Exploiting multiple cores in a computer or grid of computers can reduce the time required to solve a mixed-integer programming (MIP) model. Here, we develop a parallel branch-and-bound algorithm for a chemical production scheduling problem using a discrete-time model. The algorithm consists of initialization, submission, branching, collection, bounding, and pruning steps. We branch by adding a constraint to bound the total number of times each task runs. Each subproblem is solved as an MIP on a single core of a computer, so that many sub problems can be solved simultaneously. Also, we propose an algorithm, executed at each node of our branch-and-bound tree, to improve the bounds on the number of times a task is run based on the current objective value. We present computational results for several instances to show the parallel algorithm with the proposed branching strategy can solve more challenging problems than simply using the default parallel option. (C) 2013 Elsevier Ltd. All rights reserved.