# A Study on the Design and Control of the Overhead Hoist Railway-Based Transportation System
## 1 Introduction
The study additionally presents novel findings pertaining to the association between transportation risk and inventory risk, the concept of risk equilibration, the influence of service level, and the interplay among various categories of hazardous materials. Transportation expenses include both permanent and variable expenses, as well as nonrecurring expenses such as delivery management and driver scheduling. The comprehensive model emission model (CMEM) is used to calculate fuel consumption, which is connected to driving speed, driving range, and vehicle load. The design of distribution networks poses significant challenges in areas such as location-allocation, vehicle routing, and inventory control. Comprehensive models have been developed by researchers to address these issues, including location-routing, inventory-routing, and location-routing-inventory problems. The objective of these models is to simultaneously optimize the plans for placement, routing, and inventory in a logistics system that consists of multiple echelons. The inventory routing problem (IRP) is a logistic optimization challenge that involves both inventory management and vehicle routing difficulties. The location inventory routing problem (LIRP) is an alternative to the inventory routing problem (IRP) that aims to enhance the integration of location selection, vehicle routing, and inventory control. Nevertheless, the solution space of this problem is more extensive compared to those of the vehicle routing problem (VRP) and inventory routing problem (IRP) due to its significant non-linearity and NP-hardness. Genetic algorithms, variable neighborhood search algorithms, and Tabu search algorithms are frequently employed in the resolution of IRP and LIRP models. Hybrid heuristic algorithms utilize the strengths of multiple distinct algorithms to enhance their overall performance. In the field of supply chain management, managing inventory is a crucial operational challenge. In their study, [PERSON], [PERSON], and colleagues introduced an improved multi-period two-echelon location inventory routing problem (LIRP) model that incorporates time windows at merchants and accounts for vehicle fuel use [7]. The proposed model simultaneously optimizes location, inventory, and routing variables, taking into account the replenishment needs of both distribution centers and retailers over many time periods. To enhance the optimization of replenishment plans, this study suggests the use of a customized genetic algorithm and a gradient descent method. The results indicate that there are trade-offs between inventory and transportation costs. Specifically, as transportation costs and inventory holding costs decrease, there is an increase in stock-out costs. The impact of post-optimization on inventory levels in distribution centers is contingent upon the spatial distribution of retailers. It is possible to decrease or increase inventories. Additional areas for future research could involve the development of models to address uncertain and linked demand in the context of transportation, as well as exploring the application of the location inventory routing problem (LIRP) specifically for the transportation of particular items. The world now has numerous transportation systems. First is the pneumatic tube system (PTC) [8; 9]. The PTC is used to load materials of negligible load at speeds up to 5 m/s according to [8]. In [9], [PERSON] et al. pointed out the shortcomings of this system, such as only transferring loads of limited size with a weight of about 5 pounds. Next, Telelift GmbH is a company that has a more than 55-year-long history of experience in the development of internal transport systems [4; 10], and MultiCar is a good example. MultiCar has a 3-line rail system, including two lines of 24V suppliers and one line for a signal. It uses a position code to detect the shuttle's location. The velocity of MultiCar is also significant as it can carry a mass of 60 kg at a maximum speed of 0.5 m/s.