In manufacturing companies, production planning is at the top level of production management and is crucial to successful production management because its performance greatly affects the performance of production control and supply chain management. This paper investigates a decision-making problem in the production planning stage, a multi-objective multi-site order scheduling problem in a medium-term planning horizon, by developing an effective methodology for the problem.
1.1. Multi-site order scheduling in production planning
Consider the real-world production environment of the manufacturing company with multiple plants (sites), multiple production departments and multiple production processes. The manufacturing company receives a large number of production orders from different customers, which need to be assigned to the company’s self-owned or collaborative plants for production. The production of a product (or a production order) involves multiple production processes, including ordinary processes and special processes. Each plant can produce all ordinary processes. However, not every plant can produce special processes because some plants do not have the production department required for the corresponding special processes. As a variety of production orders need to be assigned to appropriate plants for production, it is probable that different production processes of an order need to be assigned to different plants. The manufacturer must determine how to assign each production process of this order to an appropriate plant (site) and determine the beginning time of each process in a planning horizon of several months, which is called the multi-site order scheduling (MSOS) problem. This problem is faced by a large number of manufacturing companies from labor-intensive industries such as the apparel industry. The investigation on this problem is very important because its performance greatly affects the performance of downstream production control and the entire supply chain.
The MSOS problem is a complicated combinatorial optimization problem with a huge solution space. Take a simple order scheduling problem considering 10 production orders and 3 factories as an example. There are 310 candidate solutions for this problem even if each order has only one production process. The real-world problems have a much greater solution space because they need to handle the production of a large number of production orders (often more than 100) with multiple production processes in a longer time period and determine the values of a large number of variables. There does not exist an effective methodology for this problem nowadays. The order scheduling process in today’s labor-intensive manufacturing mainly rests on the experience and subjective assessment of the production planner.
1.2. Research issues in production planning decision-making
Production planning decision-making involves a wide variety of research issues, including master production schedule (Sahin et al., 2008 and Venkataraman and Nathan, 1994), material requirements planning (Dolgui and Prodhon, 2007 and Le et al., 2004), manufacturing resource planning (MRP II) (Sawyer, 1990 and Wazed et al., 2010), enterprise resource planning (Ehie and Madsen, 2005 and Parush et al., 2007), and aggregate planning (Jamalnia and Soukhakian, 2009 and Lee et al., 1983). A great number of papers have been published in this area and some researchers provided comprehensive review papers (Dolgui and Prodhon, 2007, Mula et al., 2010, Wang et al., 2009 and Wazed et al., 2010).
Some researchers investigated the decision-making problems in production planning from other perspectives. Li, Man, Tang, Kwong, and Ip (2000) addressed the production planning and scheduling problems in a multi-product and multi-process production environment with the lot-size consideration. Jozefwska and Zimniak (2008) presented a decision support system for short-term production planning and scheduling in production plants characterized by a single-operation manufacturing process. Some researchers investigated the multi-site production planning problem (Guinet, 2001, Leung et al., 2007 and Timpe and Kallrath, 2000), which consider each site as an independent and parallel production unit and usually belong to aggregate planning problems. However, few studies have focused on release and scheduling of production orders (or processes) among different sites in production planning stage so far.
Ashby and Uzsoy (1995) presented a set of heuristic rules to integrate order release, group scheduling and order sequencing in a single-stage production system. Axsater (2005) addressed the order release problem in a multi-stage assembly system, which focused on determining the starting time of different production operations but did not consider where the process was produced. Chen and Pundoor (2006) addressed order allocation and scheduling at the supply chain level, which focused on assigning orders to different production plants and exploring a schedule for processing the assigned orders in each plant. However, their study has not considered the effects of different production departments and their production capacities on scheduling performance. Each production department indicates a type of shop floor. The order release and scheduling problem in the production planning stage, considering multiple plants and multiple production departments and multiple production processes, has not been investigated.
This paper will investigate the MSOS problem with the consideration of multiple production plants and multiple types of production processes. Due to the complexity of the investigated problem, the values of objective functions of each candidate order scheduling solutions cannot be obtained directly by mathematical formulas, which can only be derived by simulating the production of all production processes in appropriate plants. Unfortunately, no simulation model is available so far.
In this paper, the mathematical model of the investigated MSOS problem in the production planning stage will be established firstly. Based on the mathematical model, an effective optimization model is developed to solve the MSOS problem. In the optimization model, a simulation model, called the production process simulator, is proposed to simulate the production of different production orders in multiple plants.
1.3. Multi-objective optimization techniques in production decision-making
In real-world production decision-making, it is usual that multiple production objectives need to be considered and achieved simultaneously. Some researchers use the weighted sum method to turn the multi-objective problems to single-objective ones (Guo et al., 2008a and Ishibuchi and Murata, 1998). However, it is difficult for some problems to determine the weights of different objectives. It is also impossible to have a single solution which can simultaneously optimize all objectives when multiple objectives are conflicting. To handle this problem, some researchers used the concept of Pareto optimality to provide more feasible solutions (Pareto optimal solutions) to the production decision-maker (Chitra et al., 2011, Ishibashi et al., 2000, Jozefwska and Zimniak, 2008, Liu et al., 2009 and Zhang and Gen, 2010).
The GA is the most commonly used meta-heuristic technique for multi-objective optimization problems (Chang and Chen, 2009, Deb et al., 2002, Guo et al., 2009, Guo et al., 2008a, Guo et al., 2008b, Jones et al., 2002 and Zhang and Gen, 2010). Some researchers focused on developing multi-objective GAs to seek Pareto optimal solutions (Deb et al., 2002 and Ishibashi et al., 2000). A significant paper for multi-objective GA was published by Deb et al. (2002), in which a fast elitist non-dominated sorting GA (NSGA-II) was proposed. Since then, the NSGA-II has attracted more and more attention, and was used and modified for various optimization problems. However, the NSGA-II has not been reported to handle the combinatorial optimization problems in production planning. The existing NSGA-II cannot be directly used to handle the MSOS problem because different chromosome representations and genetic operators are required for different optimization problems.
An effective Pareto optimization model, which combines a NSGA-II-based optimization process and a production process simulator, is developed to provide Pareto optimal solutions for the investigated MSOS problem. To construct the NSGA-II-based optimization process, the chromosome representation and genetic operators are modified to handle the MSOS problem.
The rest of this paper is organized as follows. Section 2 presents the mathematical model of the investigated MSOS problem. In Section 3, a Pareto optimization model is developed to solve the problem. In Section 4, experimental results to validate the performance of the proposed model are presented. Finally, this paper is summarized and future research direction is suggested in Section 5.
This paper investigates a multi-objective multi-site order scheduling problem in the production planning stage with the consideration of multiple plants, multiple production departments and multiple production processes. The mathematical model for the investigated problem has been established, which considers three production objectives, including minimizing the total tardiness and throughput time of all orders as well as the total idle time in all production departments. These objectives are particularly useful for manufacturing companies to meet due dates and improve management performance.
A Pareto optimization model has been developed to generate the Pareto optimal solutions for the problem investigated, in which a NSGA-II-based optimization process was proposed to seek candidate solutions and an effective production process simulator was developed to evaluate the performance of the candidate solutions. In the NSGA-II-based optimization process, a novel chromosome representation and modified genetic operators were presented to handle the investigated problem while a heuristic pruning and final selection decision-making process was developed to select out the final preferred solution from the set of Pareto optimal solutions. In the simulator, a series of heuristic rules were introduced to effectively simplify the processes of optimization seeking and production simulation of all production processes.
The effectiveness of the proposed optimization model has been validated by using the industrial data from a labor-intensive manufacturing company. The experimental results demonstrate that the proposed model could handle the investigated problem effectively by providing Pareto optimal solutions much superior to the industrial solutions.
The proposed optimization model can be easily extended to handle production outsourcing in labor-intensive industries by considering an outsourcing factory as a production plant. This research is also helpful for manufacturers to make due date negotiations with their customers. Further research will consider the effects of various production uncertainties on production planning, such as uncertain production orders and possible material shortage, and investigate the performances of other pruning methods such as data clustering in final preferred solution and compare its results with those generated by the ranking preference method used in this research. In addition, it is also a desirable direction to develop other intelligent multi-objective optimization models, based on other meta-heuristics such as simulated annealing, evolution strategy, and ant colony algorithm, for the investigated problem and compared the performances of these models with the Pareto optimization model proposed in this research.
