## 1 Introduction
Moreover, authors, such as [5], highlighted that the generalization of the VRP with time windows and driver-specific times or VRP with multiple synchronization constraints could be designated by the Delivery and Installation Routing Problem (DIRP). Hence, route problems or VRPs are one of the most studied combinatorial problems due to the issues arising in numerous real contexts [24] and, additionally, due to their significant contribution, at a theoretical level, to the area of combinatorial optimization [25]. Transportation tasks have become progressively complex, and according to [26], there is a need to find a general system that can model the many variants of transportation tasks. In [23], it was highlighted that finding solutions to VRPs may reduce the overall transportation costs within an organization, representing a reduction of about 10% to 20% of the organization's total costs. The conditions and restrictions on routes developed for VRPs will vary widely from organization to organization and according to their activity [27]. Restrictions on routes can be determined by the nature or type of products to be transported, by the characteristics of the end customer, by the features of the fleet, or by the level of service [23]. When it comes to companies that use vehicles to serve customers, decisions are based on experience and tacit knowledge of the service to be provided [28]. In this sense, heuristics can help make quick decisions without the need to spend much time searching and analyzing information [24]. However, although heuristics can \"speed up\" problem-solving, they can introduce errors and make it challenging to perceive alternative solutions [29]. Using heuristics to solve route problems and their variants has gained interest and attracted researchers due to the possibility of obtaining solutions using few resources and reducing costs [15; 30]. A particular case of last-mile delivery occurs in the furniture industry, where a customer can tailor the products by selecting the parts and components needing assembly and installation at their own house. In Ref. [5], the authors emphasized that issues concerning the minimization of the total cost of having separated and synchronizing delivery from assembly/installation have been receiving increasing interest. Route planning problems were introduced by [PERSON] and [PERSON] in 1959 through a real problem of gas delivery to several gas stations [31]. However, since then, problems related to route planning with a time window and stochastic service times [32; 33], route planning with stochastic service [25] and travel times [32; 34; 35], or route planning with a heterogeneous fleet [36] have been found in the literature. Some examples of the application of heuristics to VRPs dealing with time windows, heterogeneous fleets, or DIRPs found in the literature are described in Table 1.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  
There is a lack of studies that include historical data regarding product assembly [43], and only a few studies focus on the delivery and assembly of furniture, such as: [44] that analyzed delivery and assembly operations using discrete event simulation; ref. [45] explored home furniture delivery and assembly services using times series forecasting methods, such as the Holt-Winters method, ref. [46] developed a performance measurement system for a home furniture delivery and logistic assembly provider; and [47] that used a SCOR-based performance framework for last-mile delivery of home furniture items. To the best of our knowledge, ref. [5] is the first to deal with a delivery problem with such a flexible setting for installation services. This paper aims to provide more insights into the literature around DIRP. It focuses on the problem where a company needs to find a way to determine last-mile routes for the delivery, assembly, and installation of furniture.