## 2 Synchronization Issues with Various Part-to-Picker Systems and a Literature Review
### Synchronization Problems in Cross-Docking
Time-dependent scheduling is a branch of classical scheduling theory that has two common assumptions: preemptive scheduling and unit processing time scheduling. The best truck docking or scheduling sequence for both inbound and outbound trucks was proposed by [PERSON] and [PERSON] By using these, a cross-docking system [61] can reduce total operation time and maximize throughput. To minimize the total number of products that pass through the system, a heuristic algorithm was created, producing solutions that are close to the global optimal solutions, as in Figure 8.  
In retail, grocery, and other distribution industries, cross-docking is a new logistics technique that transfers shipments directly from inbound to outbound trailers without any storage in between. [PERSON] and [PERSON] conducted research on a two-machine scheduling model for the logistics cross-docking problem. It was demonstrated that the problem is strongly NP-hard and that the branch-and-bound algorithm can optimally solve problems in up to 60 tasks. And the two-stage hybrid cross-docking scheduling issue  
Figure 8: A practical operation of a cross-docking system [61]. Figure 7: A technique for classifying pickup and delivery problems [59]. with the goal of minimizing the make span is introduced in Figure 9. Four heuristics were presented to examine the performance of moderate and large size cases. [PERSON]'s rule-based LPT heuristic outperforms the combinational best heuristic (BH), which has an average loss of 37% in comparison to the lower limit, according to computational investigations. A technique that can be reversed to improve all heuristics and the bottom band was proposed [62]. [PERSON] and [PERSON] proposed a classification for deterministic truck scheduling with the objective of structuring and advancing scientific progress in real distribution networks. This method also applies to a classification of vehicle scheduling problems using tuple notation to review existing research and identify future research needs [55]. Additionally, their research in 2009 indicated that truck sequencing must be integrated into the truck sequencing problem (TRSP). Their algorithms also took into account the truck-specific processing times when loading or unloading times differ due to diverging numbers or types of carried products [63]. Cross-docks usually consist of multiple inbound and outbound doors as the Figure 10, with one side dedicated to inbound operations and the other to outbound operations. [PERSON] developed a novel truck scheduling problem in zero-inventory cross-docking to ensure a synchronized flow of goods across the dock [64]. Figure 10: Infrastructure in cross-docking terminals [64]. Figure 9: Distribution facility with cross-docks [62]. Three operational objectives are considered: the minimization of flow time, processing time, and tardiness. In practice, the underlying problem setting is important because the zero-inventory policy is often used to avoid obstacles for material handling devices. [PERSON] and [PERSON] examined the concept, categorized relevant cross-dock situations, and identified significant decision issues [65]. Terminals typically have rectangular structures with multiple dock doors, allowing incoming trucks to be loaded onto outgoing trucks and transported to their respective destinations. This activity is shown in Figure 11.  
Cargo shipments are then transferred across the dock to the temporary storage area of their respective outbound destinations. During this time, additional services are carried out as the designated outbound truck is in transit. The terminal is then loaded with trucks en route to their original destinations. Cross-docking terminals are used to unload arriving trucks, register cargo, sort it by destination, transport it across the dock, and load it onto departing trucks. Value-added services can be performed while waiting for the planned departing truck. Shunting yards are utilized to separate freight trains and reassemble new trains, which results in time and cost savings.