**1. Introduction**

With the development of intelligent logistics equipment and technology, automated storage and retrieval systems (AS/RSs) are widely used in manufacturing enterprise logistics due to the advantages of high efficiency and space utilization [1,2]. The use of AS/RS in the factory warehouse is conducted with the just-in-time (JIT) contribution of various materials in the workshop. To realize the JIT distribution, the AS/RS scheduling must be closely connected with the production scheduling, which affects the efficiency of the integrated scheduling. In addition, the different scheduling optimization objectives in the AS/RS and hybrid flowshop are to maximize the efficiency of storage and retrieval and minimize the makespan. With a high warehousing efficiency, the completion time of the producing material distribution may not meet the required demand or may be unable to greatly increase the line inventory. However, the production scheduling with the minimum completion time may cause the warehouse scheduling tasks to be stacked at a certain time and cannot meet the production demand. Therefore, it is important to cooperate with the scheduling that contains the storage allocation, task sequences, and retrieval task sequences in production, which is a significant practice in manufacturing systems.

At present, the main research in AS/RS concerns storage allocation and task scheduling [3–5]. Roshan et al. [6] formulated a multi-objective model in AS/RS considering energy consumption optimization and energy sustainability. Hachemi et al. [7] determined the integration of the storage allocation and picking paths based on storage and retrieval requests with the objective of travel time. Song and Mu [8] studied the sequence sorting problem with large-scale storage/retrieval requests in AS/RS and proposed a heuristic algorithm based on assignment. Geng et al. [9] proposed a new improved Genetic Algorithm (GA)

**Citation:** Lu, J.; Xu, L.; Jin, J.; Shao, Y. A Mixed Algorithm for Integrated Scheduling Optimization in AS/RS and Hybrid Flowshop. *Energies* **2022**, *15*, 7558. https://doi.org/10.3390/ en15207558

Academic Editor: George S. Stavrakakis

Received: 30 August 2022 Accepted: 10 October 2022 Published: 13 October 2022

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to solve the scheduling problem in AS/RS, and indicated that it is an effective approach. Wu et al. [10] investigated the scheduling problem of retrieval jobs in double-deep type AS/RS, whose objective is to minimize the working distance.

In the hybrid flowshop, Colak et al. [11] conducted a systematic literature survey for hybrid flowshop scheduling problems, which provided a beneficial road map for the following researchers. Zhang et al. [12] proposed a muti-objective migratory birds optimization (MBO) algorithm based on the decomposition of the multi-objective flowshop rescheduling problem, which has proven to be better than other evolutionary algorithms. Zhang et al. [13] introduced lots of streaming into the hybrid flowshop scheduling problem with consistent sublots to fit the real-world scenarios, which verified the feasibility to solve the integrated scheduling problem with the hybrid flowshop. Li et al. [14] researched the distributed hybrid flowshop scheduling problem with sequenced dependent setup time, which was solved by a discrete artificial bee colony algorithm. Reddy et al. [15] solved a muti-objective problem in a flexible manufacturing system, which considered machine and vehicle scheduling. According to these studies in AS/RS and hybrid flowshop, most researchers have ignored the related effects. However, the connection between AS/RS and hybrid flowshop is important to develop smart manufacturing systems.

Problems with storage allocation, operation scheduling, and workshop scheduling are NP-hard problems that lead to low efficiency and time-consumption by using exact algorithms [16,17]. The intelligent optimization algorithm provides an effective and fast method for solving the above complex problems [18–20]. Li et al. [21] conducted a comprehensive survey of the learning-based intelligent algorithm. Katoch et al. [22] discussed the advances and introduced the pros and cons of GA. Duman et al. [23] proposed a new nature-inspired metaheuristic approach named MBO, which was proven to be an effective formation in energy saving. The algorithms of GA, MBO, and their improvement algorithms are used to solve the scheduling problems and achieve better performance. The scheduling objective in AS/RS is usually the total operation time, but it has a shortcoming by neglecting two situations. The first one is that the number of storage tasks is not equal to the number of retrieval tasks, and the other one is that retrieval arrival time needs to be considered in the connection of AS/RS and hybrid flowshop [24,25]. To obtain a better solution to the integrated scheduling problem in AS/RS and hybrid flowshop, the main contributions in this study include: (1) formulation of a bi-objective model to minimize the operation time in AS/RS and the makespan in the hybrid flowshop; (2) proposal of a two-stage mixed algorithm called GA-MBO that combines the strong global optimization ability of GA and the strong local search ability of MBO.

The structure of this paper is as follows: In Section 2, we described and modeled the integrated scheduling problem in AS/RS and hybrid flowshop. In Section 3, we designed the GA-MBO and presented the operation details. In Section 4, experiments were introduced in AS/RS and hybrid flowshop, and the results were analyzed to verify the effectiveness of the GA-MBO. Finally, Section 5 presents the conclusions.

#### **2. Materials and Methods**

#### *2.1. Problem Description*

AS/RS is an information technology based on the Internet of Things, which is widely used to store and retrieve materials without any human participation. An AS/RS mainly consists of racks, cranes, input/output (I/O) points, and conveyors. The system has a crane in each aisle and a main I/O point along a conveyor. The top view of the layout schematic diagram is shown in Figure 1. The redesign of the material distribution connection in the AS/RS and hybrid flowshop saves the storage area and lowers the handling cost of the production material. The crane can be used to realize the distribution between different tiers. Under the production conditions of the workshop, intelligent logistics equipment, such as conveyors and automatic guided vehicles (AGVs), can be used to distribute materials with JIT to achieve lean logistics. The material distribution problem with the connection between

the AS/RS and the hybrid flowshop is researched. The material distribution diagram is shown in Figure 2.

**Figure 1.** Layout schematic diagram of AS/RS. 1. Crane. 2. Rack. 3. Aisle. 4. Input point. 5. Conveyor. 6. Output point.

**Figure 2.** Material distribution diagram in AS/RS and hybrid flowshop.

The integrated scheduling problem in AS/RS and hybrid flowshop is related to the storage allocation, system scheduling, and flowshop scheduling. The objective of the scheduling problem is to minimize the total operation time in AS/RS and the makespan in hybrid flowshop. The research objects are AS/RS and multi-stage hybrid flowshop.

AS/RS can be described as: in a warehouse with a determined status that racks have *X* rows, *Y* columns, and *Z* tiers. The corresponding material locations are the *O* retrieval task locations, and the number of retrieval tasks is greater than the number of the retrieval material types. The free rack locations are the *I* retrieval task locations. These storage and retrieval tasks are operated by *S* cranes, whose operation time is related to task storage allocations (multi-tasks with the same material) and the task operation sequence. Hybrid flowshop can be described as: the *O* retrieval tasks with the same operation sequence are processed at the *K* stages. Stage *k* has *Ek* > 1 independent parallel machines. At this stage, the task processing time is related to both the task material type and the processing machine type. The end operation time of the retrieval task in AS/RS directly affects the starting time of the production task in the hybrid flow workshop scheduling.

In the scheduling of AS/RS, operation modes for storage and retrieval goods are: single command (SC) where the crane completes for storage task or retrieval task and double command (DC) where the crane completes for storage and retrieval tasks. The DC operation should be adopted to improve the efficiency in the system. At the same time, considering the deadline requirements of retrieval tasks, the SC has a shorter retrieval time.

In addition, the mixed command of SC and DC is researched in the operation scheduling problem, which exists under the assumption that the numbers of storage and retrieval tasks are unequal. These situations form a mixed scheduling sequence.

The alternation of storage and retrieval tasks leads to the dwell-point change that affects the task operation time. The location selections of storage and retrieval tasks affect the operation sequence, the system efficiency, and the end operation time of retrieval tasks. The retrieval sequence affects the product sequence and the production efficiency in the hybrid flowshop. This paper integrates and optimizes a batch of storage and retrieval tasks in AS/RS by determining the storage location so that the total operation time in AS/RS and the makespan in workshop production are minimized. Storage selection, task sequences, and production sequences need to be studied at the same time.

#### *2.2. Problem Modelling*
