Gray markets, also known as parallel imports, are marketplaces for trading genuine products that are diverted from authorized distribution channels. They have created fierce competition for manufacturers in many industries and each year billions of dollars worth of products are traded in these markets. Using a gametheoretic model, we analyze the impact of parallel importation on a price-setting manufacturer that serves two markets with uncertain demand. We characterize the optimal joint price and quantity decisions of the manufacturer which determine whether the manufacturer should ignore, block, or allow parallel importation.We also show that parallel importation forces the manufacturer to reduce her price gap while demand uncertainty forces her to lower prices in both markets. Moreover, we observe that parallel importation may force the manufacturer to exit the low-profit market. Through extensive numerical experiments, we explore the impact of market conditions (size and price elasticity) and product characteristics (a fashion item or a commodity) on the manufacturer's reaction to parallel importation. In addition, we provide interesting insights about the value of strategic pricing for coping with gray markets versus the uniform pricing policy that has been adopted by some companies to eliminate gray markets.

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Every year, companies that produce consumer tax preparation software struggle with a massive amount of work imposed by thousands of state and federal changes to tax laws and forms. With their release not even beginning before August, these changes still must be processed and incorporated into the application by midDecember. Three companies dominate this competitive market with its short selling season so that release delays create significant losses. Though systematic resource allocation and process management are crucial, the volume and complexity of the changes, the brief timeframe to implement them, and feedback loops built into the system for error resolution make it extremely difficult to analyze the process. One of the leading tax software providers tasked us with developing systematic approaches for managing the process flow and staffing each stage so that the company met the deadline at the lowest cost. Based on the characteristics of the process, we develop deterministic models that partition tax forms into groups and determine the staffing levels for each group. Partitioning the development process into groups has the benefit of simplifying workflow management and making it easier to find staffing levels. To provide the company with a range of resource configurations, we use two modeling approaches to obtain lower and upper bounds on the number of resources at each stage. Numerical experiments indicate that the models successfully capture the features of the process and the heuristics perform well. Implementing our models at the company has resulted in 31% reduction in overtime and 13% reduction in total resource costs.

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