Production,Process Investment,and the Survival of Debt‐Financed Startup Firms

Whether to invest in process development that can reduce the unit cost and thereby raise future profits or to conserve cash and reduce the likelihood of bankruptcy is a key trade‐off faced by many startup firms that have taken on debt. We explore this trade‐off by examining the production quantity and cost reducing R&D investment decisions in a two period model wherein a startup firm must make a minimum level of profit at the end of the first period to survive and operate in the second period. We specify a probabilistic survival measure as a function of production and investment decisions to track and manage the risk exposure of the startup depending on three key market factors: technology, demand, and competitor's cost. We develop managerial insights by characterizing how to create operational hedges against the bankruptcy risk: if a startup makes a “conservative” investment decision, then it also selects an optimal quantity that is less than the monopoly level and hence sacrifices some of first period expected profits to increase its survival chances. If it decides to invest “aggressively,” then it produces more than the monopoly level to cover the higher bankruptcy risk. We also illustrate that debt constraint shrinks the decision space, wherein such process investments are viable.     

Capacity Planning with Financial and Operational Hedging in Low‐Cost Countries

The authors of this article outline a capacity planning problem in which a risk‐averse firm reserves capacities with potential suppliers that are located in multiple low‐cost countries. While demand is uncertain, the firm also faces multi‐country foreign currency exposures. This study develops a mean‐variance model that maximizes the firm's optimal utility and derives optimal utility and optimal decisions in capacity and financial hedging size. The authors show that when demand and exchange rate risks are perfectly correlated, a risk‐averse firm, by using financial hedging, will achieve the same optimal utility as a risk‐neutral firm. In this study as well, a special case is examined regarding two suppliers in China and Vietnam. The results show that if a single supplier is contracted, financial hedging most benefits the highly risk‐averse firm when the demand and exchange rate are highly negatively related. When only one hedge is used, financial hedging dominates operational hedging only when the firm is very risk averse and the correlation between the two exchange rates have become positive. With both theoretical and numerical results, this study concludes that the two hedges are strategic tools and interact each other to maximize the optimal utility.     

Measuring the Impact of Increased Product Substitution on Pricing and Capacity Decisions Under Linear Demand Models

We consider two substitutable products and compare two alternative measures of product substitutability for linear demand functions that are commonly used in the literature. While one leads to unrealistically high prices and profits as products become more substitutable, the results obtained using the other measure are in line with intuition. Using the more appropriate measure of product substitutability, we study the optimal investment mix in flexible and dedicated capacities in both monopoly and oligopoly settings. We find that the optimal investment in manufacturing flexibility tends to decrease as the products become closer substitutes; this is because (1) pricing can be used more effectively to balance supply and demand, and (2) the gains obtained by shifting production to the more profitable product are reduced due to increased correlation between the price potentials of the substitutable products. The value of flexibility always increases with demand variability. We also show that, as long as the optimal investments in dedicated capacity for both products are positive, the optimal expected prices and production quantities do not depend on the cost of the flexible capacity. Manufacturing flexibility simply allows the firm to achieve those expected values with lower capacity, while leading to higher expected profits.     

Impact of Price Postponement on Capacity and Flexibility Investment Decisions

Investments in dedicated and flexible capacity have traditionally been based on demand forecasts obtained under the assumption of a predetermined product price. However, the impact on revenue of poor capacity and flexibility decisions can be mitigated by appropriately changing prices. While investment decisions need to be made years before demand is realized, pricing decisions can easily be postponed until product launch, when more accurate demand information is available. We study the effect of this price decision delay on the optimal investments on dedicated and flexible capacity. Computational experiments show that considering price postponement at the planning stage leads to a large reduction in capacity investments, especially in the more expensive flexible capacity, and a significant increase in profits. Its impact depends on demand correlation, elasticity and diversion, ratio of fixed to variable capacity costs, and uncertainty remaining at the times the pricing and production decisions are made.     

随机供需条件下装配商的订购-定价联合决策问题

针对随机供需条件下装配商的订购与定价联合决策这一难题，运用随机非线性规划方法，以装配商期望利润最大化为目标，建立零部件订购量与最终产品定价的多维优化模型。刻画了给定价格时的最优订购量和给定订购量时的最优价格，最后给出关于最优订购-定价的必要条件。通过数值算例验证了模型结论并进一步探讨随机供需的影响，为装配商的订购-定价决策以及供应商改进提供有益的管理启示。     

需求不确定条件下的制造商订单分配模型

制造商的订单分配作为供应链模型微观层面的重要组成部分,对提升整个供应链效率有很大影响,但需求层面的不确定因素加大了订单分配的难度。以按比例分配为原则,讨论在需求不确定条件下完全信息与不完全信息两类多供应商-单制造商的订单分配模型。重点研究完全信息条件下各方的分散决策和集中决策,由于后者能避免各参与方对其他决策方的边际影响,所以能够实现供应链总利润的最大化;其次又将不完全信息引入模型,讨论制造商如何通过折算因子结合已有信息对供应商的私人信息进行估计,进而做出决策。最后以需求服从正态分布为例对两类模型进行验证。     

有限产能直销优先策略下双渠道供应链的定价博弈模型

针对产能约束下的双渠道供应链,考虑实际中常用的直销优先分配产能的策略,基于Stackelberg博弈研究制造商(领导者)和零售商(追随者)的定价决策,刻画均衡解并深入分析直销优先策略下产能约束对双渠道供应链利润的影响。研究发现,在不同产能水平下,制造商对两个渠道的依赖程度会发生变化。当产能短缺时,其利润主要源于直销渠道;而当产能相对充足时,其愿意分享更多的产能以换取零售渠道上的批发利润,且此时增大产能可能会损害制造商的利益。对零售商而言,当产能短缺时,其采用高溢价来弥补获得较少产能的劣势;当产能相对充足时,其采用薄利多销的策略来获取更多的利润。当产能过剩时,双方的利润不再受产能的影响,且产能过剩对双方而言不一定是最好的情况。研究结论为制造商的定价与在双渠道中的产能分配策略选择提供有益的管理启示。     

Coordinating pricing and production decisions for multiple products

We consider a dynamic problem of joint pricing and production decisions for a profit-maximizing firm that produces multiple products. We model the problem as a mixed integer nonlinear program, incorporating capacity constraints, setup costs, and dynamic demand. We assume demand functions to be convex, continuous, differentiable, and strictly decreasing in price. We present a solution approach which is more general than previous approaches that require the assumption of a specific demand function. Using real-world data from a manufacturer, we study problem instances for different demand scenarios and capacities and solve for optimal prices and production plans. We present analytical results that provide managerial insights on how the optimal prices change for different production plans and capacities. We extend some of the earlier works that consider single product problems to the case of multiple products and time variant production capacities. We also benchmark performance of proposed algorithm with a commercial solver and show that it outperforms the solver both in terms of solution quality and computational times.     

Multi‐Product Quality Competition: Impact of Resource Constraints

We study a multi‐product firm with limited capacity where the products are vertically (quality) differentiated and the customer base is heterogeneous in their valuation of quality. While the demand structure creates opportunities through proliferation, the firm should avoid cannibalization between its own products. Moreover, the oligopolistic market structure puts competitive pressure and limits the firm's market share. On the other hand, the firm has limited resources that cause a supply‐side fight for adequate and profitable production. We explicitly characterize the conditions where each force dominates. Our focus is on understanding how capacity constraints and competition affect a firm's product‐mix decisions. We find that considering capacity constraints could significantly change traditional insights (that ignore capacity) related to product‐line design and the role of competition therein. In particular, we show that when the resources are limited, the firm should offer only the product that has the highest margin per unit capacity. We find that this product could be the diametrically opposite product suggested by the existing literature. In addition, we show that for intermediate capacity levels, whereas the margin per unit capacity effect dominates in a less competitive market, proliferation and cannibalization effects dominate in a more competitive market.     

Coordination in Games with Strategic Complementarities: An Experiment on Fixed vs. Random Matching

In this article, we study behavior in a series of two‐player supply chain game experiments. Each player simultaneously chooses a capacity before demand is realized, and sales are given by the minimum of realized demand and chosen capacities. We focus on the differences in behavior under fixed pairs and random rematching. Intuition suggests that long‐run relations should lead to more profitable outcomes. However, our results go against this intuition. While subjects' capacity choices are better aligned (i.e., closer together) under fixed pairs, average profits are more variable. Moreover, learning is slower under fixed pairs—so much so that over the last five periods, average profits are actually higher under random rematching. The underlying cause for this finding appears to be a “first‐impressions” bias, present only under fixed matching, in which the greater the misalignment in initial choices, the lower are average profits.     

Branch‐and‐Price Methods for Prescribing Profitable Upgrades of High‐Technology Products with Stochastic Demands*

This paper develops a model that can be used as a decision support aid, helping manufacturers make profitable decisions in upgrading the features of a family of high‐technology products over its life cycle. The model integrates various organizations in the enterprise: product design, marketing, manufacturing, production planning, and supply chain management. Customer demand is assumed random and this uncertainty is addressed using scenario analysis. A branch‐and‐price (B&P) solution approach is devised to optimize the stochastic problem effectively. Sets of random instances are generated to evaluate the effectiveness of our solution approach in comparison with that of commercial software on the basis of run time. Computational results indicate that our approach outperforms commercial software on all of our test problems and is capable of solving practical problems in reasonable run time. We present several examples to demonstrate how managers can use our models to answer “what if” questions.     

Supply Diversification with Responsive Pricing

We study sourcing and pricing decisions of a firm with correlated suppliers and a price‐dependent demand. With two suppliers, the insight—cost is the order qualifier while reliability is the order winner—derived in the literature for the case of exogenously determined price and independent suppliers, continues to hold when the suppliers' capacities are correlated. Moreover, a firm orders only from one supplier if the effective purchase cost from him, which includes the imputed cost of his unreliability, is lower than the wholesale price charged by his rival. Otherwise, the firm orders from both. Furthermore, the firm's diversification decision does not depend on the correlation between the two suppliers' random capacities. However, its order quantities do depend on the capacity correlation, and, if the firm's objective function is unimodal, the total order quantity decreases as the capacity correlation increases in the sense of the supermodular order. With more than two suppliers, the insight no longer holds. That is, when ordering from two or more suppliers, one is the lowest‐cost supplier and the others are not selected on the basis of their costs. We conclude the paper by developing a solution algorithm for the firm's optimal diversification problem.     

On service degrade at a discount: Capacity, demand pooling, and optimal discounting

In this paper we study the capacity investment decisions and operational strategies of a firm providing two-class services facing uncertain demands. The capacity decisions of the resources are made before demands are observed. Each service can be implemented by its corresponding resource. Should a mismatch between the capacity and the actual demand for the services arise, the low-class resource can be used as a substitute for the high-class service. We introduce an operational strategy called degrade-at-a-discount, where a price discount is offered to motivate customers to accept a lower class service when their original choice is out of capacity. By formulating the problem as a one-period, two-stage stochastic problem, we analyze how to set up the optimal capacity and the optimal discount. We also conduct a comprehensive numerical study to show the benefits of the degrade-at-a-discount strategy.     

Committed Versus Contingent Pricing Under Competition

Should capacitated firms set prices responsively to uncertain market conditions in a competitive environment? We study a duopoly selling differentiated substitutable products with fixed capacities under demand uncertainty, where firms can either commit to a fixed price ex ante, or elect to price contingently ex post, e.g., to charge high prices in booming markets, and low prices in slack markets. Interestingly, we analytically show that even for completely symmetric model primitives, asymmetric equilibria of strategic pricing decisions may arise, in which one firm commits statically and the other firm prices contingently; in this case, there also exists a unique mixed strategy equilibrium. Such equilibrium behavior tends to emerge, when capacity is ampler, and products are less differentiated or demand uncertainty is lower. With asymmetric fixed capacities, if demand uncertainty is low, a unique asymmetric equilibrium emerges, in which the firm with more capacity chooses committed pricing and the firm with less capacity chooses contingent pricing. We identify two countervailing profit effects of contingent pricing under competition: gains from responsively charging high price under high demand, and losses from intensified price competition under low demand. It is the latter detrimental effect that may prevent both firms from choosing a contingent pricing strategy in equilibrium. We show that the insights remain valid when capacity decisions are endogenized. We caution that responsive price changes under aggressive competition of less differentiated products can result in profit‐killing discounting.     

The Impact of Product Lifecycle on Capacity Planning of Closed‐Loop Supply Chains with Remanufacturing

Product recovery operations in reverse supply chains face rapidly changing demand due to the increasing number of product offerings with reduced lifecycles. Therefore, capacity planning becomes a strategic issue of major importance for the profitability of closed‐loop supply chains. This work studies a closed‐loop supply chain with remanufacturing and presents dynamic capacity planning policies developed through the methodology of System Dynamics. The key issue of the paper is how the lifecycles and return patterns of various products affect the optimal policies regarding expansion and contraction of collection and remanufacturing capacities. The model can be used to identify effective policies, to conduct various “what‐if” analyses, and to answer questions about the long‐term profitability of reverse supply chains with remanufacturing. The results of numerical examples with quite different lifecycle and return patterns show how the optimal collection expansion/contraction and remanufacturing contraction policies depend on the lifecycle type and the average usage time of the product, while the remanufacturing capacity expansion policy is not significantly affected by these factors. The results also show that the collection and remanufacturing capacity policies are insensitive to the total product demand. The insensitivity of the optimal policies to total demand is a particularly appealing feature of the proposed model, given the difficulty in obtaining accurate demand forecasts.     

A Note on the Relationship Among Capacity,Pricing, and Inventory in a Make‐to‐Stock System

We address the simultaneous determination of pricing, production, and capacity investment decisions by a monopolistic firm in a multi‐period setting under demand uncertainty. We analyze the optimal decision with particular emphasis on the relationship between price and capacity. We consider models that allow for either bi‐directional price changes or models with markdowns only, and in the latter case we prove that capacity and price are strategic substitutes.     

基于随机产出与随机需求的农产品供应链风险共担合同

本文采用单位价格补贴的风险共担机制,分析了农产品供应链中随机产出和随机需求下供应商-制造商采取不同的风险共担合同对农资投入、供应商、制造商以及整个供应链的利润的影响。文中的风险共担合同包括风险无共担合同、需求风险共担合同、产出风险共担合同、产出-需求风险共担合同,结合算例,结论得出:需求风险分担可以使供应链利润增加;产出风险分担可以增加供应商的利润收益,而赋予制造商控制供应商农资投入积极性的权利;产出-需求共担合同既能增加供应链及各成员的利润收益,同时还使得双方相互制约、相互协调,促使供应链良好发展。最后,结合非线性补贴的风险分担形式对上述合同的有效性进行了验证,研究表明,不同的补贴形式只在量上对决策存在影响,而本质上的结论并没有变化。     

产能不确定供应商的风险厌恶行为对供应链的影响

针对具有产能不确定性的风险厌恶供应商和风险中性零售商组成的供应链系统,本文采用经典的风险指标Value-at-risk(VaR)衡量供应商的风险厌恶程度,并将其作为供应商的优化约束条件之一。在斯坦伯格顺序博弈的模型框架下,零售商做定价和订货量决策,供应商做批发价决策。本文求得供应商批发价在VaR约束下的理论上下界,研究了风险厌恶程度对最优批发价的影响。与风险中性环境下的结果相比,在设立合理目标利润的前提下,高风险厌恶程度可能使得供应商提高批发价,低风险厌恶程度则对供应商批发价无影响。当目标利润设立很高时,供应商为了逐利将会降低批发价诱导零售商提高订货量。     

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

When firms invest in a shared supplier, one key concern is whether the invested capacity will be used for a competitor. In practice, this concern is addressed by restricting the use of the capacity. We consider what happens when two competing firms invest in a shared supplier. We consider two scenarios that differ in how capacity is used: exclusive capacity and first‐priority capacity. We model firms' investment and production decisions, and analyze the equilibrium outcomes in terms of the number of investing firms and capacity levels for each scenario; realized capacity is a stochastic function of investment levels. We also identify conditions under which the spillover effect occurs, where one firm taps into the other firm's invested capacity. Although the spillover supposedly intensifies competition, it actually discourages firms' investment. We also characterize the firms' and supplier's preference about the capacity type. While the non‐investing firm always prefers spillovers from the first‐priority capacity, the investing firm does not always want to shut off the other firm's access to its leftover capacity, especially when allowing spillover induces the other firm not to invest. The supplier's preference depends on the trade‐off between over‐investment and flexibility.     

Pay‐Back‐Revenue‐Sharing Contract in Coordinating Supply Chains with Random Yield

We consider coordination issues in supply chains where supplier's production process is subject to random yield losses. For a simple supply chain with a single supplier and retailer facing deterministic demand, a pay back contract which has the retailer paying a discount price for the supplier's excess units can provide the right incentive for the supplier to increase his production size and achieve coordination. Building upon this result, we consider coordination issues for two other supply chains: one with competing retailers, the other with stochastic demand. When retailers compete for both demand and supply, they tend to over‐order. We show that a combination of a pay back and revenue sharing mechanism can coordinate the supply chain, with the pay back mechanism correcting the supplier's under‐producing problem and the revenue sharing mechanism correcting the retailers' over‐ordering problem. When demand is stochastic, we consider a modified pay‐back‐revenue‐sharing contract under which the retailer agrees to not only purchase the supplier's excess output (beyond the retailer's order), but also share with the supplier a portion of the revenue made from the sales of the excess output. We show that this contract, by giving the supplier additional incentives in the form of revenue share, can achieve coordination.