Step by step. The benefits of stage-based R&D licensing contracts

We examine how a licensor can optimally design licensing contracts for multi-phase R&D projects when he does not know the licensee’s project valuation, leading to adverse selection, and cannot enforce the licensee’s effort level, resulting in moral hazard. We focus on the effect of the phased nature typical of such projects, and compare single-phase and multi-phase contracts. We determine the optimal values for the upfront payment, milestone payments and royalties, and the optimal timing for outlicensing. Including multiple milestones and accompanying payments can be an effective way of discriminating between licensees holding different valuations, without having to manipulate the royalty rate, which induces licensees to invest less, resulting in lower project values and socially suboptimal solutions. Interestingly, we also find that multiple milestone payments are beneficial even when the licensor is risk-averse, contrary to standard contract theory results, which recommend that only an upfront payment should be used. In terms of licensing timing, we show that the optimal time depends on the licensor’s risk aversion, the characteristics of the licensee and the project value.     

Qualifying for a government’s scrappage program to stimulate consumers’ trade-in transactions? Analysis of an automobile supply chain involving a manufacturer and a retailer

We investigate an automobile supply chain where a manufacturer and a retailer serve a market with a fuel-efficient automobile under a scrappage program by the government. The program awards a subsidy to each consumer who trades in his or her used automobile with a new fuel-efficient automobile, if the manufacturer’s suggested retail price (MSRP) for the new one does not exceed a cutoff level. We derive the conditions assuring that the manufacturer has an incentive to qualify for the program, and find that when the cutoff level is low, the manufacturer may be unwilling to qualify for the program even if the subsidy is high. We also show that when the manufacturer qualifies for the program, increasing the MSRP cutoff level would raise the manufacturer’s expected profit but may decrease the expected sales. A moderate cutoff level can maximize the effectiveness of the program in stimulating the sales of fuel-efficient automobiles, whereas a sufficiently high cutoff level can result in the largest profit for the manufacturer. The retailer’s profit always increases when the manufacturer chooses to qualify for the program. Furthermore, we compute the government’s optimal MSRP cutoff level and subsidy for a given sales target, and find that as the program budget increases, the government should raise the subsidy but reduce the MSRP cutoff level to maximize sales.     

Make-or-buy service capacity decision in a supply chain providing after-sales service

We consider a supply chain comprising a manufacturer and a retailer. The manufacturer supplies a product to the retailer, while the retailer sells the product bundled with after-sales service to consumers in a fully competitive market. The sales volume is affected by the retailer’s service-level commitment. The retailer can build service capacity in-house at a deterministic price before service demand is realized, or buy the service from an outsourcing market at an uncertain price after service demand realization. We find that the outsourcing market encourages the retailer to make a higher level of service commitment, while prompting the manufacturer to reduce the wholesale price, resulting in more demand realization. We analyze how the expected cost of the service in the outsourcing market and the retailer’s risk attitude affect the decisions of both parties. We derive the conditions under which the retailer is willing to build service capacity in-house and under which it will buy the service from the outsourcing market. Moreover, we find that the manufacturer’s sharing with the retailer the cost to build service capacity improves the profits of both parties.     

Product-design and pricing strategies with remanufacturing

In this paper, we consider a supply chain that consists of an original equipment manufacturer (OEM) producing new products and a remanufacturer recovering the used items. The OEM often faces a strategic dilemma when determining the degree of disassemblability of its product design, as high disassemblability decreases the OEM’s production costs as well as the remanufacturer’s recovery costs. However, high disassemblability may be harmful to the OEM in a market in which the remanufacturer is encouraged to intensify price competition with the OEM because design for high disassemblability leads to larger cost savings in remanufacturing. We first formulate a two-period model to investigate the OEM’s product-design strategy and the remanufacturer’s pricing strategy in an extensive-form game, in which the equilibrium decisions of the resulting scenarios are derived. Next, we show the thresholds that determine whether remanufacturing is constrained by collection, the thresholds for the remanufacturer’s choice of a profitable pricing strategy, and the thresholds for determining the OEM’s product-design strategy. Finally, we expand the model for a multiple-period problem to show that the main insights obtained from the two-period model can be applied.     

Lead-time hedging and coordination between manufacturing and sales departments using Nash and Stackelberg games

In a firm, potential conflict exists between manufacturing and sales departments. Salespersons prefer to order from manufacturing departments in advance so that they can secure products in the amount they need to satisfy customers in time. This time in advance strategy is defined as “lead-time hedging.” While this hedging strategy is good for the sales department to guarantee the right quantity at the right time for customers, it adds additional costs and pressure to the manufacturing department. One scheme to resolve this conflict is to introduce a fair “internal price,” charged by the manufacturing department to the sales department. In this paper, two models involving a fair internal price are introduced. In one model, a Nash game is played to reach an optimal strategy for both parties. In the other model, a Stackelberg game is played in which the manufacturing department serves as the leader. We show that these two models can successfully reduce lead-time hedging determined by the salesperson and can increase the firm’s overall profit, as compared to the traditional model without considering the internal price. More insights have also been analyzed that include the comparisons of the manufacturer’s and the salesperson’s profits among the traditional model, the Nash game model, the Stackelberg game model, and the centralized global optimization model.     

Launching new products through exclusive sales channels

When launching a new product, a manufacturer usually sells it through competing retailers under non-exclusive arrangements. Recently, many new products (cellphones, electronics, toys, etc.) are sold through a single sales channel via an exclusive arrangement. In this paper we present two separate models that examine these two arrangements. Each model is based on a Stackelberg game in which the manufacturer acts as the leader by setting the wholesale price and the retailers act as the followers by choosing their retail prices. For each model, we solve the Stackelberg game by determining the manufacturer’s optimal wholesale price and each retailer’s optimal retail price in equilibrium. Then we examine the conditions under which the manufacturer should sell the new product through an exclusive retailer. In addition, we examine the impact of postponing the wholesale price decision and the impact of demand uncertainty on the manufacturer’s optimal profit under both arrangements.     

Minimizing the probability of lifetime ruin under stochastic volatility

We assume that an individual invests in a financial market with one riskless and one risky asset, with the latter’s price following a diffusion with stochastic volatility. Given the rate of consumption, we find the optimal investment strategy for the individual who wishes to minimize the probability of going bankrupt. To solve this minimization problem, we use techniques from stochastic optimal control.     

Inventory and sales effort management under unobservable lost sales

A retailer needs to make decisions regarding how much to order and how much sales effort to exert in an environment with uncertain demand. One intrinsic complexity in a typical retail environment is caused by the fact that the retailer can obtain information about demand only based on sales, as demand itself is unobservable. Taking a Bayesian approach, Lariviere and Porteus (1999) show that in such a setting a retailer should stock more to increase the probability of an exact demand observation. In this article, we extend their work by allowing the retailer to control both the stocking quantity and sales effort, which can be used to affect demand. We show that their insights with respect to information stalking carry over to this setting. In addition, our model allows gaining a better understanding of optimal sales effort strategies. We find that demand management has a dual role in supporting information gathering: while at the beginning of a product life cycle it is optimal to support learning effects by sharply reducing sales effort, at later stages of the product life cycle an aggressive strategy of increased promotional activities can be used to harvest the information gathered in earlier periods.     

双寡头垄断结构下的技术授权及社会福利分析——基于内生技术创新的视角

在具有水平差异且进行古诺竞争的双寡头结构中考虑技术拥有企业内生决定降低成本技术的创新程度,分析不同授权方式下技术拥有者利润、消费者剩余以及社会总福利的变化,并对不同授权方式下的技术创新程度进行比较。研究表明:技术拥有者通过双重收费、特许权收费方式总能实现利润增加,且双重收费方式能带来最大利润,而固定收费方式可能降低其利润;固定收费方式下消费者剩余、社会总福利高于双重收费,更高于特许权收费方式;技术创新程度与技术授权方式以及产品替代程度有关,且无论产品的替代程度如何,双重收费方式下的技术创新程度达到最大。     

Single firm product diffusion model for single-function and fusion products

The prosperity of multifunction products (also referred to as fusion products) has changed the landscape of the marketplace for several electronics products. To illustrate, as fusion products gain popularity in cellular phones and office machines, we observe that single-function products (e.g., stand-alone PDAs and stand-alone scanners) gradually disappear from the market as they are supplanted by fusion products. This paper presents a product diffusion model that captures the diffusion transition from two distinct single-function products into one fusion product. We investigate the optimal launch time of the fusion product under various conditions and conduct a numerical analysis to demonstrate the dynamics among the three products. Similar to previous multi-generation single product diffusion models, we find that the planning horizon, the products’ relative profit margin, and substitution effects are important to the launch time decision. However, there are several unique factors that warrant special consideration when a firm introduces a fusion product to the market: the firm’s competitive role, buyer consolidation of purchases to a multi-function product, the fusion technology and the age of current single-function products.     

Competitive advantage through take-back of used products

Motivated by a recent antitrust ruling against Hill–Rom, one of the two dominant American suppliers of hospital beds, we develop a stylized model to investigate the consequences of used product take-back on firms, industry and customers. Our findings suggest that by taking back and reselling refurbished products, a manufacturer can increase both profit margins and sales––to the detriment of a non-interfering competitor. In our model, customers are always better off under product take-back, but it depends on the degree of competition, whether firms use the benefits of take-back primarily to increase their margins or to pass them on to the customers by lowering their prices. The first firm to offer take-back, in some cases, can deter its competitors from following this profitable strategy, especially if it has an existing advantage in terms of lower production cost or higher market share. Contrary to the claim of Hill–Rom's competitor, we find a “legitimate business justification” for Hill–Rom's reduction of new product prices.     

Contract type and decision right of sales promotion in supply chain management with a capital constrained retailer

From the practices of Chinese consumer electronics market, we find there are two key issues in supply chain management: The first issue is the contract type of either wholesale price contracts or consignment contracts with revenue sharing, and the second issue is the decision right of sales promotion (such as advertising, on-site shopping assistance, rebates, and post-sales service) owned by either manufacturers or retailers. We model a supply chain with one manufacturer and one retailer who has limited capital and faces deterministic demand depending on retail price and sales promotion. The two issues interact with each other. We show that only the combination (called as chain business mode) of a consignment contract with the manufacturer’s right of sales promotion or a wholesale price contract with the retailer’s right of sales promotion is better for both members. Moreover, the latter chain business mode is realized only when the retailer has more power in the chain and has enough capital, otherwise the former one is realized. But which one is preferred by customers? We find that the former is preferred by customers who mainly enjoy low price, while the latter is preferred by those who enjoy high sales promotion level.     

The role of store brand positioning for appropriating supply chain profit under shelf space allocation

We consider a retailer’s decision of developing a store brand (SB) version of a national brand (NB) and the role that its positioning strategy plays in appropriating the supply chain profit. Since the business of the retailer can be regarded as selling to NB manufacturers the shelf space at its disposal, we formulate a game-theoretical model of a single-retailer, single-manufacturer supply chain, where the retailer can decide whether to launch its own SB product and sells scarce shelf-space to a competing NB in a consumer good category. As a result, the most likely equilibrium outcome is that the available selling amount of each brand is constrained by the shelf-space available for its products and both brands coexist in the category. In this paper, we conceptualize the SB positioning that involves both product quality and product features. Our analysis shows that when the NB cross-price effect is not too large, the retailer should position its SB’s quality closer to the NB, more emphasize its SB’s differences in features facing a weaker NB, and less emphasize its SB’s differences in features facing a stronger NB. Our results stress the importance of SB positioning under the shelf-space allocation, in order to maximize the retailer’s value appropriation across the supply chain.     

The newsvendor’s optimal incentive contracts for multiple advertisers

We consider a newsvendor who earns a revenue from the sales of her product to end users as well as from multiple advertisers paying to obtain access to those end users. We study the optimal decisions of a price-taking and a price-setting newsvendor when the advertisers have private information about their willingness to pay. We focus on the impact of the number of advertisers on the newsvendor’s optimal decisions. We find that regardless of the number of advertisers, the newsvendor may exclude advertisers with a low willingness to pay and distort the price and inventory from their system-efficient levels to screen the advertisers. Moreover, the newsvendor’s decision to exclude an advertiser is based exclusively on that advertiser’s characteristics, and the newsvendor’s optimal decision thus reveals independence among the advertisers. Nonetheless, the profits of the newsvendor and the advertisers also display network effects as both increase in the number of advertisers. Finally, our numerical results show that the newsvendor prefers an equivalent single advertiser to multiple advertisers due to the pooling effect.     

Coordinating a supply chain with effort and price dependent stochastic demand

This paper investigates the issue of channel coordination for a supply chain facing stochastic demand that is sensitive to both sales effort and retail price. In the standard newsvendor setting, the returns policy and the revenue sharing contract have been shown to be able to align incentives of the supply chain’s members so that the decentralized supply chain behaves as well as the integrated one. When the demand is influenced by both retail price and retailer sales effort, none of the above traditional contracts can coordinate the supply chain. To resolve this issue, we explore a variety of other contract types including joint return policy with revenue sharing contract, return policy with sales rebate and penalty (SRP) contract, and revenue sharing contract with SRP. We find that only the properly designed returns policy with SRP contract is able to achieve channel coordination and lead to a Pareto improving win–win situation for supply chain members. We then provide analytical method to determine the contract parameters and finally we use a numerical example to illustrate the findings and gain more insights.     

The Impact of Risk Attitude on the Optimal Compensation Plan in a Multi-product Situation

This paper examines the role of uncertainty and risk in determining the optimal commission rates a company should choose for each product of a salesman's product line. We assume that sales for each product are a stochastic function of the time (sales effort) allocated to that product. When sales are assumed to be deterministic, we achieve optimality when each product's commission is the same fraction of its gross margin. However, we determine here that when sales are stochastic this may no longer be true. Optimality conditions require explicit consideration of the utility function of the salesman and the moments of the sales response function.     

A singular control model with application to the goodwill problem

We consider a stochastic system whose uncontrolled state dynamics are modelled by a general one-dimensional Itô diffusion. The control effort that can be applied to this system takes the form that is associated with the so-called monotone follower problem of singular stochastic control. The control problem that we address aims at maximising a performance criterion that rewards high values of the utility derived from the system’s controlled state but penalises any expenditure of control effort. This problem has been motivated by applications such as the so-called goodwill problem in which the system’s state is used to represent the image that a product has in a market, while control expenditure is associated with raising the product’s image, e.g., through advertising. We obtain the solution to the optimisation problem that we consider in a closed analytic form under rather general assumptions. Also, our analysis establishes a number of results that are concerned with analytic as well as probabilistic expressions for the first derivative of the solution to a second-order linear non-homogeneous ordinary differential equation. These results have independent interest and can potentially be of use to the solution of other one-dimensional stochastic control problems.     

Dynamic pricing and warranty policies for products with fixed lifetime

We consider a repairable product with known market entry and departure times. A warranty policy is offered with product purchase, under which a customer can have a failed item repaired free of charge in the warranty period. It is assumed that customers are heterogeneous in their risk attitudes toward uncertain repair costs incurred after the warranty expires. The objective is to determine a joint dynamic pricing and warranty policy for the lifetime of the product, which maximizes the manufacturer’s expected profit. In the first part of the analysis, we consider a linearly decreasing price function and a constant warranty length. We first study customers’ purchase patterns under several different pricing strategies by the manufacturer and then discuss the optimal pricing and warranty strategy. In the second part, we assume that the warranty length can be altered once during the product lifetime in developing a joint pricing and warranty policy. Numerical studies show that a dynamic warranty policy can significantly outperform a fixed-length warranty policy.     

Does stock return predictability affect ESO fair value?

Executive Stock Options (ESOs) are modified American options that cannot be valued using standard methods. With a few exceptions, the literature has discussed the ESO fair value by assuming unpredictable stock returns which are not supported by the available empirical evidence. In this paper we obtain the fair value of American ESOs when stock returns are predictable and, specifically, driven by the trending Ornstein–Uhlenbeck process of Lo and Wang (1995). We solve the executive’s portfolio allocation problem for a simple buy-and-hold strategy when his wealth can be distributed between a risk-free asset and a market portfolio. This problem is jointly solved with the executive’s optimal exercise policy. We find that executives tend to wait longer the higher the predictability, independently of the composition of executive’s asset menu. We have also analyzed the implications under the FAS123R proposals for the ESO fair value and found that, even for low autocorrelations, there is a meaningful mispricing when unpredictable returns are erroneously assumed.