TABLE OF CONTENTS When a producer has discretion to accept or deny production orders under limited capacity, determining the best set of orders to accept based on both revenue and production/delivery cost implications can be quite challenging. We have proposed several capacitated versions of a combined order selection and production planning model that addresses this challenge. We considered variants of the problem both with and without fixed delivery charges, as well as contexts that permit the producer to satisfy any chosen fraction of any order quantity, thus allowing the producer to ration its capacity. We provided three linear programming relaxations that produce strong upper bound values on the optimal net profit from integrated order selection and production planning decisions. We also provided a set of three effective heuristic solution methods for the OSP. Computational tests performed on a broad set of randomly generated problems demonstrated the effectiveness of our heuristic methods and upper bounding procedures. Problem instances in which the producer has the flexibility to determine any fraction of each order it will supply, and no fixed delivery charges exist, were easily solved using the MIP solver in CPLEX. When fixed delivery charges are present, however, the problem becomes more difficult, particularly as the number of available orders increases. Optimal solutions were still obtained, however, for nearly all test instances within one hour of computing time when partial order satisfaction was allowed. When the producer must take an all-or-nothing approach, satisfying the entire amount of each...
