative exponential customer sellup function. The second option is 'ki' for Karl Isler's method, which is a discrete pricing adjustment method that assumes no particular functional form of the customer sellup function. It is also possible to select None for no fare adjustment, although this is not usually recommended except for restricted product sets.
fare_adjustment_scale (float, default: 0.5 ) –

Specifies the scale factor to use for fare adjustment in the conditional path forecasting algorithm. This factor determines the magnitude of the fare adjustment applied to the forecasts. A value of 1.0 applies the full adjustment, while values less than 1.0 scale down the adjustment. In practice, smaller values are used when the product sets are more restricted, and higher values are used when the product sets are less restricted. Theoretically, the full fare adjustment scale of 1.0 would be appropriate for completely unrestricted product sets, while no fare adjustment (0.0) should be used for heavily restricted product sets. The default setting of 0.5 is a moderate adjustment that works reasonably well in cases with semi-restricted product sets.
regression_weight ((None, sellup, sellup ^ 2, fare, none), default: None ) –

Specifies the type of regression weight to use in the conditional path forecasting algorithm. Options are 'sellup' to weight by sellup factor, 'sellup^2' to weight by the square of the sellup factor, 'fare' to weight by fare amount, 'none' for no weighting.
variance_rollup_algorithm ((tf, dep), default: 'tf' ) –

Specifies how to roll up variance when combining priceable and yieldable forecasts. Options are 'tf' to roll up variance by time frame, or 'dep' to roll up variance to departure. This setting has no effect if the variance_is_ratio_of_mean parameter is set to a value greater than zero.
variance_is_ratio_of_mean (float, default: 2.0 ) –

Assume that the variance is this ratio of the mean. When this is set to a value greater than zero, the variance of the forecast is set to this fixed ratio of the mean. Note that many algorithms for optimization use the forecast standard deviation, which is the square root of the variance, but it is the variance that is set to this ratio times the mean. When set to zero (the default), the variance is computed from mean squared error of the linear regression model used to compute the mean, and is not a fixed ratio of the mean. The default value of 2.0 is reflective of methods used in practice.
max_cap (float, default: 0.0 ) –

Maximum weighting factor for the conditional forecast. If set to a value greater than zero, the weighting factor used in the conditional forecast is capped at this maximum value to prevent excessively high weights from extreme sellup factors. The max cap will be more important when the regression weight is set to 'sellup^2', as this weighting can grow very large for extreme sellup factors. If this is applied, it is recommended to set the cap to 10.0, which is consistent with prior work on hybrid forecasting methods.
q_allocation_algorithm ((tf, dep), default: 'tf' ) –

Specifies how to allocate variance from aggregate Q forecasts to class-level forecasts. Options are 'tf' to allocate variance by time frame, or 'dep' to allocate variance to departure. This setting has no effect if the variance_is_ratio_of_mean parameter is set to a value greater than zero.

Notes

This RM system consists of the following actions executed in order:

EM Untruncation of Leg Demands This step applies the EM algorithm to untruncate observed leg sales into inferred true demand levels. It runs only once at the beginning of each sample day, and detruncates demand for all timeframes.
Standard Leg Forecasting This step generates leg-level demand forecasts using a standard class-based forecasting algorithm (additive pickup by default). It runs full computations to produce leg forecasts for the entire booking horizon in one pass at the beginning of each sample day, and on later DCPs it simply moves a pointer forward through that array of forecasts to provide the correct forecast values at that time.
EMSR-B Optimization Optimizes leg-level seat availability using the Expected Marginal Seat Revenue Version B (EMSR-B) algorithm. This step runs on each DCP to update the seat availability controls based on the current leg forecasts, current sales, and the EMSR optimization logic.

availability_control `class-attribute` `instance-attribute`

availability_control = 'leg'

This RM system uses leg-level class allocation availability controls.

M

Bases: RmSys

A standard RM system of type "M".

This RM system uses path-level bid price controls with Pro-BP optimization, along with EM untruncation of yieldable demand and hybrid conditional path forecasting.

Parameters:

forecast_algorithm ((additive_pickup, exp_smoothing, multiplicative_pickup), default: 'additive_pickup' ) –

Specifies which leg-level forecasting algorithm to use for generating leg demand forecasts. Options are 'additive_pickup', 'exp_smoothing', or 'multiplicative_pickup'. The default is 'additive_pickup'.
bid_price_vector (bool, default: True ) –

If True, enables bid price vector optimization in ProBP. If False, uses scalar bid prices.
fare_adjustment ((mr, ki, None), default: 'mr' ) –

Specifies the type of fare adjustment to apply in the conditional path forecasting algorithm. The first option is 'mr' for marginal revenue adjustment, inspired by the work of Fiig, Isler, Hopperstad, and Belobaba (2010), which assumes a continuous pricing curve with a negative exponential customer sellup function. The second option is 'ki' for Karl Isler's method, which is a discrete pricing adjustment method that assumes no particular functional form of the customer sellup function. It is also possible to select None for no fare adjustment, although this is not usually recommended except for restricted product sets.
fare_adjustment_scale (float, default: 0.5 ) –

Specifies the scale factor to use for fare adjustment in the conditional path forecasting algorithm. This factor determines the magnitude of the fare adjustment applied to the forecasts. A value of 1.0 applies the full adjustment, while values less than 1.0 scale down the adjustment. In practice, smaller values are used when the product sets are more restricted, and higher values are used when the product sets are less restricted. Theoretically, the full fare adjustment scale of 1.0 would be appropriate for completely unrestricted product sets, while no fare adjustment (0.0) should be used for heavily restricted product sets. The default setting of 0.5 is a moderate adjustment that works reasonably well in cases with semi-restricted product sets.
regression_weight ((None, sellup, sellup ^ 2, fare, none), default: None ) –

Specifies the type of regression weight to use in the conditional path forecasting algorithm. Options are 'sellup' to weight by sellup factor, 'sellup^2' to weight by the square of the sellup factor, 'fare' to weight by fare amount, 'none' for no weighting.
variance_rollup_algorithm ((tf, dep), default: 'tf' ) –

Specifies how to roll up variance when combining priceable and yieldable forecasts. Options are 'tf' to roll up variance by time frame, or 'dep' to roll up variance to departure. This setting has no effect if the variance_is_ratio_of_mean parameter is set to a value greater than zero.
variance_is_ratio_of_mean (float, default: 2.0 ) –

Assume that the variance is this ratio of the mean. When this is set to a value greater than zero, the variance of the forecast is set to this fixed ratio of the mean. Note that many algorithms for optimization use the forecast standard deviation, which is the square root of the variance, but it is the variance that is set to this ratio times the mean. When set to zero (the default), the variance is computed from mean squared error of the linear regression model used to compute the mean, and is not a fixed ratio of the mean. The default value of 2.0 is reflective of methods used in practice.
max_cap (float, default: 0.0 ) –

Maximum weighting factor for the conditional forecast. If set to a value greater than zero, the weighting factor used in the conditional forecast is capped at this maximum value to prevent excessively high weights from extreme sellup factors. The max cap will be more important when the regression weight is set to 'sellup^2', as this weighting can grow very large for extreme sellup factors. If this is applied, it is recommended to set the cap to 10.0, which is consistent with prior work on hybrid forecasting methods.
q_allocation_algorithm ((tf, dep), default: 'tf' ) –

Specifies how to allocate variance from aggregate Q forecasts to class-level forecasts. Options are 'tf' to allocate variance by time frame, or 'dep' to allocate variance to departure. This setting has no effect if the variance_is_ratio_of_mean parameter is set to a value greater than zero.

Notes

This RM system consists of the following actions executed in order:

EM Untruncation of Leg Demands This step applies the EM algorithm to untruncate observed path sales into inferred true demand levels. It runs only once at the beginning of each sample day, and detruncates demand for all timeframes.
Hybrid-Conditional Path Forecasting This step generates path-level demand forecasts using a hybrid conditional class-based forecasting algorithm (additive pickup by default). It runs full computations to produce path forecasts for the entire booking horizon in one pass at the beginning of each sample day, and on later DCPs it simply moves a pointer forward through that array of forecasts to provide the correct forecast values at that time.
Path Forecast Daily Decay Adjustment This step applies a daily decay adjustment to the path-level forecasts, to account for the changes in expected demand to come in between DCPs. It runs every day that isn't a DCP, to adjust the path forecasts accordingly.
ProBP Optimization Optimizes path-level bid prices using the Probabilistic Bid Price (ProBP) algorithm. This step runs every day, to update the bid price controls based on the current path forecasts, current sales, and the ProBP optimization logic.

References

Fiig, T., Isler, K., Hopperstad, C., & Belobaba, P. (2010). "Optimization of mixed fare structures: Theory and applications." Journal of Revenue and Pricing Management, 9(1/2), 152-170.

availability_control `class-attribute` `instance-attribute`

availability_control = 'bp'

V

Bases: RmSys

A standard RM system of type "V".

This RM system uses path-level bid price controls with UDP optimization, along with EM untruncation of yieldable demand and hybrid conditional path forecasting.

Parameters:

forecast_algorithm ((additive_pickup, exp_smoothing, multiplicative_pickup), default: 'additive_pickup' ) –

Specifies which leg-level forecasting algorithm to use for generating leg demand forecasts. Options are 'additive_pickup', 'exp_smoothing', or 'multiplicative_pickup'. The default is 'additive_pickup'.
arrivals_per_time_slice (float, default: 0.5 ) –

Specifies the expected number of customer arrivals per time slice used in the dynamic program optimization. This value affects the granularity of the discrete time approximation of the Poisson arrivals process; smaller values lead to finer granularity and a closer match to the theoretical continuous-time model, but increased computational time. Note that achieving a closer match to the continuous-time model may not always lead to better RM performance, as the actual customer arrival process may deviate from the Poisson assumption in practice (and in PassengerSim simulations). The default value is 0.5, which provides reasonably fast computational speed, while still capturing all forecast demand in the dynamic program.
fare_adjustment ((mr, ki, None), default: 'mr' ) –

Specifies the type of fare adjustment to apply in the conditional path forecasting algorithm. The first option is 'mr' for marginal revenue adjustment, inspired by the work of Fiig, Isler, Hopperstad, and Belobaba (2010), which assumes a continuous pricing curve with a negative exponential customer sellup function. The second option is 'ki' for Karl Isler's method, which is a discrete pricing adjustment method that assumes no particular functional form of the customer sellup function. It is also possible to select None for no fare adjustment, although this is not usually recommended except for restricted product sets.
fare_adjustment_scale (float, default: 0.5 ) –

Specifies the scale factor to use for fare adjustment in the conditional path forecasting algorithm. This factor determines the magnitude of the fare adjustment applied to the forecasts. A value of 1.0 applies the full adjustment, while values less than 1.0 scale down the adjustment. In practice, smaller values are used when the product sets are more restricted, and higher values are used when the product sets are less restricted. Theoretically, the full fare adjustment scale of 1.0 would be appropriate for completely unrestricted product sets, while no fare adjustment (0.0) should be used for heavily restricted product sets. The default setting of 0.5 is a moderate adjustment that works reasonably well in cases with semi-restricted product sets.
regression_weight ((None, sellup, sellup ^ 2, fare, none), default: None ) –

Specifies the type of regression weight to use in the conditional path forecasting algorithm. Options are 'sellup' to weight by sellup factor, 'sellup^2' to weight by the square of the sellup factor, 'fare' to weight by fare amount, 'none' for no weighting.
variance_rollup_algorithm ((tf, dep), default: 'tf' ) –

Specifies how to roll up variance when combining priceable and yieldable forecasts. Options are 'tf' to roll up variance by time frame, or 'dep' to roll up variance to departure. This setting has no effect if the variance_is_ratio_of_mean parameter is set to a value greater than zero.
variance_is_ratio_of_mean (float, default: 2.0 ) –

Assume that the variance is this ratio of the mean. When this is set to a value greater than zero, the variance of the forecast is set to this fixed ratio of the mean. Note that many algorithms for optimization use the forecast standard deviation, which is the square root of the variance, but it is the variance that is set to this ratio times the mean. When set to zero (the default), the variance is computed from mean squared error of the linear regression model used to compute the mean, and is not a fixed ratio of the mean. The default value of 2.0 is reflective of methods used in practice.
max_cap (float, default: 0.0 ) –

Maximum weighting factor for the conditional forecast. If set to a value greater than zero, the weighting factor used in the conditional forecast is capped at this maximum value to prevent excessively high weights from extreme sellup factors. The max cap will be more important when the regression weight is set to 'sellup^2', as this weighting can grow very large for extreme sellup factors. If this is applied, it is recommended to set the cap to 10.0, which is consistent with prior work on hybrid forecasting methods.
q_allocation_algorithm ((tf, dep), default: 'tf' ) –

Specifies how to allocate variance from aggregate Q forecasts to class-level forecasts. Options are 'tf' to allocate variance by time frame, or 'dep' to allocate variance to departure. This setting has no effect if the variance_is_ratio_of_mean parameter is set to a value greater than zero.

Notes

This RM system consists of the following actions executed in order:

EM Untruncation of Leg Demands This step applies the EM algorithm to untruncate observed path sales into inferred true demand levels. It runs only once at the beginning of each sample day, and detruncates demand for all timeframes.
Hybrid-Conditional Path Forecasting This step generates path-level demand forecasts using a hybrid conditional class-based forecasting algorithm (additive pickup by default). It runs full computations to produce path forecasts for the entire booking horizon in one pass at the beginning of each sample day, and on later DCPs it simply moves a pointer forward through that array of forecasts to provide the correct forecast values at that time.
UDP Optimization Optimizes path-level bid prices using the Unbucketed Dynamic Program (UDP) algorithm. This step re-solves the dynamic program with updated displacement values based on actual sales and current forecasts only on the DCPs; however, it still updates the bid prices every day, using daily average bid price vectors taken from the most recent DP solution..

availability_control `class-attribute` `instance-attribute`

availability_control = 'bp'

Standard RM Systems

E

availability_control class-attribute instance-attribute

P

availability_control class-attribute instance-attribute

U

availability_control class-attribute instance-attribute

L

availability_control class-attribute instance-attribute

M

availability_control class-attribute instance-attribute

V

availability_control class-attribute instance-attribute

availability_control `class-attribute` `instance-attribute`

availability_control `class-attribute` `instance-attribute`

availability_control `class-attribute` `instance-attribute`

availability_control `class-attribute` `instance-attribute`

availability_control `class-attribute` `instance-attribute`

availability_control `class-attribute` `instance-attribute`