In this paper, we address a variant of the marketing mix optimization (MMO) problem which is commonly encountered in many industries, e.g., retail and consumer packaged goods (CPG) industries. This problem requires the spend for each marketing activity, if adjusted, be changed by a non-negligible degree (minimum change) and also the total number of activities with spend change be limited (maximum number of changes). With these two additional practical requirements, the original resource allocation problem is formulated as a mixed integer nonlinear program (MINLP). Given the size of a realistic problem in the industrial setting, the state-of-the-art integer programming solvers may not be able to solve the problem to optimality in a straightforward way within a reasonable amount of time. Hence, we propose a systematic reformulation to ease the computational burden. Computational tests show significant improvements in the solution process.

翻译：在本文中,我们讨论了许多行业(如零售和消费品包装产品行业)通常遇到的营销混合优化问题的变式,这一问题要求每次营销活动的支出(如果调整的话)以不可忽略的程度(最小变化)加以改变,同时对有支出变化的活动的总数加以限制(变动的最大数量),由于这两个额外的实际要求,最初的资源分配问题被表述为混合整数非线性方案(MILP),鉴于工业环境中一个现实问题的规模,最先进的整数程序制定者可能无法在合理的时间内以直截了当的方式解决问题,使之达到最佳。因此,我们建议系统地调整,以减轻计算负担。