## 2 Synchronization Issues with Various Part-to-Picker Systems and a Literature Review
### Synchronization Problems in Cross-Docking  
Cross-docking is a logistics method that transfers incoming shipments directly to outgoing vehicles without storing them in between, [PERSON] costs and consolidating shipments to achieve transportation savings. Cost reduction, shorter delivery lead time, improved customer service, faster inventory turnover, fewer overstocks, and reduced risk for loss and damage are all benefits of it. Cross-docks require a synchronization between inbound trucks that provide products and outgoing vehicles that receive them. The synchronization process is crucial for facilitating a swift and effective trans-shipment process. [PERSON], [PERSON], and [PERSON] [54] conducted a comprehensive survey on cross-docking, while [PERSON] and [PERSON] [55] specialized in synchronized truck scheduling. Modeling shows that there is no discernible difference between the transportation of commodities via bins or truck trailers. As a result, the entire synchronization problem has significant similarities. [PERSON] and [PERSON] focused on identifying the optimal door assignments, docking sequences, and product assignments for the truck scheduling problem to reduce the number of late trucks at a cross-docking terminal [56]. The standard flow in a cross-docking terminal is depicted in Figure 6.  
By negotiating transportation terms and reducing unit purchase costs, consolidation can reduce total logistics cost. An inventory theoretic algorithm was presented by [PERSON] to evaluate the cost-effectiveness of alternative heuristics after examining the relationships between relevant variables and costs [57]. The three most important questions are what inventory grouping system is acceptable, what heuristics should be employed, and what key elements define the proper degree of consolidation. [PERSON] and [PERSON] provided design assistance for companies engaged in order fulfillment system design. The aim of this study was to identify the optimal door assignments, docking sequences, and product assignments for the truck scheduling problem at a cross-docking terminal. The results of this were reducing the number of late truck descriptive models based on demand levels, labor rates, order sizes, and other factors [58]. An analytical model was provided to evaluate the impact of new technology, management schemes, and worker productivity on the batching level. The transportation of products or persons between origins and destinations is required for pickup and delivery issues (PDPs). [PERSON] et al. provided a broad framework and a three-field categorization technique for these situations [59]. G = (V, A) represents a graph with vertex sets. V = 0,..., n; H = 1,..., p; D = (duh); K = 1,..., m; T V denotes trans-shipment vertices; and the total route costs were reduced. This study uses a commodity matrix to develop a framework for addressing issues such as many-to-many, one-to-many-to-one, and one-to-one. The simulation of many-to-many difficulties with trans-shipments was also possible with it. The availability of information was an essential factor in PDPs. They included static issues that are predictable and known as a priori, dynamic problems that are increasingly disclosed through time, and stochastic problems that are random variables with known distributions. See Figure 7.  
Figure 6: The movement of items during a typical cross-docking operation [56]. The attention on machine scheduling problems with time-dependent processing times has increased in recent years, and classical scheduling theory models have been simplified. Through research on time-dependent problems, new properties of and effective methodological approaches to algorithm design and NP-complete reduction have been discovered. A framework was presented by [PERSON], [PERSON], and [PERSON] to demonstrate the generalization of machine scheduling models from classical scheduling theory. And they also introduced enumerative and heuristic solution algorithms in 2004 [60].