mixed integer programming

Sustainable development is defined as development that meets the needs of the present generation without compromising the ability of future generations to meet their own needs. It encompasses economic, social, and environmental dimensions that must be considered simultaneously. With the increasing importance of sustainable development, many companies worldwide are motivated, either proactively or reactively, to collect their used products. In such circumstances, establishing a reverse logistics network based on sustainable development is essential. The decision to outsource logistics has gained significance due to the need to avoid fixed costs, heavy investment, and achieve economic advantages, with many companies recognizing the potential benefits of high-quality logistics services.

This research presents a mixed integer programming model for planning reverse logistics outsourcing in the assembly cycle of the automotive industry, focusing on a cost-oriented objective function. The research scope includes the assembly cycle of production lines, specifically prioritizing high-volume car manufacturers (light vehicles), and focuses on the Saipa Automotive Industrial Group, including the Ryan Saipa Leasing Group. The research period spans from 1389 to 1398 in the Iranian calendar. Variables such as non-commercial receivables, total assets, operating profit, net profit, and market value were evaluated using MATLAB software based on published statistics from Saipa.

The research findings indicate that among the variables of non-commercial receivables, total assets, operating profit, net profit, and market value, net profit to operating profit and sales (operating income) are of significant importance. The highest amount of non-commercial receivables for Saipa occurred in 1398 during the summer, while the highest total assets were recorded in 1392 during the summer. The highest operating profit was observed in 1398 during the winter, and the highest net profit was in 1390 during the spring. The degree of data convergence was calculated in the regression charts of sales (operating income) to operating profit and net profit to operating profit for the years 1389-1398. The degree of data convergence in the regression chart of sales to operating profit based on the conceptual model in 1398 was 0.9895, and for net profit to operating profit in 1398, it was 0.9961. The regression rate for the conceptual model in the test phase was 0.79, and in the overall processing stage, it was also 0.79. The histogram error rate was calculated for all three stages of learning, validation, and testing, with an error rate of 0.002375, which is acceptable due to its proximity to zero. Comparing these results with other studies shows an improvement in the regression and error rate in the analysis of the objective function.

Based on the calculated weight of the criteria in two-way assembly line balancing issues, it can be concluded that the decision team pays special attention to strategic issues in addition to production issues. The production rate of the line, which is the inverse of the production cycle time, affects the company's market share in the long term and increases its market share.

In recent years, significant energy consumption and facing global warming have led to concern worldwide. Therefore, governments have turned to deterrent actions such as imposing daily tariffs in different intervals to tackle energy consumption. This article addresses unrelated parallel machine energy-efficient scheduling problems by considering sequence-independent setup times and energy consumption tariffs. The objective function is that jobs should be assigned to machines and processed in different intervals so that the cost of consumed energy becomes as less as possible. It should be noted that the assumed sequence-independent setup times are addressed in two different modes, setup times jointed to processing time and setup times disjointed from processing time. Design/methodology/approach: To optimize the total energy consumption cost in unrelated parallel machine scheduling problems with sequence-independent setup times jointed to processing time and disjointed from processing time, mixed-integer linear programming (MILP) models have been proposed from two different points of view. The first model has been formulated according to the predecessor jobs of a special job, while the second model has been conducted based on the immediate predecessor job. Also, a fix and relax heuristic (FRH) algorithm has been conducted to solve large- scale instances. All mathematical models and the heuristic algorithm have been coded in the Visual C# 2017 environment and implemented using the CPLEX 12.8 Concert Technology on a PC with 32GB RAM and Intel Corei7 4.0 GHz CPU (4 cores). Also, a sizeable number of instances have been solved to evaluate the efficiency of mathematical models and the heuristic algorithm and to ensure their accuracy.

According to numerical analysis, both mathematical models solved the instances of up to 20 jobs and 80 machines optimally for sequence-independent setup-times jointed to processing time, and sequence-independent disjointed from processing time problems. However, generally speaking, the mathematical model based on predecessor jobs was more efficient than another mathematical model, especially in terms of run time. Moreover, the proposed fix and relax-based heuristic algorithm solved instances of up to 20 machines and 190 jobs for the disjointed setup times problem, and up to 20 and 220 instances for the jointed setup times problem. It should be noted that all instances were generated analogously to the literature.

A vast number of exogenous factors contributed to the scheduling problems in the real world, which can disturb the scheduling process easily, frequent power outages, machine breakdown, and operator absence. Besides, considering all the real world's possibilities raises extreme complexity in problems. Therefore, similar to other studies, some assumptions were considered as follows: - machines are always available at all times; - idle is allowable for machines; - the energy consumption rate of various machines is different for each job; - each machine's energy consumption rate during processing and setups is different for each job, it is assumed as constant; - preemption is not allowed in the job's processing and setups; - all jobs are available at the beginning of the planning horizon; and - each machine can process or do the setup for only one job at a time.

Given that unrelated parallel machines are one of the most practical scheduling environments, this article can be effective in production sites and operation lines that contain such a kind of machine. Besides, unrelated parallel machines cover identical and related parallel machines. Consequently, this paper is the building blocks of cost-effective and environmentally friendly scheduling programs. Also, the application of unrelated parallel machines is not merely restricted to production problems. In other words, unrelated parallel machine scheduling problems can be used in other real-world cases, such as airplane scheduling and elevator scheduling. Originality/value - In this paper, unrelated parallel machine energy-efficient scheduling has been addressed considering sequence-independent setup times. Since it was a common belief that sequence-independent setup times could be included in processing times, sequence-independent setup times have been neglected so far. However, in this innovative study for the first time, an unrelated parallel machine energy efficient problem was investigated with sequence-independent setup times. Mathematical programming models and a heuristic algorithm were proposed for such a practical problem.

In this paper the integrated Master Surgical Scheduling program and Case Mix Planning is investigated. A new two-step approach is proposed for creating and updating this program. In the first step, a model is proposed for creating master surgical schedule considering the demand distributions of different surgery kind of each surgeon. In the second step, having the weekly waiting list of patients, a model is proposed for updating this program in order to cope with demand fluctuations and maximize the use of operating rooms capacity in weekly period. In this paper the limitation of down-stream resources is also considered. Three objectives are considered for this problem: minimizing over time cost and idle time cost of operating rooms, maximizing the surgeons’ preferences and minimizing the not fulfilled demand. The real data from Al-Zahra hospital of Isfahan, Iran is used to evaluate the models and analyze the results. The proposed approach is evaluated using these real data in several problem instances. The experiments show that the proposed approach leads to better results than real program of hospital with significant different which displays the efficiency of the proposed approach.

Hazardous waste management incorporates collection, separation, treatment, recycling and disposal of hazardous wastes. In this paper, a new multi-objective mixed integer model is presented for hazardous waste collection problem. The model aims to minimize transportation and construction costs, and environmental and population risks in hazardous waste management systems. This model is applied in a case study of Iran in order to help decision makers to decide on the location of separation, treatment, recycle, disposal centers, and established technology in treatment center. Moreover, this paper specifies routes between different facilities in collection network. For addressing population and environmental impacts and economical costs, three objective functions including total costs, total population exposure risk, and environmental risks are considered. An augmented ε-constraint method is used to generate Pareto optimal solution for these conflicting objectives. Finally, proposed model is utilized in our case study and numerical results and some managerial insights are provided

In the scheduling problems, it is commonly assumed that processing times are fixed and known. In the literature of project scheduling emphasizes that the time of each activity/operation can be multi-mode and by assigning more resources, the activity time can be reduced. In these problems, in addition to activity scheduling, allocation of available limited resources to the activities should also be carried out. This assumption that processing time of activities is fixed is a weakness in scheduling literature. This paper develops the classic problem flow shop scheduling to multi-mode resource-cosntrainted flow shop scheduling problem. This paper discusses comprehensively about mathematical modeling. In this regard, two mixed integer linear programming models with two differnet concepts are presented. The first model is location-based model and the second is sequence-based. The performance of the models are evaluated by comparing their size and computational complexities. In the size complexity, the first model requires more variables but less constraints than second Model. In the computational complexity, the first model significantly outperforms than the second Model. Also, the first model, besides solving more problems as optimally, requires less time to solve than the second model .

Nowadays, energy management is highly regarded throughout the world. High energy consumption leads to high costs for consumers in the long term and at the national level. In this study by modified consumption patterns and presenting a proposed plan, it has been tried to optimize electrical energy consumption in hospitals.The proposed model is a goal programming model. Objective functions consist of minimization of peak energy consumption and minimization of electricity costs. Some constraints such as daily energy requirements and user preferences have been modeled using mixed integer programming. Regarding objective functions, three different scenarios have been considered.The developed model can be easily performed in a hospital unit. The combined scenario that has been considered both objectives simultaneously is the best.The proposed model is a practical one for intelligent management of electrical consumption. Thus, performing the model in hospitals is recommended.