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W e propose and test a new pricing procedure for solving large-scale structured linear programs. The procedure interactively solves a relaxed subproblem to identify potential entering basic columns. The subproblem is chosen to exploit special structure, rendering it easy to solve. The effect of the procedure is the reduction of the number of pivots needed to solve the problem. Our approach is motivated by the column-generation approach of Dantzig-Wolfe decomposition. We test our procedure on two sets of multicommodity flow problems. One group of test problems arises in routing telecommunications traffic and the second group is a set of logistics problem which have been widely used to test multicommodity flow algorithms.

Research Summary: Inquiry into CSR as a human capital management tool has suggested that firms benefit from such activities because employees value the meaningfulness of these activities, which influences motivation and retention. We propose an alternate avenue through which firms can benefit from an important type of socially responsible activity—pro bono services—that does not require that employees derive utility from the meaningfulness of the activity. We propose that pro bono activities can benefit firms through human capital learning and screening mechanisms, given the stretch roles that pro bono engagements allow. We formalize this argument in the legal services industry, where we provide primary evidence, a formal model, and empirical results using a panel dataset of the top 200 law firms to support this argument. Managerial Summary: We examine a type of CSR activity, pro bono engagements, in the context of the top 200 law firms in the United States. We show that firms can benefit from these engagements through human capital learning and screening mechanisms, due to the stretch roles that pro bono engagements allow junior lawyers. Our findings suggest that firms in which pro bono engagements provide stretch roles for junior employees can benefit from pro bono activities regardless of whether their employees value the meaningfulness or social impact of the pro bono work.