Econometrics
Yield Management and econometrics center on detailed forecasting and mathematical optimization of marginal revenue opportunities. The opportunities arise from segmentation of consumer willingness to pay. If the market for a particular good follows the simple straight line Price/Demand relationship illustrated below, a single fixed price of $50 there is enough demand to sell 50 units of inventory. This results in $2500 in revenues. However the same Price/Demand relationship yields $4000 if consumers are presented with multiple prices.
In practice, the segmentation approach relies on adequate fences between consumers so that everyone doesn't buy at the lowest price offered. The airlines use time of purchase to create this segmentation, with later booking customers paying the higher fares. The fashion industry uses time in the opposite direction, discounting later in the selling season once the item is out of fashion or inappropriate for the time of year. Other approaches to fences involve attributes that create substantial value to the consumer at little or no cost to the seller. A backstage pass at a concert is a good example of this. Initially Yield Management avoided the complexity caused by the interaction of absolute price and price position by using surrogates for price such as booking class. By the mid-1990s, most implementation incorporated some measures of price elasticity. The airlines were exceptional in this case, preferring to focus on more detailed segmentation by implementing O&D (Origin & Destination) systems.
At the heart of yield management decision-making process is the trade-off of marginal yields from segments that are competing for the same inventory. In capacity-constrained cases, there is a bird-in-the-hand decision that forces the seller to reject lower revenue generating customers in the hopes that the inventory can be sold in a higher valued segment. The tradeoff is sometimes mistakenly identified as occurring at the intersection of the marginal revenue curves for the competing segments. While this is accurate when it supports marketing decisions where access to both segments is equivalent, it is wrong for inventory control decisions. In these cases the intersection of the marginal revenue curve of the higher valued segment with the actual value of the lower segment is the point of interest.
In the case illustrated here, a car rental company must set up protection levels for its higher valued segments. By estimating where the marginal revenue curve of the luxury segment crosses the actual rental value of the midsize car segment the company can decide how many luxury cars to make available to midsize car renters. Where the vertical line from this intersection point crosses the demand (horizontal) axis determines how many luxury cars should be protected for genuine luxury car renters. The need to calculate protection levels has led to a number of heuristic solutions, most notable EMSRa and EMSRb, which stands for Expected Marginal Seat Revenue version a and b respectively. The balancing point of interest is found using Littlewood's rule which states that demand for should be accepted as long as
2 11
where
is the value of the lower valued segment
is the value of the higher valued segment
is the demand for the higher valued segment and
is the capacity left
This equation is re-arranged to compute protection levels as follows:
1−121
In words, you want to protect 1 units of inventory for the higher valued segment where 1 is equal to the inverse probability of demand of the revenue ratio of the lower valued segment to the higher valued segment. This equation defines the EMSRa algorithm which handles the two segment case. EMSRb is smarter and handles multiple segments by comparing the revenue of the lower segment to a demand weighted average of the revenues of the higher segments. Neither of these heuristics produces the exact right answer and increasingly implementations make use of Monte Carlo simulation to find optimal protection levels.
Since the mid 1990s increasingly sophisticated mathematical models have been developed such as the dynamic programming formulation pioneered by Talluri and Van Ryzin which has led to more accurate estimates of bid prices. Bid prices represent the minimum price a seller should accept for a single piece of inventory and are popular control mechanisms for Hotels and Car Rental firms. Models derived from developments in financial engineering are intriguing but have been unstable and difficult to place the parameters in practice. Yield management tends to focus on environments that are less rational than the financial markets.
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