The purpose of this study is to solve a complex multi-product four-layer capacitated location-routing problem (LRP) in which two specific constraints are taken into account: 1) plants have limited production capacity, and 2) central depots have limited capacity for storing and transshipping products. The LRP represents a multi-product four-layer distribution network that consists of plants, central depots, regional depots, and customers. A heuristic algorithm is developed to solve the four-layer LRP. The heuristic uses GRASP (Greedy Randomized Adaptive Search Procedure) and two probabilistic tabu search strategies of intensification and diversification to tackle the problem. Results show that the heuristic solves the problem effectively.

Distribution is an indispensable component of logistics and supply chain management. Location-Routing Problem (LRP) is an NP-hard problem that simultaneously takes into consideration location, allocation, and vehicle routing decisions to design an optimal distribution network. Multi-layer and multi-product LRP is even more complex as it deals with the decisions at multiple layers of a distribution network where multiple products are transported within and between layers of the network. This paper focuses on modeling a complicated four-layer and multi-product LRP which has not been tackled yet. The distribution network consists of plants, central depots, regional depots, and customers. In this study, the structure, assumptions, and limitations of the distribution network are defined and the mathematical optimization programming model that can be used to obtain the optimal solution is developed. Presented by a mixed-integer programming model, the LRP considers the location problem at two layers, the allocation problem at three layers, the vehicle routing problem at three layers, and a transshipment problem. The mathematical model locates central and regional depots, allocates customers to plants, central depots, and regional depots, constructs tours from each plant or open depot to customers, and constructs transshipment paths from plants to depots and from depots to other depots. Considering realistic assumptions and limitations such as producing multiple products, limited production capacity, limited depot and vehicle capacity, and limited traveling distances enables the user to capture the real world situations.

Injuries due to inhalation of hot gas are commonly encountered when dealing with fire and combustible material, which is harmful and threatens human life. In the literature, various studies have been conducted to investigate heat and mass transfer characteristics in the human respiratory tract (HRT). This study focuses on assessing the injury taking place in the upper human respiratory tract and identifying acute tissue damage, based on level of exposure. A three-dimensional heat transfer simulation is performed using Computational Fluid Dynamics (CFD) software to study the temperature profile through the upper HRT consisting of the nasal cavity, oral cavity, trachea, and the first two generations of bronchi. The model developed is for the simultaneous oronasal breathing during the inspiration phase with a high volumetric flow rate of 90 liters/minute and the inspired air temperature of 100 degrees Celsius. The geometric model depicting the upper HRT is generated based on the data available and literature cited. The results of the simulation give the temperature distribution along the center and the surface tissue of the respiratory tract. This temperature distribution will help to assess the level of damage induced in the upper respiratory tract and appropriate treatment for the damage. A comparison of nasal breathing, oral breathing, and oronasal breathing is performed. Temperature distribution can be utilized in the design of the respirator systems where inlet temperature is regulated favoring the human body conditions.