Sequencing interval situations and related games

Uncertainty accompanies almost every situation in real world and it influences our decisions. In sequencing situations it may affect parameters used to determine an optimal order in the queue, and consequently the decision of whether (or not) to rearrange the queue by sharing the realized cost savings. This paper extends the analysis of one-machine sequencing situations and their related cooperative games to a setting with interval data, i.e. when the agents’ costs per unit of time and/or processing time in the system lie in intervals of real numbers obtained by forecasting their values. The question addressed here is: How to determine an optimal order (if the initial order in the queue is not so) and which approach should be used to motivate the agents to adopt the optimal order? This question is an important one that deserves attention both in theory and practice.     

Contract design for technology sharing between two farmers

Technology sharing among farmers has become common but controversial in recent years. To address it, we consider two farmers engaged in Cournot competition to investigate motivations of technology sharing and provide suggestions on contract design. One farmer (a licensor) has developed some technology and decides whether to share technology with the other farmer (a licensee). The licensee chooses whether to buy technology under a fixed-rate contract or a royalty-fee contract. We propose a technology sharing ratio between two farmers to characterize the degree of technology sharing. We find a win–win outcome for both farmers when the technology sharing ratio is higher than a threshold under the fixed-fee contract. While under the royalty-fee contract, the licensor only shares technology with an additional constraint that they have similar production costs. When the licensor can design contracts, he prefers the royalty-fee contract to the fixed-fee contract. We further interpret why the licensor may not benefit more under the two-part tariff contract than the fixed-fee or the royalty-fee contract. Moreover, we find that in supply chain settings, a win–win outcome for both farmers exists if and only if the technology sharing ratio is smaller than a threshold under the fixed-fee contract while technology sharing will not be realized under the royalty-fee contract. Finally, we show that the strategy of whether to share technology is robust to yield uncertainty, and both the licensor and licensee may benefit more from technology sharing because of yield uncertainty.

     

Intergenerational risk sharing in closing pension funds

We model intergenerational risk sharing in closing funded pension plans. Specifically, we consider a setting in which in each period, the pension fund’s investment and indexation policy is the outcome of a bargaining process between representatives of the then living generations. Because some generations might be under- or overrepresented in the board, we use the asymmetric Nash bargaining solution to allow for differences in bargaining powers. In a numerical study, we compare the welfare that the generations derive from the outcome of this repeated bargaining to the welfare that they would derive if a social planner’s optimal policy would instead be implemented. We find that as compared to the social optimum, older generations benefit substantially from the repeated bargaining, even if all generations are equally well-represented in the board. If older generations are relatively over-represented, as is sometimes argued, these effects are attenuated.     

Optimal promotion planning—depth and frequency—for a two-stage supply chain under Markov switching demand

In considering the retailer–supplier supply chain, this paper analyzes how a retailer reasonably decides both the depth and frequency of the price discount promotion including or excluding a supplier’s inventory decision. Assuming that the promotion frequency used by the retailer is probabilistic, we model a promotion-inventory decision under an AR(1) demand with a Markov switching promotion regime. After obtaining the optimal promotion plan, our analysis also considers the behavior of the optimal promotion decision; the retailer’s price format selection, either an Every-Day-Low-Price policy (EDLP) or a Promotion policy (HiLo); and the impact of information sharing of promotion status on the system’s performance. Our results suggest that a retailer tends to overpromote if inventory cost is excluded in its promotion decision, that increasing the market share is a preferable action for both the retailer and the supplier, that total margin and price-elasticity play an important role in selecting the price format, and that the profitability for a supplier of sharing promotion information depends on the transition probabilities of the Markov switching regime.     

Management of legacy nutrient stores through nitrogen and phosphorus fertilization,catch crops,and gypsum treatment

We develop a modeling framework, based on discrete-time dynamic optimization, to study the effect of legacy nutrient stores and soil nutrient dynamics on optimal nutrient management and agri-environmental policy in crop production. Three alternative measures are studied to reduce nutrient loss: reduced fertilization, nonlegume catch crop cultivation and gypsum amendment. According to our results, landowner can bring down excessively high phosphorus stocks causing environmental damage within decades, by simultaneous optimization of the nitrogen and phosphorus fertilizers on the economic basis of profit maximization. Our results suggest that nitrogen loss abatement with catch crops is socially optimal, whereas the use of gypsum is well justified as a temporary measure on soils with high soil phosphorus levels. A dynamic tax-subsidy-scheme, which takes into account the current soil nutrient levels and field attributes such as soil texture, can enforce the socially optimal outcome. The welfare losses of the static steady-state-based tax-subsidy-schemes are increasing functions of the legacy nutrient stores and soil's ability to hold nutrients. Recommendations for Resource Managers

• We develop a modeling framework to study the effect of the legacy nutrient stores and the soil nutrient dynamics on the optimal nutrient management and agri-environmental policy in crop production.
• Nonlegume catch crop cultivation is a socially optimal long-term measure for nitrogen loss abatement, whereas phosphorus loss abatement with gypsum is socially optimal on soils with high soil phosphorus levels.
• A dynamic tax-subsidy-scheme, which is adjusted annually according to the soil nutrient stocks, leads to social optimum. Although this can be difficult to implement in practice, it can be useful in the derivation of the simpler, static tax-subsidy-schemes.
• If a gypsum subsidy is paid for those years, where the soil P level is above the threshold level for the gypsum application, the welfare loss of the static steady-state-based tax-subsidy-schemes is almost zero.
• Simultaneous adjustment of the N and P fertilizer rates enables the use of simple, static and soil-texture-ignorant tax-subsidy schemes, without a notable social welfare loss

     

考虑品牌差异的双渠道供应链减排与低碳宣传策略

针对双渠道供应链低碳减排、低碳宣传与品牌策略问题,构建微分博弈模型,运用汉密尔顿-雅可比-贝尔曼方程分别求得集中决策和Stackelberg博弈下的低碳减排投入、低碳宣传投入和低碳宣传分担率。研究发现:集中决策情形下产品的减排量始终高于Stackelberg博弈情形下的减排量;产品品牌差异化程度与制造商所承担零售商低碳宣传成本的比例呈正相关;供应链成员的最优低碳宣传策略除了与品牌差异程度相关,还取决于供应链成员在不同渠道边际利润的相对大小;存在一个低碳宣传成本分担率能够实现制造商和零售商协调。并用数值算例验证了本文的相关结论。     

Closed-form solution to a real option problem with regime switching

I investigate the optimal investment timing model in which investment is feasible in only one of the two regimes, which shift at Poisson jump times. I derive the option value and investment threshold in closed forms. I also prove that some solutions in previous models are obtained as the limits of the solution. The closed-form solution can be useful as a new framework to study real option problems with the illiquidity of option exercise opportunities.     

Robust optimal strategies in Markov decision problems

An optimal strategy in a Markov decision problem is robust if it is optimal in every decision problem (not necessarily stationary) that is close to the original problem. We prove that when the state and action spaces are finite, an optimal strategy is robust if and only if it is the unique optimal strategy.     

Linear programming under uncertainty: A basic property of the optimal solution

Summary We show that if the two-stage linear programming problem under uncertainty has an optimal solution, then it has an optimal solution in which the column vectors corresponding to the positive first stage decision variables are linearly independent. This leads to the result that if an optimal solution exists, then there exists an optimal solution in which not more than m + ¯m of the first stage decision variables are positive. These results extend to the multi-stage case.This research was partially supported by the Office of Naval Research under Contract Nonr-222(83), the National Science Foundation under Contract GP-4593, the Army Research Office under Contract DA-31-124-ARO-D-331 and the University of California. Reproduction in whole or part is permitted for any purpose of the United States Government.     

Optimal risk-sharing under mutually singular beliefs

We focus on the situation in which agents might have mutually singular beliefs in a maxmin expected utility framework. We show the existence of an equilibrium under fairly general conditions. We further demonstrate that the characterization of Pareto optimal allocation is significantly different from the classical situation, where all beliefs are mutually equivalent for each agent. Absent aggregate uncertainty, we prove that with common beliefs among agents, any Pareto optimal allocation is a full insurance under the upper capacities for all agents. But the full insurance feature of all Pareto optimal allocations, if true, does not necessarily ensure common beliefs. Moreover, despite agents have sharing beliefs, a full insurance Pareto optimal allocation could be associated with intricate allocation form.     

Are purchase-triggered donations advantageous with competition?

Introducing social responsibility in product development and promotional strategies can affect the cost and demand of a firm’s product, as well as the social impact. We explore whether a firm should employ a purchase-triggered donations (PTD) strategy by proposing an analytical model in which a profit-maximizing firm decides on the product price and its donation amount to the society. Two dimensions of consumer behavior are considered – price and social concern. We identify two common forms of socially responsible action: profit-maximizing ethics, through which socially responsible behavior can actually improve firm profitability, and costly philanthropy, whereby firms engage in socially responsible behavior for their ethical and social values, even if their profitability is consequently reduced. We develop managerial insights by characterizing and exploring the optimal and equilibrium solutions. Contrary to conventional wisdom, our analysis shows that both monopolistic and duopolistic firms prefer not to engage in socially responsible behavior through PTD. On the other hand, if an upper limit is applied on the PTD amount, then competing firms may find themselves in equilibrium with either profit-maximizing ethics or costly philanthropy. In this sense, we conclude that PTD-based corporate social responsibility behavior is best described as a competitive necessity for firms engaged in competition.     

The computational complexity of bilevel assignment problems

In bilevel optimization problems there are two decision makers, the leader and the follower, who act in a hierarchy. Each decision maker has his own objective function, but there are common constraints. This paper deals with bilevel assignment problems where each decision maker controls a subset of edges and each edge has a leader’s and a follower’s weight. The edges selected by the leader and by the follower need to form a perfect matching. The task is to determine which edges the leader should choose such that his objective value which depends on the follower’s optimal reaction is maximized. We consider sum- and bottleneck objective functions for the leader and follower. Moreover, if not all optimal reactions of the follower lead to the same leader’s objective value, then the follower either chooses an optimal reaction which is best (optimistic rule) or worst (pessimistic rule) for the leader. We show that all the variants arising if the leader’s and follower’s objective functions are sum or bottleneck functions are NP-hard if the pessimistic rule is applied. In case of the optimistic rule the problem is shown to be NP-hard if at least one of the decision makers has a sum objective function.     

价格和服务双因素影响的供应链协调决策模型研究

以单个制造商和存在竞争的两个零售商组成的供应链结构模型为研究对象,建立价格和服务两个重要因素影响的市场需求函数,研究供应链协调决策模型。以销售价格、服务质量和制造商批发价格作为三个决策变量,分析集中决策和分散决策两种情景的最优策略,研究收益共享、服务成本分担、收益共享成本分担等三种不同契约的供应链协调问题,并使用数值仿真方法,分析了相关参数变化对系统协调的影响。仿真结果表明:收益共享契约和成本分担契约需满足一定条件才能达到供应链协调,但其效果不一定实现帕累托最优;收益共享和成本分担契约可实现供应链协调,但收入共享系数需在合理区间取值;改进的收益共享成本分担契约能够避免共享系数的盲区,更加有效地达到供应链协调,保持供应链良好运行。     

延迟效应影响下的产学研协同创新知识共享研究

在高校和企业组成的产学研协同创新知识共享体系中,考虑成员的知识共享策略均存在延迟效应时的影响,构建了基于双延迟效应的动态微分模型。运用极大值原理,得到了协同创新主体在集中和分散两种决策下的最优知识共享策略、最优收益和体系的知识水平。研究发现:延迟时间的存在对高校和企业的知识共享策略具有负面效应,且均低于发生即时效应的情形;集中式决策并不总是优于分散式决策,两个延迟时间在满足一定的条件时,选择集中式决策为最优,否则双方企业将追求自身利益最大化而选择分散式决策;分散决策下,利润分配比例达到一定条件时,企业才愿意为高校提供补贴。且高校的知识共享延迟时间增加时,企业将提高该补贴比例。补贴比例越大,高校的知识共享水平越高,但对企业的知识共享策略没有影响。     

De-synchronized clocks in preemption games with risky prospects

We study an optimal timing decision problem where an agent endowed with a risky investment opportunity trades the benefits of waiting for additional information against a potential loss in first-mover advantage. The players’ clocks are de-synchronized in that they learn of the investment opportunity at different times. Thus, the model captures situations where players are heterogeneous with respect to the amount of information that they possess at any instant. In this framework, previous literature has uncovered an inverted-U shaped relationship between a player’s equilibrium expected expenditures and the measure of his competitors. This result no longer holds when the increase in the measure of players leads to a decrease in the degree of clock synchronization in the game. We show that the result reemerges if information arrives only at discrete times, and thus, a player’s strategic beliefs are updated between decision times in a measurably meaningful way.     

Multi-level resource allocation for HIV prevention: A model for developing countries

Funds spent on HIV prevention commonly traverse several levels of distribution. For example, funds may be allocated to regions, and regional authorities may then allocate their funds to sub-regions or targeted risk groups. Decision makers at each level often make use of heuristics that may result in suboptimal allocation of resources. We examine the impact of equity-based heuristic allocation of HIV prevention funds versus optimal allocation of HIV prevention funds when there are two levels of decision making. Our results demonstrate that if optimization can only be applied to one level of the decision making process, there are more significant gains if it is applied at the lower level than at the upper level.     

EVALUATING THE PROSPECTS OF BENEFIT SHARING SCHEMES IN PROTECTING MOUNTAIN GORILLAS IN CENTRAL AFRICA

Presently, the mountain gorilla in Rwanda, Uganda, and the Democratic Republic of Congo is endangered mainly by poaching and habitat loss. This paper sets out to investigate the possible resolution of poaching involving the local community by using benefit sharing schemes with local communities. Using a bioeconomic model, the paper demonstrates that the current revenue sharing scheme yields suboptimal conservation outcomes. It is, however, shown that a performance‐linked benefit sharing scheme in which the Park Agency makes payment to the local community based on the growth of the gorilla stock can achieve socially optimal conservation. This scheme renders poaching effort by the local community, and therefore poaching fines and antipoaching enforcement toward the local community unnecessary. Given the huge financial outlay requirements for the ideal benefit sharing scheme, the Park Agencies in central Africa could reap more financial benefits for use in conservation if they employ an oligopolistic pricing strategy for gorilla tourism.     

Sustainable growth and environmental catastrophes

In the standard AK growth model we introduce the threat of an ecological catastrophe and study the consequences for the economic variables in the long-run. We extend the basic framework by considering two environmental externalities: the first one is local and gives account of the marginal damage from emissions flow; the second one is aggregate, or global, and relates to the extreme damage which may happen if the accumulated stock of pollutants is on the threshold of a worldwide catastrophe. In this context dominated by market failures, we focus on the socially optimal solution and the search of conditions for sustainability. We identify the efficient balanced growth path, which may even show a singularity with trajectories truncating and changing course. In short, with respect to the economy’s long-run performance, we study how environment matters in different ways and at different stages, giving conditions to prevent the catastrophe and preserve (a lower) sustained growth. This paper may also be read as a clear and rigorous example of an optimal control problem involving a pure state-space constraint.     

OPTIMAL FOREST STAND MANAGEMENT WHEN BENEFITS ARE DERIVED FROM CARBON

The management of second-growth and old-growth forest stands has important implications for the global carbon cycle. This paper considers the optimal forest rotation when flows of CO₂ to carbon have positive value. If benefits are derived only from carbon, then typically it will never be optimal to harvest any forest stands. This result is a formalization and extension of Harmon et al. [1990]. Private forest owners will often maximize net returns to timber, ignoring benefits from carbon sequestration. Thus, the privately and socially optimal rotations will not generally coincide. We show that the socially optimal rotation is always greater than the privately optimal rotation and less than or equal to the rotation when only carbon is valued.     

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.