## 3 Problem Definition and Formulation  
We examine the order-picking problem (OPP) that comes after. Workers (pickers) at the logistic center (warehouse or distribution center) have a set amount of orders to fill, which they do by selecting items from racks, preparing them, and placing them in the container designated for the order. Every container that leaves the depot is clearly labeled with a list of the goods inside and the amounts the customer requested. The products are kept on the racks in the designated places. Each product in the logistics center is typically kept on a single rack, but it is possible to keep some products in many locations. Because it is often forbidden to bring new product deliveries to the previous location, they are instead placed in another area. For instance, the distributors would rather not offer customers such questionable products from distinct deliveries of products like paints, knitting, or serving threads because their suppliers cannot guarantee the same color tone in consecutive deliveries. They are willing to store such goods in various locations as a result. Of course, the majority of identical products are only kept in one location. The logistics center's one-directional conveyor, which is extended over all of the storage spaces, transports containers from the depot to the buffers. The same buffer is assigned to the racks close to it. Therefore, one buffer might be used by one or more racks. Products are selected by a single picker from one or more buffers that are assigned to him. This implies that one picker could choose products from many racks and spots on the rack in the same buffer. The pickers are not given access to racks as components of the buffer or to locations as components of the racks individually. The picker is given full control over the buffer, including all of its racks and all of its positions. The picker's time for traveling between racks or buffers is not taken into account if they are all close together and the picker is assigned to more than one rack or buffer. Because containers move via a one-way belt conveyor, only the movement time between buffers is taken into account. When a container is delivered to the buffer, the picker locates the product on the rack, chooses the necessary quantity of it, measures it, and cuts the client-ordered product as necessary before temporarily packing it and putting it in the container. Afterward, the conveyor moves the container to the next buffer or, if the order is finished, to the depot. The containers are prepared in advance with everything that needs to be inside. Once the container departs on its journey, no further items may be added to the order. The sequence in which the goods are added to the container is not required. We presume that the distribution center has enough of the client's requested goods. No stock is ever out of stock. The container must go round-trip without using the final depot due to the conveyor's one-way design in order to get to the preceding buffer. The task's makespan measures how long it takes for the container to transition between buffers. The researched OPP aims to discover how to allocate the containers that must be transported between buffers and served by the pickers in order to execute orders as rapidly as feasible while taking picker availability and transit time between buffers into consideration. An example of the distribution center with six buffers (B1-B6) is shown in Figures 1-3. The start and exit depots are buffers B0 and B7. There are 20 spots assigned to each buffer, totaling 120 places. On each rack, the key areas are highlighted in the dark. Each rack has eight spots with the same colored light. The positions of the shelves depicted on the figuresare not assigned. The locations that are present in each rack and the racks that each buffer is allocated to are displayed. Containers are moved from buffer B0-B1 to buffer B6-B7 on a one-way conveyor. Beyond depots B7 and B0, the container must do a round-trip in order to reach any of the preceding buffers.