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Mixed-integer programming models are typically not used to solve realistic-sized production scheduling problems because they require exorbitant solution times. We impose a useful taxonomy on production scheduling problems and develop alternative formulations for a wide variety of problems within the taxonomy. The linear programming relaxation of the new models is very effective in generating bounds. We show that these bounds are equal to those that could be generated using Lagrangian relaxation or column generation. The linear programming bounds increase in effectiveness as the problems become larger. Perhaps of greatest significance is that practitioners can obtain our results using only standard “off-the-shelf” codes such as LINDO or MPSX/370. We report computational experience in several computing environments (hardware and software) on problems with up to 200 products and 10 time periods (2000 0-1 variables).

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The present study was concerned with the development and evaluation of a scale of speech naturalness. Speech samples were recorded of the typical speech of 10 stutterers, 10 stutterers speaking without stuttering under 250-ms delayed auditory feedback (DAF), and 10 nonstutterers speaking normally. Using a 9-point scale, 30 unsophisticated listeners judged how natural the speech sounded in each sample. Results indicated that the stutterer samples were judged as sounding significantly more unnatural than the nonstutterer samples, and the DAF stutter-free samples were judged as sounding significantly more unnatural than the nonstutterer samples. The stutterer and DAF stutter-free samples were not judged as sounding significantly different in terms of speech naturalness. Interrater reliability, interrater agreement, and rater consistency for judging speech naturalness were all satisfactory.

Bundle pricing is a widespread phenomenon. However, despite its importance as a pricing tool, surprisingly little is known about how to find optimal bundle prices. Most discussions in the literature are restricted to only two components, and even in this case no algorithm is given for setting prices. Here we show that the single firm bundle pricing problem is naturally viewed as a disjunctive program which is formulated as a mixed integer linear program. Multiple components, and a variety of cost and reservation price conditions are investigated with this approach. Several new economic insights on the role and effectiveness of bundling are presented. An added benefit of the solution to the bundle pricing model is the selection of products which compose the firm's product line. Computational testing is done on problems with up to 21 components (over one million potential product bundles), and data collection issues are addressed.marketing, pricing, product policy, mathematical programming, mixed integer linear