摘要
出版社在印制图书时每一次印刷都会带来额外的印刷成本,因此需要尽可能减少印刷次数,同时满足市场需求且不至于积压库存造成损失.为解决此问题,首先需要对图书需求进行较好预测,其次需要量化印刷风险,从而得到最优印刷方案.本文针对出版社某类特定图书提出相应的解决方案.利用贪心算法的思路,建立条件期望模型,将期望利润作为优化目标,每一次印刷决策均使得期望利润最大,从而得到每次决策的最优印刷方案,将每次决策的最优印刷方案综合得到全年总体最优的印刷方案.计算期望利润时,假设图书年需求量服从正态分布,利用灰色预测模型估计正态分布的均值,用样本方差估计总体方差,在决策中采用分段函数减少印刷次数,利用历史数据确定分段临界值.经实际数据验证,发现模型计算结果优于实际的印刷方案.
When publishing houses print books,each printing will bring additional printing costs.Therefore,it is necessary to reduce the printing times as much as possible.However,at the same time,publishing houses need to meet the market demand without causing losses due to overstock inventory.In order to solve this problem,we will first propose a method to predict the book demand,and then we will quantify the printing risk,so as to obtain the optimal printing scheme.This paper puts forward corresponding solutions for a specific kind of books in the publishing house.With the idea of greedy algorithm,the conditional expectation model is established,and we take the expected profit as the optimization target.Each printing decision maximizes the expected profit,so as to obtain the optimal printing scheme of each decision,and synthesize the optimal printing scheme of each decision to obtain the overall optimal printing scheme of the whole year.When calculating the expected profit,it is assumed that the annual demand of books follows the normal distribution.The grey prediction model is used to estimate the mean value of the normal distribution,the sample variance is used to estimate the overall variance,the piecewise function is used to reduce the printing times in the decision-making,and the piecewise critical value is determined by historical data verified with actual data,it is found that the calculation result of the model is better than the actual printing scheme.
作者
何浩田
张铭洋
李嘉豪
王颖喆
HE Haotian;ZHANG Mingyang;LI Jiahao;WANG Yingzhe(School of Mathematical Science,Beijing Normal University,Beijing 100875,China)
出处
《数学建模及其应用》
2022年第2期19-25,共7页
Mathematical Modeling and Its Applications
基金
国家自然科学基金(11871103)
北京师范大学“本科生科研训练与创新创业”项目(国家级)。
关键词
条件期望
图书印制策略
贪心算法
conditional expectation
book printing strategy
greedy algorithm
