Dynamic Pricing of Limited Inventories When Customers Negotiate

Although take-it-or-leave-it pricing is the main mode of operation for many retailers, a number of retailers discreetly allow price negotiation when some haggle-prone customers ask for a bargain. At these retailers, the posted price, which itself is subject to dynamic adjustments in response to the pace of sales during the selling season, serves two important roles: (i) it is the take-it-or-leave-it price to many customers who do not bargain, and (ii) it is the price from which haggle-prone customers negotiate down. In order to effectively measure the benefit of dynamic pricing and negotiation in such a retail environment, one must take into account the interactions among inventory, dynamic pricing, and negotiation. The outcome of the negotiation (and the final price a customer pays) depends on the inventory level, the remaining selling season, the retailer's bargaining power, and the posted price. We model the retailer's dynamic pricing problem as a dynamic program, where the revenues from both negotiation and posted pricing are embedded in each period. We characterize the optimal posted price and the resulting negotiation outcome as a function of inventory and time. We also show that negotiation is an effective tool to achieve price discrimination, particularly when the inventory level is high and/or the remaining selling season is short even when implementing negotiation is costly.http://deepblue.lib.umich.edu/bitstream/2027.42/85781/1/1159_Ahn.pd

Rationing Capacity in Advance Selling to Signal Quality

We consider a seller who can sell her product over two periods, advance and spot. The seller has private information about the product quality, which is unknown to customers in advance and publicly revealed in spot. The question we consider is whether the seller has an incentive to signal quality in advance and, if so, how she can convey a credible signal of product quality. We characterize the seller's signaling strategy and find that rationing of capacity in the advance period is an effective tool of signaling product quality. We find that the high-quality seller can distinguish herself by allocating less capacity than the low-quality seller in the advance period. We show that this signaling mechanism exists whenever advance selling would be optimal for both the high-quality and low-quality sellers if quality information was symmetric. We compare capacity rationing with other signaling tools, such as pricing and advertising, and show that capacity rationing is the preferred one. Despite its capability of conveying quality information more efficiently than other tools, capacity rationing may still be very costly for the seller. When compared to the case when rationing was not allowed, the seller's ability to ration (rationing flexibility) sometimes makes the seller worse off, independently of her quality.http://deepblue.lib.umich.edu/bitstream/2027.42/100188/1/1204_Kapuscinski.pd

Incentive and Competition Effects of Supplier Awards

Many firms recognize exceptional supplier performance by giving out a “Supplier of the Year” or “Outstanding Supplier” award. These awards are usually symbolic since they have no immediate monetary value for a supplier and no direct cost to a buyer. Giving these awards can be beneficial for a buyer: if suppliers care about being rewarded, symbolic awards can incentivize a supplier to exert higher effort. On the other hand, in a market with multiple buyers and suppliers, an award may have another effect, which we denote “competition effect”. When good suppliers are scarce, a public award can intensify the competition to do business with a good supplier. We develop a theoretical model that captures a supplier's value for the award in a setting with two buyers and two suppliers. We show that the average provision of quality is higher when awards are available whether these are private (only observable to the recipient) or public (observable to everyone). In addition, public awards result in buyers paying a higher price to get a good supplier. We then test these results with a laboratory experiment. Our experimental results show that private symbolic awards have incentive effects and lead to higher provision of quality and higher buyer's profits. When the awards are public this profit premium disappears. This happens for two reasons, first because buyers have to pay higher prices to get the good suppliers, and second because making the award public crowds out the intrinsic value of the award for suppliers.https://deepblue.lib.umich.edu/bitstream/2027.42/136764/1/1368_Beer.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/136764/4/1368_Beer_March18.pdfDescription of 1368_Beer_March18.pdf : March 2018 revision (title change

Dynamic Pricing with Point Redemption

Many sellers allow consumers to pay with reward points instead of cash or credit card. While the revenue implications of cash purchases are transparent, the implication of reward sales is not trivial, when a firm that issues points is not a seller. In this case, a seller receives a compensation from the point issuer when a consumer purchases the good with points. We examine how reward sales influence a seller's pricing and inventory decisions. We consider a consumer who can choose to pay with cash or points based on reservation price, point balance, and the perceived value of a point. Then, we incorporate this into a pricing model where a seller earns revenues from both cash and reward sales. In contrast to an intuition that reward sales will increase sales and revenue, we show that the effect of reward sales on the seller's price is non-trivial as the seller could either add a premium or discount depending on the inventory level, time, and the reimbursement rate. Furthermore, such price adjustments can attenuate the optimal mark-up or mark-down level, and reduce the price fluctuation caused by inventory level and remaining time. We investigate settings where the seller has different operational controls over reward sales and find that allowing reward sales is still better even when the revenue from the reward sales is smaller than the cash sales. We also find that a seller with an ability to control availability (i.e., allow a reward sale or not) can achieve a revenue similar to the revenue of a seller with an ability to change point requirements and price.https://deepblue.lib.umich.edu/bitstream/2027.42/142796/1/1377_Ahn.pd

The Impact of Decision Rights on Innovation Sharing

While innovation sharing between a supplier and a buyer—a common practice in the automotive industry—can increase the efficiency of a supply chain, many suppliers are reluctant to do so. Sharing innovations leaves the supplier in a vulnerable position if the buyer exploits the information and re-shares the supplier’s innovation with competing suppliers. Anecdotal evidence from automotive suppliers tells that in some occasions the buyer’s decision is in the hands of a long-run focused employee (“engineer”), while in other occasions it is a short-run focused employee (“procurement manager”) who has more control. To examine how the allocation of decision rights to employees with different time horizons affects collaboration between the two firms, we model a buyer-supplier relationship where the buyer is a dual decision maker, consisting of long-run and short-run focused employees. We characterize the equilibrium of this model and show that the frequency of collaborative outcomes increases from a case where the decision is made by an employee with a short-term objective, to a case where the decision is made jointly, to a case where a decision is made by an employee with a long-run objective. Our experimental results verify this prediction, for the most part. An important result not predicted by the theory is that in the joint control case, both employees become significantly less trustworthy. With an additional treatment which allows for free-form communication, we identify social interaction effects in the form of a “bias to agreement” as a plausible driver of the morehttps://deepblue.lib.umich.edu/bitstream/2027.42/136770/1/1369_Beer.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/136770/4/1369_Beer_Dec2018.pdfDescription of 1369_Beer_Dec2018.pdf : December 2018 revisio

Data-Driven Pricing for a New Product

Decisions regarding new products are often difficult to make, and mistakes can have grave consequences for a firm’s bottom line. Often, firms lack important information about a new product, such as its potential market size and the speed of its adoption by consumers. One of the most popular frameworks that has been used for modeling new product adoption is the Bass model. Although the Bass model and its many variants are used to study dynamic pricing of new products, the vast majority of these models require a priori knowledge of parameters that can only be estimated from historical data or guessed using institutional knowledge. In this paper, we study the interplay between pricing and learning for a monopolist whose objective is to maximize the expected revenue of a new product over a finite selling horizon. We extend the generalized Bass model to a stochastic setting by modeling adoption through a continuous-time Markov chain with which the adoption rate depends on the selling price and on the number of past sales. We study a pricing problem in which the parameters of this demand model are unknown, but the seller can utilize real-time demand data for learning the parameters. We propose two simple and computationally tractable pricing policies with O(ln m) regret, where m is the market size

On (Re-Scaled) Multi-Attempt Approximation of Customer Choice Model and its Application to Assortment Optimization

Motivated by the classic exogenous demand model and the recently developed Markov chain model, we propose a new approximation to the general customer choice model based on random utility called multi-attempt model, in which a customer may consider several substitutes before finally deciding to not purchase anything. We show that the approximation error of multi-attempt model decreases exponentially in the number of attempts. However, despite its strong theoretical performance, the empirical performance of multi-attempt model is not satisfactory. This motivates us to construct a modification of multi-attempt model called re-scaled multi-attempt model. We show that re-scaled 2-attempt model is exact when the underlying true choice model is Multinomial Logit (MNL); if, however, the underlying true choice model is not MNL, we show numerically that the approximation quality of re-scaled 2-attempt model is very close to that of Markov chain model. The key feature of our proposed approach is that the resulting approximate choice probability can be explicitly written. From a practical perspective, this allows the decision maker to use off-the-shelf solvers, or borrow existing algorithms from literature, to solve a general assortment optimization problem with a variety of real-world constraints.http://deepblue.lib.umich.edu/bitstream/2027.42/122455/1/1322_Ahn.pd

Capacity Investment with Demand Learning

We study a firm’s optimal strategy to adjust its capacity using demand information. The capacity adjustment is costly and often subject to managerial hurdles which sometimes make it difficult to adjust capacity multiple times. In order to clearly analyze the impact of demand learning on the firm’s decision, we study two scenarios. In the first scenario, the firm’s capacity adjustment cost increases significantly with respect to the number of adjustments because of significant managerial hurdles, and resultantly the firm has a single opportunity to adjust capacity (single adjustment scenario). In the second scenario, the capacity adjustment costs do not change with respect to the number of adjustments because of little managerial hurdles, and therefore the firm has multiple opportunities to adjust capacity (multiple adjustment scenario). For both scenarios, we first formulate the problem as a stochastic dynamic program, and then characterize the firm’s optimal policy: when to adjust and by how much. We show that the optimal decision on when and by how much to change the capacity is not monotone in the likelihood of high demand in the single adjustment scenario, while the optimal decision is monotone under mild conditions and the optimal policy is a control band policy in the multiple adjustment scenario. The sharp contrast reflects the impact of demand learning on the firm’s optimal capacity decision. Since computing and implementing the optimal policy is not tractable for general problems, we develop a data-driven heuristic for each scenario. In the single adjustment scenario, we show that a two-step heuristic which explores demand for an appropriately chosen length of time and adjusts the capacity based on the observed demand is asymptotically optimal, and prove the convergence rate. In the multiple adjustment scenario, we also show that a multi-step heuristic under which the firm adjusts its capacity at a predetermined set of periods with exponentially increasing gap between two consecutive decisions is asymptotically optimal and show its convergence rate. We finally apply our heuristics to a numerical study and demonstrate the performance and robustness of the heuristics.http://deepblue.lib.umich.edu/bitstream/2027.42/122454/4/1231_Ahn_July162016.pdfDescription of 1231_Ahn_July162016.pdf : July 2016 revisionDescription of 1321_Ahn.pdf : [SUPERSEDED] Original version for reference onl

To Share or Not to Share? Capacity Reservation in a Shared Supplier

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/151965/1/poms13081_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/151965/2/poms13081-sup-0001-OnlineAppendix.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/151965/3/poms13081.pd

Investing in a Shared Supplier in a Competitive Market: Stochastic Capacity Case

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/116001/1/poms12348-sup-0001-Appendix.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/116001/2/poms12348.pd