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In this paper, we present a general formula to calculate transition probabilities for six different types of systems based on their redundancy strategy and the status of the components. The systems are under periodic inspection policy and their components are repairable. The investigated systems include system I – active redundancy without any component to be replaced or repaired; system II – active with the component(s) to be replaced and repaired; system III – active with the component(s) to be repaired; system IV – standby without any component(s) to be replaced or repaired; system V – standby with the component(s) to be replaced and repaired; and system VI – standby with the component(s) to be repaired. In addition, all components in a system are considered non-identical. To calculate the transition probabilities for systems IV, V, and VI, we first consider a system with n non-identical components and cold standby configuration (NIC-CSC) and calculate the system state probabilities using Markov theory. Then, we present the general formula transition probabilities for systems IV, V, and VI using the results of the NIC-CSC system inspection interval. We demonstrate how to calculate the transition probabilities and matrixes for the six above-mentioned systems using the provided formulas. Moreover, we use the provided formulas to optimize the inspection interval of these systems using a modified full enumeration technique. [ABSTRACT FROM AUTHOR]

The logistic and transportation plays an integral part in maintaining a well-functioning organization. One of the most extensively used, original, famous, and popular non-parametric methods for evaluating the efficiency of organizations is the Data Envelopment Analysis, DEA technique. Suppose we can formulate the concept of effectiveness in the DEA technique. In that case, we will be able to measure the productivity of organizations since productivity is a blend of efficiency and effectiveness. Several studies have been developed, e.g., the "Malmquist Productivity Index" (MPI) and the "Lunberger Productivity Index" (LPI), which assess the productivity of corporations through the DEA technique, but these models do not display all factors in a system. Also, they need at least two periods to appraise productivity. Furthermore, their two components of efficiency and effectiveness are not considerably evident. Moreover, sensitivity analysis is not possible in these models. Therefore, a model was presented that can measure the relative productivity of decision-making units through the technique of DEA, simultaneously in a period through the two elements of efficiency and effectiveness with the feature of sensitivity analysis and its solution method is more reliable due to the use of multi-objective planning method. In addition, a case study was used to indicate the application of the proposed model, which demonstrated that a branch could be efficient but unproductive. [ABSTRACT FROM AUTHOR]

This paper aims to quantify the effects of production disruptions (PDs) and physical distancing constraints due to the pandemic in a parallel-machine production environment. The machines are non-identical and are utilized for producing a finite set of jobs (parts) in a plastic injection moulding production. The production process is subjected to random production downtime disruptions. A mixed-integer linear programming (MILP) model is developed for optimizing the joint production plan and schedule, which maximizes the production's total benefit. The model is utilized to plan and schedule a set of 17 machines in a Canadian manufacturing company. To explore the effects of physical distancing and PDs on the production's total net profit, four different scenarios for normal operation and production during the pandemic, with and without production downtimes, are considered. A genetic algorithm is utilized to solve the model. The results show that considering machines' random breakdowns and physical distancing individually reduces the total profit of the production by 71.58 and 57.98%, respectively; while their joint effect results in a 88.54% reduction in the annual net profit. [ABSTRACT FROM AUTHOR]

This article solves the mathematical model of supply, planning, storage, and distribution in a supply chain using an agile supply chain. In modern supply chains, addressing financial risks in purchases and distribution, transportation for supply and distribution of products and lost policies or the storage of products in perishable products supply chains is critical. This article investigates a direct supply chain model for the executive policies of manufacturing companies and a four-stage supply chain problem using the operational financial and marketing approach under an uncertainty state, Lagrangian relaxation and Benders' decomposition evaluation. This study introduced and provided the concepts of supply chains in perishable products. Considering supply chain issues and uncertainty in this environment, a fuzzy mathematical model was provided. In the end, a literature review has shown that most research has used heuristic and meta-heuristic algorithms due to supply chain models being NP-HARD., which are inefficient due to the approximation of optimal solutions in this domain. Meanwhile, the study used a Benders decomposition and Lagrangian relaxation algorithm for mathematical solutions, which would reduce the model's solving time and provide accurate answers. [ABSTRACT FROM AUTHOR]

Due to the high sensitivity in applying electronic and mechanical equipment in functional systems, creating conditions to increase a system's reliability is always critical for system designers. In most of the studies in the reliability area, it is assumed that the failure rates of the system's components are constant but considering time-dependent failure rates for the components is more realistic and draws the models near to real conditions. This paper presents a framework to use Markov process to obtain the system's reliability under some assumptions. In this regard, we worked on a load-sharing system with identical time-dependent failure rate components and used Markov process to calculate the system reliability. First, we define the requirements for using Markov process, and it is shown that it is possible to use it to calculate the considered system's reliability. Then, a formula is presented to calculate the reliability of the considered system using the Markov process through solving the Chapman Kolmogorov equation, when the components' life has Weibull Distribution. Next, we validate the results of the presented formula using the simulation technique. Finally, we compare the computational time of the proposed model for solving large-size problems with the simulation technique. The results show the superiority of the proposed model in terms of computational time. [ABSTRACT FROM AUTHOR]