Abstract:In this paper we propose a methodology to set prices of perishable items in the context of a retail chain with coordinated prices among its stores and compare its performance with actual practice in a real case study. We formulate a stochastic dynamic programming problem and develop heuristic solutions that approximate optimal solutions satisfactorily. To compare this methodology with current practices in the industry, we conducted two sets of experiments using the expertise of a product manager of a large ret… Show more
“…The only theoretical models and methods that partially address choice behavior issues are dynamic pricing models, such as those studied by Bitran et al [12], Feng and Gallego [19] and Gallego and van Ryzin [20], [21]. While these models allow demand to depend on the current price (the control in this case), they assume only one product is sold at one price at any point in time.…”
Customer choice behavior, such as "buy-up" and "buy-down", is an important phenomenon in a wide range of revenue management contexts. Yet most revenue management methodologies ignore this phenomenon -or at best approximate it in a heuristic way. In this paper, we provide an exact and quite general analysis of this problem. Specifically, we analyze a single-leg yield management problem in which the buyers' choice behavior is modeled explicitly. The choice model is perfectly general and simply specifies the probability of purchasing each fare product as function of the set of fare products offered. The control problem is to decide which subset of fare products to offer at each point in time. We show that the optimal policy is of a simple form. Namely, it consists of 1) identifying the ordered family of "nondominated" subsets S 1 , ..., S m , and 2) at each point in time opening one of these sets S k , where the optimal index k is increasing in the remaining capacity x. That is, the more capacity we have available, the further the optimal set is along this sequence. Moreover, we show that the optimal policy is nested if and only if the ordered sets are increasing, that is S 1 ⊆ S 2 ⊆ ... ⊆ S n , and we give a complete characterization of when nesting by fare order is optimal. We then show that two important models, the independent demand model and the multinomial logit model (MNL), satisfy this later condition and hence nested-by-fare-order policies are optimal in these cases. We also develop an estimation procedure for this setting based on the expectation-maximization (EM) method that jointly estimates arrival rates and choice model parameters when no-purchase outcomes are unobservable. Numerical results are given to illustrate both the model and estimation procedure.
“…The only theoretical models and methods that partially address choice behavior issues are dynamic pricing models, such as those studied by Bitran et al [12], Feng and Gallego [19] and Gallego and van Ryzin [20], [21]. While these models allow demand to depend on the current price (the control in this case), they assume only one product is sold at one price at any point in time.…”
Customer choice behavior, such as "buy-up" and "buy-down", is an important phenomenon in a wide range of revenue management contexts. Yet most revenue management methodologies ignore this phenomenon -or at best approximate it in a heuristic way. In this paper, we provide an exact and quite general analysis of this problem. Specifically, we analyze a single-leg yield management problem in which the buyers' choice behavior is modeled explicitly. The choice model is perfectly general and simply specifies the probability of purchasing each fare product as function of the set of fare products offered. The control problem is to decide which subset of fare products to offer at each point in time. We show that the optimal policy is of a simple form. Namely, it consists of 1) identifying the ordered family of "nondominated" subsets S 1 , ..., S m , and 2) at each point in time opening one of these sets S k , where the optimal index k is increasing in the remaining capacity x. That is, the more capacity we have available, the further the optimal set is along this sequence. Moreover, we show that the optimal policy is nested if and only if the ordered sets are increasing, that is S 1 ⊆ S 2 ⊆ ... ⊆ S n , and we give a complete characterization of when nesting by fare order is optimal. We then show that two important models, the independent demand model and the multinomial logit model (MNL), satisfy this later condition and hence nested-by-fare-order policies are optimal in these cases. We also develop an estimation procedure for this setting based on the expectation-maximization (EM) method that jointly estimates arrival rates and choice model parameters when no-purchase outcomes are unobservable. Numerical results are given to illustrate both the model and estimation procedure.
“…Thus, Bitran et al [20] extend the research in [21] to allow for prices to be coordinated across multiple stores with different arrival patterns. As before, customers have a non-homogeneous arrival rate (now to each store in the chain), and the seller knows the probability distribution of the reservation price of a customer.…”
“…Bitran et al consider the one product markdown problem in more than one store and model it by using dynamic programming, but in practice, since the state space is large, the solutions of these problems are impossible by using classical dynamic programming. Because of this, they develop a heuristic and test with the retailing sector real data 10 . Mantrala and Rao developed a stochastic dynamic-programming model-based decisionsupport system, specifically to help retail-store buyers of fashion goods decide on optimal merchandise order quantities and markdown prices.…”
We consider the markdown optimization problem faced by the leading apparel retail chain. Because of substitution among products the markdown policy of one product affects the sales of other products. Therefore, markdown policies for product groups having a significant crossprice elasticity among each other should be jointly determined. Since the state space of the problem is very huge, we use Approximate Dynamic Programming. Finally, we provide insights on the behavior of how each product price affects the markdown policy.
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