区间数多产品多计划期生产计划问题的目标规划求解方法

doi:10.3969/j.issn.1007-7375.2018.04.003

摘要/Abstract

摘要： 针对多目标、多产品、多计划期和需求、生产费用、生产能力等参数不确定的综合生产计划问题进行了研究。引入区间数描述生产计划问题中存在的不确定性，建立了以生产成本最小和设备利用率最大为优化目标的目标规划模型。为求解模型，运用区间规划理论和基于区间序关系的可能度定义，实现了区间目标规划模型的清晰等价转换，并采用Lingo软件完成模型求解。该方法解决了传统不确定优化方法在获取概率分布和模糊隶属度函数较为困难的不足，能根据决策者的偏好以交互方式分析出不同置信水平对目标的影响，为决策者在不确定环境下进行生产计划决策提供理论依据。最后，通过算例说明方法的有效性和灵活性。

关键词: 参数不确定, 生产计划, 区间数, 目标规划

Abstract: A multi-objective, multi-period and multi-product aggregate production planning (APP) problem with uncertain demand and uncertain parameters, such as operating cost, production capacity and so on, is studied. An interval goal programming model is developed through introducing interval numbers to represent uncertainties in the APP problem, in which two objectives are taken into consideration, one to minimize the total production cost and the other to maximize machine utilization rate. To solve the uncertain model, the theory of interval programming and the possibility definition based on interval ordinal relation are adopted to transform the uncertain model into its equivalent crisp one, and Lingo software is used to solve the model. The approach overcomes the deficiency of traditional uncertain optimization methods in obtaining precise probability distributions and fuzzy membership functions. In addition, the approach is able to interactively analyze impacts of different confidence levels on the objective function according to the decision maker's preference. Theoretical basis is provided for decision makers to make a rational production plan in uncertain environment. Finally, an industrial example is used to illustrate the validity and flexibility of the proposed method.

Key words: parameter uncertainty, production planning, interval number, goal programming

中图分类号:

TH186

朱斌, 郭岳, 张富强. 区间数多产品多计划期生产计划问题的目标规划求解方法[J]. 工业工程, 2018, 21(4): 15-22.

ZHU Bin, GUO Yue, ZHANG Fuqiang. An Interval Goal Programming Approach for Multi-Period and Multi-Product Aggregate Production Planning Problem[J]. Industrial Engineering Journal , 2018, 21(4): 15-22.

参考文献

[1] 钟海. 大数据在工业制造业的应用与研究[J]. 企业技术开发:学术版, 2015, 34(5):104-105 ZHONG Hai. Application and research of big data in industrial manufacturing[J]. Technological Development of Enterprise, 2015, 34(5):104-105
[2] Liang Tienfu. Fuzzy multi-objective production/distribution planning decisions with multi-product and multi-time period in a supply chain[J]. Computers & Industrial Engineering, 2008, 55(3):676-94
[3] 唐加福, 汪定伟, 许宝栋. 多品种集约生产计划问题的模糊方法[J]. 管理科学学报, 2003, 6(1):44-50 TANG Jiafu, WANG Dingwei, XU Baodong. Fuzzy modeling approach to aggregate production planning with multi-product[J]. Journal of Management Sciences in China, 2003, 6(1):44-50
[4] ENTEZAMINIA, Arezoo, HEIDARI Mahdi, RAHMANI Donya. Robust aggregate production planning in a green supply chain under uncertainty considering reverse logistics:a case study[J]. International Journal of Advanced Manufacturing Technology, 2017, 90(5-8):1507-1528
[5] 徐学军, 顾培亮. 随机综合生产计划模型及其求解研究[J]. 工业工程, 2001, 4(3):12-15 XU Xuejun, GU Peiliang. Study on stochastic aggregate production planning models and solution procedure[J]. Industrial Engineering Journal, 2001, 4(3):12-15
[6] MULA J, POLER R, GARCIA-SABATER JP, et al. Models for production planning under uncertainty:a review[J]. International Journal of Production Economics, 2006, 103(1):271-285
[7] 彭锦, 刘宝碇. 不确定规划的研究现状及其发展前景[J]. 运筹与管理, 2002, 11(2):1-10 PENG Jin, LIU Baoding. Uncertain programming:current status and future prospects[J]. Operations Research and Management Science, 2002, 11(2):1-10
[8] 严洪森, 张晓东, 王浩. 满足产品需求条件下的车间最优随机生产计划与控制[J]. 中国机械工程, 200213(3):228-232 YAN Hongsen, ZHANG Xiaodong, WANG Hao. Optimal stochastic production planning and control for workshops with demand constraints[J]. China Mechanical Engineering, 200213(3):228-232
[9] Al-E-HASHEM S M J Mirzapour, BABOLI A, SAZVAR Z. A stochastic aggregate production planning model in a green supply chain:considering flexible lead times, nonlinear purchase and shortage cost functions[J]. European Journal of Operational Research, 2013, 230(1):26-41
[10] YAN H S. Hierarchical stochastic production planning with delay interaction[J]. Journal of Optimization Theory and Applications, 2000, 104(3):659-689
[11] 白进达, 曹喆, 张东凯, 等. 模糊批量生产计划问题的可信性规划模型与算法[J]. 模糊系统与数学, 2007, 21(2):113-120 BAI Jinda, CAO Zhe, ZHANG Dongkai, et al. Credibility programming approach to lot sizing production planning in fuzzy environment[J]. Fuzzy Systems and Mathematics, 2007, 21(2):113-120
[12] 唐加福, 董颖, 刘士新, 等. 模糊需求和模糊能力约束的集约生产计划[J]. 控制理论与应用, 2003, 20(6):894-896 TANG Jiafu, DONG Ying, LIU Shixin, et al. Aggregate production planning with fuzzy demands and fuzzy capacity[J]. Control theory & Applications, 2003, 20(6):894-896
[13] GUO Q Y. Two-stage fuzzy production planning expected value model and its approximation method[J]. Applied Mathematical Modelling, 2012, 36(6):2429-2445
[14] 葛健, 李燕风, 夏国平. 不确定环境下跨国供应链生产计划研究[J]. 计算机集成制造系统, 2005, 11(8):1120-1126 GE Jian, LI Yanfeng, XIA Guoping. Research on global supply chain production planning under uncertain environment[J]. Computer Integrated Manufacturing Systems, 2005, 11(8):1120-1126
[15] 姜潮. 基于区间的不确定性优化理论与算法[D]. 长沙:湖南大学, 2008 JIANG Chao. Theories and algorithms of uncertain optimization based on interval[D]. Changsha:Hunan University, 2008
[16] 邱涤珊, 贺川, 朱晓敏. 基于概率可信度的区间数排序方法[J]. 控制与决策, 2012, 27(12):1894-1898 QIU Dishan, HE Chuan, ZHU Xiaomin. Ranking method research of interval numbers based on probability reliability distribution[J]. Control and Decision, 2012, 27(12):1894-1898
[17] 肖峻, 张跃, 付川. 基于可能度的区间数排序方法比较[J]. 天津大学学报, 2011, 44(8):705-711 XIAO Jun, ZHANG Yue, FU Chuan. Comparison between methods of interval number ranking based on possibility[J]. Journal of Tianjin University, 2011, 44(8):705-711
[18] 张全, 樊治平, 潘德惠. 不确定性多属性决策中区间数的一种排序方法[J]. 系统工程理论与实践, 1999(5):129-133 ZHANG Quan, FAN Zhiping, PAN Dehui. A ranking approach for interval numbers in uncertain multiple attribute decision making problems[J]. Systems Engineering-Theory & Practice, 1999(5):129-133
[19] 达庆利, 刘新旺. 区间数线性规划及其满意解[J]. 系统工程理论与实践, 1999(4):3-7 DA Qingli, LIU Xinwang. Interval number linear programming and its satisfactory solution[J]. Systems Engineering-theory & Practice, 1999(4):3-7
[20] DUBIOS D, PARADE H. Ranking fuzzy numbers in the setting of possibility theory[J]. Information Sciences, 1983, 30(3):183-224
[21] JIANG C, HAN X, LIU G R. A nonlinear interval number programming method for uncertain optimization problems[J]. European Journal of Operational Research, 2008, 188(1):1-13