Production planning and scheduling problems are highly interdependent as scheduling provides optimum allocation of resources and planning is an optimum utilization of these allocated resources to serve multiple customers. Researchers have solved production planning and scheduling problems by the sequential method. But, in this case, the solution obtained by the production planning problem may not be feasible for scheduling method. Hence, production planning and scheduling problems must be solved simultaneously. Therefore, in this work, a mathematical model is developed to integrate production planning and scheduling problems. The solution to this integrated planning and scheduling problem is attempted by using a discrete artificial bee colony (DABC) algorithm. To speed up the DABC algorithm, a k-means clustering algorithm is used in the initial population generation phase. This k-means clustering algorithm will help to converge the algorithm in lesser time. A real-life case study of a soap manufacturing industry is presented to demonstrate the effectiveness of the proposed approach. An objective function to minimize overall cost, which comprises the processing cost, material cost, utility cost, and changeover cost, is considered. The results obtained by using DABC algorithm are compared with those obtained by CPLEX software. There is a saving of ₹2 23 324 for weeks 1–4 in overall cost compared with the results obtained by using CPLEX software.

中文翻译：

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具有需求不确定性和不同生产能力的连续平行生产线的生产计划和调度问题

生产计划和计划问题高度相互依赖，因为计划提供了最佳的资源分配，而计划是对这些分配的资源的最佳利用，以服务多个客户。研究人员已经通过顺序方法解决了生产计划和调度问题。但是，在这种情况下，由生产计划问题获得的解决方案对于调度方法可能不可行。因此，必须同时解决生产计划和调度问题。因此，在这项工作中，开发了一个数学模型来集成生产计划和计划问题。通过使用离散人工蜂群（DABC）算法尝试解决此集成的计划和调度问题。为了加快算法DABC，一个ķ-均值聚类算法用于初始种群生成阶段。这种k均值聚类算法将有助于在更短的时间内收敛该算法。提出了肥皂制造行业的实际案例研究，以证明所提出方法的有效性。考虑了使总成本最小化的目标函数，包括处理成本，材料成本，公用事业成本和转换成本。将使用DABC算法获得的结果与通过CPLEX软件获得的结果进行比较。与使用CPLEX软件获得的结果相比，第1-4周的总成本节省了₹2 23 324。