Dynamic Pricing of Substitutable Products in the Presence of Capacity Flexibility

Firms that offer multiple products are often susceptible to periods of inventory mismatches where one product may face shortages while the other has excess inventories. In this paper, we study a joint implementation of price- and capacity-based substitution mechanisms to alleviate the level of such inventory disparities. We consider a firm producing substitutable products via a capacity portfolio consisting of both product-dedicated and flexible resources and characterize the structure of the optimal production and pricing decisions. We then explore how changes in various problem parameters affect the optimal policy structure. We show that the availability of a flexible resource helps maintain stable price differences across products over time even though the price of each product may fluctuate over time. This result has favorable ramifications from a marketing standpoint because it suggests that even when a firm applies a dynamic pricing strategy, it may still establish consistent price positioning among multiple products if it can employ a flexible replenishment resource. We provide numerical examples for the price stabilization effect and discuss extensions of our results to a more general multiple product setting

A nonparametric self-adjusting control for joint learning and optimization of multi-product pricing with finite resource capacity

We study a multi-period network revenue management problem where a seller sells multiple products, made from multiple resources with infinite capacity, in an environment where the underlying demand function is a priori unknown (in the nonparametric sense). The objective of the seller is to simultaneously learn the unknown demand function and dynamically price his products to minimize the expected revenue loss. For the problem where the number of selling periods and initial capacity are scaled by k > 0, it is known that the expected revenue loss of any non-anticipating pricing policy is (pk). However, there is a considerable gap between this theoretical lower bound and the performance bound of the best known heuristic control in the literature. In this paper, we propose a Nonparametric Self-adjusting Control and show that its expected revenue loss is O(k1=2+ log k) for any arbitrarily small >0, provided that the underlying demand function is sufficiently smooth. This is the tightest bound of its kind for the problem setting that we consider in this paper and it significantly improves the performance bound of existing heuristic controls in the literature; in addition, our intermediate results on the large deviation bounds for spline estimation and nonparametric stability analysis of constrained optimization are of independent interest and are potentially useful for other applications

Dynamic Pricing and Replenishment with Customer Upgrades

We study a joint implementation of price‐ and availability‐based product substitution to better match demand and constrained supply across vertically differentiated products. Our study is motivated by firms that utilize dynamic pricing as well as customer upgrades, as ex ante and ex post mechanisms, respectively, to mitigate inventory mismatches. To gain insight into how offering product upgrades impacts optimal price selection, we formulate a multiple period, nested two‐stage model where the firm first sets prices and replenishment levels for each product while the demand is still uncertain, and after observing the demand, decides how many (if any) of the customers to upgrade to a higher quality product. We characterize the structure of the optimal upgrade, pricing and replenishment policies and find that firms having greater flexibility to offer product upgrades can restrain their reliance on dynamic pricing, enabling them to better protect the price differentiation between the products. We also show how the quality differential between the products or changes in the replenishment cost structures influence the optimal policy. Using insights gained from the optimal policy structure, we construct a heuristic policy and find that it performs well across various parameter values. Finally, we consider an extension in which the firm dynamically sets upgrade fees in each period. Our results overall help further our understanding of the intricate relationship among a firm's decisions on pricing, replenishment, and product upgrades in an effort to better match demand and constrained supply

Optimal control of an assembly system with demand for the end-product and intermediate components

This article considers the production and admission control decisions for a two-stage manufacturing system where intermediate components are produced to stock in the first stage and an end-product is assembled from these components through a second-stage assembly operation. The firm faces two types of demand. The demand for the end-product is satisfied immediately if there are available products in inventory while the firm has the option to accept the order for later delivery or to reject it when no inventory is available. Demand for intermediate components may be accepted or rejected to keep components available for assembly purposes. The structure of demand admission, component production and product assembly decisions are characterized. The proposed model is extended to take into account multiple customer classes and a more general revenue collecting scheme where only an upfront partial payment is collected if a customer demand is accepted for future delivery with the remaining revenue received upon delivery. Since the optimal policy structure is rather complex and defined by switching surfaces in a multidimensional space, a simple heuristic policy is proposed for which the computational load grows linearly with the number of products and its performance is tested under a variety of example problems

Technical note - Joint learning and optimization of multi-product pricing with finite resource capacity and unknown demand parameters

We consider joint learning and pricing in network revenue management (NRM) with multiple products, multiple resources with finite capacity, parametric demand model, and a continuum set of feasible price vectors. We study the setting with a general parametric demand model and the setting with a well-separated demand model. For the general parametric demand model, we propose a heuristic that is rate-optimal (i.e., its regret bound exactly matches the known theoretical lower bound under any feasible pricing control for our setting). This heuristic is the first rate-optimal heuristic for a NRM with a general parametric demand model and a continuum of feasible price vectors. For the well-separated demand model, we propose a heuristic that is close to rate-optimal (up to a multiplicative logarithmic term). Our second heuristic is the first in the literature that deals with the setting of a NRM with a well-separated parametric demand model and a continuum set of feasible price vectors

Real-Time Dynamic Pricing with Minimal and Flexible Price Adjustment

We study a standard dynamic pricing problem where the seller (a monopolist) possesses a finite amount of inventories and attempts to sell the products during a finite selling season. Despite the potential benefits of dynamic pricing, many sellers still adopt a static pricing policy because of (1) the complexity of frequent reoptimizations, (2) the negative perception of excessive price adjustments, and (3) the lack of flexibility caused by existing business constraints. In this paper, we develop a family of pricing heuristics that can be used to address all these challenges. Our heuristic is computationally easy to implement; it requires only a single optimization at the beginning of the selling season and automatically adjusts the prices over time. Moreover, to guarantee a strong revenue performance, the heuristic only needs to adjust the prices of a small number of products and do so infrequently. This property helps the seller focus his effort on the prices of the most important products instead of all products. In addition, in the case where not all products are equally admissible to price adjustment (due to existing business constraints such as contractual agreement, strategic product positioning, etc.), our heuristic can immediately substitute the price adjustment of the original products with the price adjustment of similar products and maintain an equivalent revenue performance. This property provides the seller with extra flexibility in managing his prices

Procurement Mechanisms with Post-Auction Pre-Award Cost-Reduction Investigations

A buyer seeking to outsource production may be able to and ways to reduce a potential supplier's cost, e.g., by suggesting improvements to the supplier's proposed production methods. We study how a buyer could use such \cost-reduction investigations" by proposing a three-step supplier selection mechanism: First, each of several potential suppliers submits a price bid for a contract. Second, for each potential supplier, the buyer can exert an effort to see if she can identify how the supplier could reduce his cost to perform the contract; the understanding is that if savings are found, they are passed on to the buyer if the supplier is awarded the contract. Third, the buyer awards the contract to whichever supplier has the lowest updated bid (the supplier's initial bid price minus any cost-reduction the buyer was able to identify for that supplier). For this proposed process, we characterize how the buyer's decision on which suppliers to investigate cost reductions for in step 2 is affected by the aggressiveness of the suppliers' bids in step 1. We show that even if the buyer does not share the cost savings she identifies in step 2, ex ante symmetric suppliers are actually better off (ex ante) in our proposed mechanism than in a setting without such cost-reduction investigations, resulting in a win-win for the buyer and suppliers. When suppliers' cost and cost-reduction distributions become very heterogeneous, the win-win situation may no longer hold, but every supplier still has an incentive to allow the buyer to investigate him in step 2 because it increases his chance of winning the contract. Using an optimal mechanism analysis, our numerical studies show that our proposed Bid-Investigate-Award mechanism helps the buyer achieve near-optimal performance, despite its simplicity

When to Deploy Test Auctions in Sourcing

We investigate when a buyer seeking to procure multiple units of an input may find it advantageous to run a “test auction” in which she has incumbent suppliers bid on a portion of the desired units. The test auction reveals incumbent supplier cost information that helps the buyer determine how many entrants (if any) to recruit at a cost prior to awarding the remaining units. The optimal number of entrant suppliers to recruit follows a threshold policy that is monotonic in the test auction’s clearing price unless the underlying supplier cost distribution is not regular. When setting her reserve price in the test auction, the buyer uses supplier recruitment as her “outside option”: if the reserve price is not met in the test auction, the buyer recruits new suppliers and runs a second auction. We compare the attractiveness of the test auction procedure relative to the more conventional procedure in which the buyer auctions off her entire demand in one auction. Since the buyer can choose ex ante which procedure to use, we propose using whichever has lower ex ante total (purchase plus recruitment) cost. Finally, using an optimal mechanism analysis, we find a lower bound on the buyer’s cost, and use that cost as a benchmark to show that our proposed sourcing strategy performs well given its ease of implementation

Self-Control of Traffic Lights and Vehicle Flows in Urban Road Networks

Based on fluid-dynamic and many-particle (car-following) simulations of traffic flows in (urban) networks, we study the problem of coordinating incompatible traffic flows at intersections. Inspired by the observation of self-organized oscillations of pedestrian flows at bottlenecks [D. Helbing and P. Moln\'ar, Phys. Eev. E 51 (1995) 4282--4286], we propose a self-organization approach to traffic light control. The problem can be treated as multi-agent problem with interactions between vehicles and traffic lights. Specifically, our approach assumes a priority-based control of traffic lights by the vehicle flows themselves, taking into account short-sighted anticipation of vehicle flows and platoons. The considered local interactions lead to emergent coordination patterns such as ``green waves'' and achieve an efficient, decentralized traffic light control. While the proposed self-control adapts flexibly to local flow conditions and often leads to non-cyclical switching patterns with changing service sequences of different traffic flows, an almost periodic service may evolve under certain conditions and suggests the existence of a spontaneous synchronization of traffic lights despite the varying delays due to variable vehicle queues and travel times. The self-organized traffic light control is based on an optimization and a stabilization rule, each of which performs poorly at high utilizations of the road network, while their proper combination reaches a superior performance. The result is a considerable reduction not only in the average travel times, but also of their variation. Similar control approaches could be applied to the coordination of logistic and production processes

On the Introduction of an Agile, Temporary Workforce into a Tandem Queueing System

We consider a two-station tandem queueing system where customers arrive according to a Poisson process and must receive service at both stations before leaving the system. Neither queue is equipped with dedicated servers. Instead, we consider three scenarios for the fluctuations of workforce level. In the first, a decision-maker can increase and decrease the capacity as is deemed appropriate; the unrestricted case. In the other two cases, workers arrive randomly and can be rejected or allocated to either station. In one case the number of workers can then be reduced (the controlled capacity reduction case). In the other they leave randomly (the uncontrolled capacity reduction case). All servers are capable of working collaboratively on a single job and can work at either station as long as they remain in the system. We show in each scenario that all workers should be allocated to one queue or the other (never split between queues) and that they should serve exhaustively at one of the queues depending on the direction of an inequality. This extends previous studies on flexible systems to the case where the capacity varies over time. We then show in the unrestricted case that the optimal number of workers to have in the system is non-decreasing in the number of customers in either queue.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47647/1/11134_2005_Article_2441.pd