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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 formulate 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.

Increasing incentives in a competitive market impels companies 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 generalized 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 distribution 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 competition, 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. Moreover, 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 facilities 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 manufacturing 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 submodels. The proposed approach outperforms commercial optimization 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 et al., 2010, Goksal et al., 2012 and Martins et al., 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 are reported, which will help the managers to make suitable production decisions. The rest of the paper is organized as follows. A comprehensive review on production planning problem is presented in Section 2. The problem is stated and mathematically formulated in Section 3. A particle swarm optimization-based approach to address the model is proposed in Section 4. Numerous computational experiments are reported in Section 5, and, the managerial insights of the problem are explored. Finally, the conclusions are drawn and the future research directions are outlined in Section 6.

We study a collaborative production planning problem in make-to-order manufacturing, which is an extension of the classical production planning problem subject to production time windows, order-splitting and assignment, and balance of production loads among the plants. The simultaneous decisions make the problem more complicated and intractable. Thus, we present a decomposition scheme to divide the model into two tractable submodels and then propose a hybrid approach based on the particle swarm optimization framework to address the proposed model. Numerous computational experiments illustrate the advantage of the approach in solution quality and CPU time. Moreover, the experiments show the order-splitting policy’s contribution to the reduction of the total costs. The higher flexibility of the plants can reduce the total cost as well. We also find that balancing the production among the plants can lead to an increase in cost. Finally, we outline the future research directions. First, we will study the trade-off between fairness and effectiveness in production planning by using bi-objective programming technique. Second, the stochastic version of the problem will be a natural extension of the study. Third, it will be interesting to study the impact of various policies such as order acceptance and available-to-promising (ATP) in make-to-order manufacturing on the production planning problem.