## 2 Literature Review  
A brief review of multi-depot, heterogeneous fleet, time window, multi-product, and inventory restriction and solution is presented in this section. Figure 1: Flowchart of hen and egg production in the case study company. Pick-up and delivery problems (PDPs) are concerned with a type of vehicle routing problem (VRP) in which goods or persons come from different origins and go to different destinations [4]. PDP issues occur in various contexts, including logistics, ambulatory care and robotics [5; 6]. Vehicles available to pick up and deliver cargo can have heterogeneous capacities. Each vehicle's load must not exceed its capability. However, depending on the problem, additional assumptions, and restrictions on vehicle paths, such as time windows or repeated visits at certain vertices, can be presented. [PERSON] et al. [7] proposed an exact method and a constructive heuristic approach from the min-max split delivery multi-depot vehicle routing problem with a minimum service time requirement. In this problem, each customer requires a specified amount of service time. They generated instance ranges from 10 to 500 and 3 to 20 for the customer and depot, respectively, to investigate the constructive heuristic. They tested the heuristic on three sets of data with 43, 21 and 258 instances. The heuristic result on the first and second sets of data was 2% and 1.5%. However, the third set of heuristics is more substantial when the average number of customers per route is small and there is a medium level of average customer service time. [PERSON] et al. [8] studied a multi-depot vehicle routing problem with multiple pick-up and delivery requests. They developed a solution approach based on Particle Swarm Optimization (PSO) to create a new particle for an assignment using a vehicle that created a decoding method to find the best solution. They used 56 sample problems with the best-known solution and divided the instance problems into 13, 17 and 26 for clustered location, random location, mixed cluster and random locations. All the instance problems were compared with their previous work and the best-known solutions. The conclusion showed that the new decoding method for PSO provided better solutions for their problems than their previous work. [PERSON] [9] developed an exact method, initial solution and Adaptive Large Neighborhood Search (ALNS) based metaheuristic on the multi-depot multi-period vehicle routing problem with a heterogeneous fleet for minimizing the total cost. They proposed 1 to 9 instances and a number of customers ranging from 50 to 75 customers. They compared the LANS algorithm results with the Large Neighborhood Search (LNS) algorithm. LANS showed higher-quality performance over LNS that averaged a computational time of 400 s and obtained an averaged percentage improvement of 55% to the constructive heuristic. Most authors have developed a mathematical model to solve multi-product vehicle routing problems and planning problems in transport-related industries, which are difficult to solve in a reasonable amount of time for medium or large-sized problems [10] and for the multi-depot vehicle routing problem [11; 12]. In 2014, [PERSON] et al. [13] proposed a mixed vehicle routing problem on the multi-depot routing with a heterogeneous vehicle and a mixed-integer linear model for solving the problem. The multi-product VRP can be better illustrated in Figure 2.  
Figure 2: The delivery route for single-product vehicle and multi-product vehicle. In the last decade, inventory restrictions have also been extensively studied to solve the problem. For example, [PERSON] et al. (2014) proposed an improved variable neighborhood search (VNS) algorithm with a heuristic to solve VRP with an unpaired pick-up, delivery and split loads. They considered a constraint about the demand of customers for each various product and inventory restriction. The inventory levels and quantity of demanded products were described that should be suitably allocated to minimize total cost. [PERSON] et al.