The Inventory Routing Problem (IRP) has been highlighted as a valuable strategy for tackling routing and inventory problems. This paper addresses the IRP but considers the forward delivery and the use of Returnable Transport Items (RTIs) in the distribution strategy. We develop an optimization model by considering inventory routing decisions with RTIs collection (backhaul customers) of a Closed-Loop Supply Chain (CLSC) within a short-term planning horizon. RTIs consider reusable packing materials such as trays, pallets, recyclable boxes, or crates. The RTIs represent an essential asset for many industries worldwide. The solution of the model allows concluding that if RTIs are considered for the distribution process, the relationship between the inventory handling costs of both the final goods and RTIs highly determines the overall performance of the logistics system under study. The obtained results show the efficiency of the proposed optimization scheme for solving the combined IRP with RTIs, which could be applied to different real industrial cases.

In the present work, modeling of hoop stress in the defect-free structural steel pipe was done under the combined effect of internal hydrostatic pressure and temperature difference using finite element analysis (FEA) and response surface methodology (RSM). The FEA simulation was done on the quarter-ellipsoidal sections of the structural steel pipe specimen using ANSYS 2022 R1 software. The calculated hoop stress using FEA was in agreement with the analytical solution of hoop stress. The thermodynamically induced hoop stress due to the temperature difference (without internal hydrostatic pressure) exhibited a compressive state at the inner wall and a tensile state at the outer wall of the specimen. This compression-tension state also provided a thermodynamic situation at which the total hoop stress becomes null at the neutral axis. However, when the specimen was subjected to internal hydrostatic pressure (in addition to the temperature difference), the initial neutral axis received a thermomechanical hoop stress of a tensile nature. A drop in the burst pressure from 11.5 MPa to 9.9 MPa was observed when the steel pipe was subjected to a maximum temperature difference of 40 °C. A new analytical equation for thermomechanical hoop stress was developed using RSM modeling by considering independent variables as the normalized position in the wall (ṝ), internal hydrostatic pressure (P), and temperature difference (ΔT). The developed analytical equation envisages that the interacting effect of independent variables ṝ(ΔT) was maximum, followed by the interacting effect of ṝ(P). An optimum internal hydrostatic pressure of 7.43 MPa was calculated considering the flow stress of the material for all possible combinations of the other two independent variables (ṝ and ΔT). Furthermore, at the optimum ΔT of 39.65 °C, the interacting effect of the ṝ(P) provided contour-curvature plots, both below the yield strength and endurance limit, considering different combinations of normalized position in the wall and internal hydrostatic pressure.

This study employs mathematical modeling to explore the effects of overtime option, rework, and discontinuous end-item issuing policy on the economic manufacturing quantity (EMQ) model. Conventional EMQ model assumed that all products fabricated are of good quality and are issued under continuous policy. In real world, however, nonconforming items are randomly produced, due to diverse unexpected factors in fabrication process. When finished items are to be distributed to outside locations, discontinuous multi-shipment policy is often used rather than continuous rule. In addition, with the intention of increasing short-term capacity or shortening replenishment cycle length to smooth the production planning, adopting overtime option can be an effective strategy. To cope with the aforementioned features in real production systems, this study incorporates overtime option, rework, and multi-shipment policy into the EMQ model and explores their joint effects on optimal lot size and number of shipments, and on other relevant system parameters. Mathematical modeling and Hessian matrix equations enable us to derive the optimal policies to the problem. Through the use of numerical example, the applicability of research result is exhibited and a variety of significant effects of these features on the proposed system are revealed.

The presented article deals with the mathematical modeling of aircraft ground handling on the service apron to utilize ground personnel more efficiently in the case of existing substitutability of workers. This article proposes a supporting decision-making tool for effective planning of the aircraft ground handling. This tool will be used for a selected type of aircraft and using the minimum number of personnel participating in the aircraft ground handling procedure. The optimization is based on the original mathematical programming model and its solution. Computational experiments verifying the functionality of the proposed model were performed on current data from the Ostrava International Regional Airport in the Czech Republic. The originality of the proposed approach (apart from the original model) comes with introducing the substitutability of workers of individual qualifications and the decomposition of workgroups composed of workers of the same qualification down to the level of individual workers. Above-mentioned decomposition of workgroups enables the flexible and separate transfer of individual workers included in the same groups between activities in the event of downtime of the given group and the existence of an activity that is not covered by the required number of workers. The substitutability of workers and the decomposition of individual groups down to the level of individual workers will make it possible to lower the number of workers or verify that the number of workers is optimal and eliminate potential staff downtime.

Globalization and increasing competition in global markets have forced businesses to provide a high level of service to their customers. Time-sensitive transportation systems which are used in transportation of perishable goods, express mail delivery, and emergency services are playing a very important role in this regard. This paper addresses the problem of uncapacitated multiple allocation p-hub center problem (UMApHCP) which is fundamental in proper functioning of time-sensitive transportation systems. A mixed-integer programming formulation is proposed for the problem and a highly efficient Benders decomposition algorithm is developed for solving it. The proposed algorithm is capable of solving large-scale instances of the problem to optimality in order of seconds.

In this paper, a heuristic algorithm based on Tabu Search Approach for solving the Vehicle Routing Problem with Backhauls (VRPB) is proposed. The problem considers a set of customers divided in two subsets: Linehaul and Backhaul customers. Each Linehaul customer requires the delivery of a given quantity of product from the depot, whereas a given quantity of product must be picked up from each Backhaul customer and transported to the depot. In the proposed algorithm, each route consists of one sub-route in which only the delivery task is done, and one sub-route in which only the collection process is performed. The search process allows obtaining a correct order to visit all the customers on each sub-route. In addition, the proposed algorithm determines the best connections among the sub-routes in order to obtain a global solution with the minimum traveling cost. The efficiency of the algorithm is evaluated on a set of benchmark instances taken from the literature. The results show that the computing times are greatly reduced with a high quality of solutions. Finally, conclusions and suggestions for future works are presented.

Mathematical modeling has become an important tool for understanding and controlling infectious diseases. It allows researchers to simulate and predict the spread of diseases, identify key transmission factors, assess the impact of interventions, and inform decision-making for disease control. Researchers can use mathematical models to explore different scenarios, evaluate the effectiveness of various interventions, and estimate the potential outcomes of different control strategies. This enables policymakers and public health professionals to make informed decisions and implement targeted measures to mitigate the impact of infectious diseases. In addition, mathematical models can be used to examine and evaluate the effectiveness of control strategies such as vaccination, social restrictions, and drug use. The results show that prevention strategies such as population vaccination and social restrictions can significantly help reduce the spread of influenza. This article presents a mathematical model for Influenza A (H1N1), as well as two other models specifically for Influenza A (H1N1) after quarantine and treatment. The purpose of the article is to provide a brief review of these models and compare them.

Emergency medical services (EMS) stations reduce mortality and irreparable damage from injuries through the timely treatment of patients. After performing the initial measures at the scene of the accident, if necessary, they transfer the patient to the hospital. In such cases, the goal is to save human lives. Thus, suggestions and solutions that can improve the performance of these centers are very welcome. One of the most important parameters in providing high-quality EMS is the timing of these services. Therefore, the location of these centers plays a key role in diminishing the response time to demand. In that regard, the location of these centers in cities, especially large and densely populated cities, is very important. In this study, in order to answer the mentioned questions, a linear mathematical model based on the maximum expected coverage model is presented. In this model, by considering the relative coverage conditions, the best locations in the city, as well as the coverage of demand points and distance traveled by the vehicles will be obtained. Furthermore, robust optimization (RO) is used to provide better situations for the operation of the model. Finally, according to the results, it is found that the proposed model has a better resolution time than nonlinear models and is also able to solve cases with high input data. The proposed model is implemented in District 10 of Tehran, Iran.