Collaborative production planning with production time windows and order splitting in make-to-order manufacturing q Tianyi Pan, Zhi-Hai Zhang ⇑ , Hui Cao Department of Industrial Engineering, Tsinghua University, Beijing 100084, China article info Article history: Received 26 September 2012 Received in revised form 2 September 2013 Accepted 14 October 2013 Available online 22 October 2013 Keywords: Production planning Make-to-order Time window Order splitting Particle swarm optimization abstract In this paper, we study a generalized production planning problem, that simultaneously investigates the two decisions that play critical roles in most firms, namely, production planning and order splitting and assignment. The problem takes into consideration the production time windows and capacities. We for- mulate the integrated problem as a linear mixed-integer program with a minimized total cost. A particle swarm optimization-based approach is developed to address the problem. Extensive computational experiments show that the proposed approach outperforms a commercial optimization package. Some managerial insights are also explored and reported. Finally, concluding remarks and future research directions are provided. Ó 2013 Elsevier Ltd. All rights reserved. 1. Introduction Increasing incentives in a competitive market impels compa- nies to undertake collaborative decision-making activities that will help to achieve their cost-minimization or profit-maximization objectives. The core partial decision faced by a company is the production planning problem. In this paper, we address a general- ized production planning problem, that simultaneously considers several important decision activities under complicated constraints and limitations in real situations. This study originated from our collaboration with the business division of an iron and steel company in China. The business division originally consisted of a headquarter and several distribu- tion centers. It was mainly responsible for handling customer orders such as procurement, order quantity allocation, distribution and inventory of the products. Due to the increasing market com- petition, various value-added services are provided to improve customer satisfaction. For example, based on the shapes of the customers’ products, steel sheet cutting and bending processes are carried out by the company instead of the customers. More- over, a make-to-order strategy is used to provide ‘‘the right item in the right quantity at the right time at the right place for the right price in the right condition to the right customer’’ (Van Lear & Sisk, 2010). Thus, manufacturing facilities are integrated to the division, and, the managers realize the importance of integrated decision-making activities, in which, production planning is a basic operational decision. In comparison with the classical production planning decision, managers face a more complicated setting that includes the constraints of production time windows, production capacities, balanced production loads among manufacturing facili- ties as well as the decisions of production planning, order splitting and assignment. The main contributions of our study are summarized as follows: (a) from the modeling perspective, we present a mixed integer program to formulate a generalized production planning problem that considers order splitting and assignment, production time windows, production capacity, and utilization of the manufactur- ing facilities; (b) from the algorithm perspective, we develop an efficient particle swarm optimization-based (PSO) approachto solve the model by introducing a new way of representing the solutions and then decomposing the model into two tractable sub- models. The proposed approach outperforms commercial optimi- zation software in the formulation of the problem. The advantages of the PSO algorithm such as quick convergence, easy implementation, and few parameters to adjust (Sun, Liu, & Lan, 2010; Goksal, Karaoglan, & Altiparmak, 2012; Martins, Fuchs, Pando, Luders, & Delgado, 2013) motivate us to develop the PSO- based algorithm to address the problem. Moreover, PSO has been successfully applied in the fields of combinatorial optimization problems such as the production planning problems, the vehicle routing problems, and the scheduling problems. Mostly PSO gets better results with less computational effort compared to other methods (Hu, 2011); and (c) some interesting managerial insights 0360-8352/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.cie.2013.10.006 q This manuscript was processed by Area Editor Simone Zanoni. ⇑ Corresponding author. Tel.: +86 010 62772874; fax: +86 010 62794399. E-mail addresses: tianyipan0411@gmail.com (T. Pan), zhzhang@tsinghua.edu.cn (Z.-H. Zhang), caohui@tsinghua.edu.cn (H. Cao). Computers & Industrial Engineering 67 (2014) 1–9 Contents lists available at ScienceDirect Computers & Industrial Engineering journal homepage: www.elsevier.com/locate/caie