Product bundling has become increasingly prevalent not only in consumer goods but also in the industrial sector. We study a purchasing problem in which a buyer must obtain necessary numbers of various stock items from a variety of vendors who charge different prices, have limited capacities and different levels of quality, and offer bundled products at discounted prices.We examine relationships among different bundling scenarios and show that the most general scenario is one in which free items are given to the buyer when sufficient quantities are purchased. We develop a mixed integer linear program that finds the purchasing strategy for the buyer that minimizes the total purchase cost. We present computational results which indicate that the problem is very tractable to solve optimally on a personal computer with standard optimization software. Finally, three extensions of the model are discussed.Subject Areas: Mathematical Programming and Production/Operations Management.

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Abstract:We examine behavior of the core and value of certain classes of cooperative games in which a dynamic aspect is introduced. New players are added to the games while the underlying structure is held constant. This is done by considering games that satisfy properties like convexity, or games that are derived from optimization problems in which a player's addition can be defined naturally. For such games we give conditions regarding monotonicity of the core and value.