针对由一个制造工厂和多个区域服务中心组成的服务型制造企业，研究了考虑生产时间和服务时间均具有随机性且工期可指派的产品服务系统（PSS）订单调度问题。首先以最小化订单提前、误工和工期指派费用的期望总额为目标构建问题的优化模型，然后分析目标函数近似值的最优性条件，据此提出加权最短平均生产时间排序规则，并结合该规则与插入邻域局部搜索设计了启发式算法对问题进行求解，最后通过数值仿真验证算法的可行性和有效性。研究表明，提前费用偏差对PSS订单调度与工期指派决策的影响很小，因此企业管理者无需准确估计库存费用也能制定出比较有效的PSS订单调度策略；而工期指派费用偏差对决策结果的影响非常大，因此企业管理者在决策时必须谨慎估计该项费用。
With the market competition growing ever more tense and the profit space of the product compressing continuously,the traditional manufacturing industry begins to transform from product-oriented manufacturing to service-oriented manufacturing. Instead of selling products only, the service-oriented manufacturing (SOM) firms offers the customers the integrated solutions of products and services which are called product service systems (PSSs). In order to delivery PSS orders on time and to reduce operating costs incurred by inventory and tardiness, the SOM firms need to assign reasonable due dates to the orders and make effective scheduling plans. However, the production times and service times of PSS orders may be stochastic due to customized demand, which adds more difficulty and complexity to the due date assignment in sequencing PSS orders. Therefore, how to jointly schedule PSS orders and assign due dates in a stochastic environment is a significant problem for SOM firms.
In this paper, the stochastic scheduling problem of PSS orders with due date assignment is addressed for a SOM firm consisting of one single manufacturing plant and multiple regional service centers. It is assumed that the production times and service times are independent and normally distributed with the mean and variance provided. The objective is to minimize the total expected earliness, tardiness and due date assignment costs. To solve this problem, the mean value theorem of integrals is applied to obtain an approximate objective function of the original one and the optimality conditions are analyzed. A sequencing rule called the weighted shortest average production time is presented, based on which three heuristics are proposed. In the numerical experiments, the sensitivity analysis is carried out and the effectiveness and robustness of the proposed heuristics is illustrated.
The results indicate that the unit earliness cost deviation has little influence on the total expected costs, hence there is no need for the dispatchers to ensure the accuracy of the unit inventory cost. Whereas the unit due date assignment cost has a significant impact on the results of the scheduling decision, which suggests that the dispatchers should pay great attention to the accuracy of this cost. Our research sheds light on reducing the operating costs and increasing the service levels of the SOM firms, since it can assist the dispatchers of SOM firms in scheduling PSS orders and setting due dates effectively.
[1] 中国政府网. 三部门关于印发《发展服务型制造专项行动指南》的通知[EB/OL]. http://www.gov.cn/xinwen/2016-07/28/content_5095552.htm, 2016.
[2] Mont O K. Clarifying the concept of product-service system[J]. Journal of Cleaner Production, 2002, 10(3):237-245.
[3] Slotnick S A, Sobel M J. Manufacturing lead-time rules:Customer retention versus tardiness costs[J]. European Journal of Operational Research, 2005, 163(3):825-856.
[4] Tsay A A, Agrawal N. Channel dynamics under price and service competition[J]. Manufacturing & Service Operations Management, 2000, 2(4):372-391.
[5] Lee S, Yoo S, Kim D. When is servitization a profitable competitive strategy?[J]. International Journal of Production Economics, 2016, 173:43-53.
[6] Xie Wenming, Jiang Zhibin, Zhao Yingxue, et al. Contract design for cooperative product service system with information asymmetry[J]. International Journal of Production Research, 2014, 52(6):1658-1680.
[7] 刘宇熹, 谢家平. 再制造下租赁产品服务系统节约共享契约研究[J]. 中国管理科学, 2016, 24(3):99-108.
[8] Xie Wenming, Jiang Zhibin, Zhao Yingxue, et al. Capacity planning and allocation with multi-channel distribution[J]. International Journal of Production Economics, 2014, 147(1):108-116.
[9] Li Gang, Huang Fengfeng, Cheng T C E, et al. Make-or-buy service capacity decision in a supply chain providing after-sales service[J]. European Journal of Operational Research, 2014, 239(2):377-388.
[10] 姚树俊, 陈菊红. 考虑渠道权利结构的产品服务能力竞争机制研究——制造商服务视角[J]. 中国管理科学, 2014, 22(7):107-115.
[11] Li Na, Jiang Zhibin. Modeling and optimization of a product-service system with additional service capacity and impatient customers[J]. Computers & Operations Research, 2013, 40(8):1923-1937.
[12] Wang Kangzhou, Jiang Zhibin, Li Na, et al. Optimal production and admission control for a stochastic SOM system with demands for product and PSS[J]. International Journal of Production Research, 2013, 51(23-24):7270-7288.
[13] Gordon V, Proth J M, Chu C. A survey of the state-of-the-art of common due date assignment and scheduling research[J]. European Journal of Operational Research, 2002, 139(1):1-25.
[14] Saghafian S. Flowshop-scheduling problems with makespan criterion:A review[J]. International Journal of Production Research, 2005, 43(14):2895-2929.
[15] Ribas I, Leisten R, Framinan J M. Review and classification of hybrid flow shop scheduling problems from a production system and a solutions procedure perspective[J]. Computers & Operations Research, 2010, 37(8):1439-1454.
[16] Shahidehpour M, Marwali M. Maintenance scheduling in restructured power systems[M]. New York:Springer US, 2000.
[17] Kaandorp G C, Koole G. Optimal outpatient appointment scheduling[J]. Health Care Management Science, 2007, 10(3):217-229.
[18] Garcia J M, Lozano S. Production and delivery scheduling problem with time windows[J]. Computers & Industrial Engineering, 2005, 48(4):733-742.
[19] Li K, Ganesan V K, Sivakumar A I. Scheduling of single stage assembly with air transportation in a consumer electronic supply chain[J]. Computers & Industrial Engineering, 2006, 51(2):264-278.
[20] Low C, Li R, Chang C. Integrated scheduling of production and delivery with time windows[J]. International Journal of Production Research, 2013, 51(3):897-909.
[21] 马士华, 吕飞. 基于Supply-Hub的生产与配送协同模式研究[J]. 中国管理科学, 2014, 22(6):50-60.
[22] Shabtay D, Steiner G. Optimal due date assignment and resource allocation to minimize the weighted number of tardy jobs on a single machine[J]. M&Som-Manufacturing & Service Operations Management, 2007, 9(3):332-350.
[23] Grimmett G, Stirzaker D. Probability and random processes[M]. Third Edition. New York:Oxford University Press, 2001.
[24] Baker K R. Minimizing earliness and tardiness costs in stochastic scheduling[J]. European Journal of Operational Research, 2014, 236(2):445-452.
