Bi-objective Model Research Articles

A Lagrangian relaxation algorithm for optimizing a bi-objective agro-supply chain model considering CO2 emissions

In this research, an agro-supply chain in the context of both economic and environmental issues has been investigated. To this end, a bi-objective model is formulated as a mixed-integer linear programming that aims to minimize the total costs and CO2 emissions. It generates the integration between purchasing, transporting, and storing decisions, considering specific characteristics of agro-products such as seasonality, perishability, and uncertainty. This study provides a different set of temperature conditions for preserving products from spoilage. In addition, a robust optimization approach is used to tackle the uncertainty in this paper. Then, $$\varepsilon$$ -constraint method is used to convert the bi-objective model to a single one. To solve the problem, Lagrangian relaxation algorithm is applied as an efficient approach giving lower bounds for the original problem and used for estimating upper bounds. At the end, a real case study is presented to give valuable insight via assessing the impacts of uncertainty in system costs.

A Bi-Objective Home Health Care Routing and Scheduling Model with Considering Nurse Downgrading Costs.

In recent years, the management of health systems is a main concern of governments and decision-makers. Home health care is one of the newest methods of providing services to patients in developed societies that can respond to the individual lifestyle of the modern age and the increase of life expectancy. The home health care routing and scheduling problem is a generalized version of the vehicle routing problem, which is extended to a complex problem by adding special features and constraints of health care problems. In this problem, there are multiple stakeholders, such as nurses, for which an increase in their satisfaction level is very important. In this study, a mathematical model is developed to expand traditional home health care routing and scheduling models to downgrading cost aspects by adding the objective of minimizing the difference between the actual and potential skills of the nurses. Downgrading can lead to nurse dissatisfaction. In addition, skillful nurses have higher salaries, and high-level services increase equipment costs and need more expensive training and nursing certificates. Therefore, downgrading can enforce huge hidden costs to the managers of a company. To solve the bi-objective model, an ε-constraint-based approach is suggested, and the model applicability and its ability to solve the problem in various sizes are discussed. A sensitivity analysis on the Epsilon parameter is conducted to analyze the effect of this parameter on the problem. Finally, some managerial insights are presented to help the managers in this field, and some directions for future studies are mentioned as well.

A novel bi-objective model for a job shop scheduling problem with consideration of Fuzzy parameters, modified learning effects and multiple preventive maintenance activities

This paper aims at introducing a novel bi-objective model for a Job Shop Scheduling Problem (JSSP) in order to minimize makespan and maximum tardiness simultaneously. Some realistic assumptions, i.e. Fuzzy processing times and due dates involving triangular possibility distributions, transportation times, availability constraints, modified position-based learning effects on processing times, and sum-of-processing-time based learning effects on duration of maintenance activities have been considered, to provide a more general and practical model for the JSSP. Based on the learning effects, Processing times decrease as a machine performs an operation frequently, and workers gain working skills and experiences. In this paper based on DeJong’s learning effect a novel and modified formulation has been proposed for this effect. According to the above-mentioned assumptions, a novel mixed-integer linear programming (MILP) model for the JSSP is suggested. The proposed model is first converted to an auxiliary crisp model, given that model is a possibilistic programming, it is then solved by the TH and ε-constraint methods for small instances, and the results are compared. For medium and large instances, five metaheuristic algorithms, including NSGA-ΙΙΙ, PESA-ΙΙ, SPEA-ΙΙ, NSGA-ΙΙ, and MOEA/D are utilized, and the results are finally compared on the basis of three performance metrics.

Solve a New Robust Bi-Objective Model for Designing Blood Supply Chain Network by NSGA II and Imperialist Competitive Algorithm

In this supply chain, blood and blood products are investigated as a product from donor to patient. Specific characteristics of blood supply chain such as perishability and existence of uncertainty in the structure of this chain have caused problems for planning in this regard. However, this point should be considered that the importance of this supply chain cannot be compared to perishable products. Life and death issue of this product is the main difference between blood and other perishable products. Therefore, a comprehensive model was presented in this study to locate blood bank components within a network and to determine the allocation of these components considering blood donation centers, blood testing and processing laboratories, distribution centers or blood banks, and demand centers. Since designing supply chain and locating issues at large dimensions are NP-hard, the suggested models at small sizes were compared using the exact method (GAMS), non-dominated genetic sorting algorithm, and multi-objective imperialist competitive algorithm. The results were compared with GAMS. This shows normal performance of the proposed algorithms and led to using these two algorithms at average and large sizes for research questions. Also, by analyzing sensitivity on important parameters, important managerial findings are suggested for similar conditions.

Bi-objective dynamic weapon-target assignment problem with stability measure

In this paper, we develop a new bi-objective model for dynamic weapon-target assignment problem. We consider that the initial weapon assignment plan of defense is disrupted during engagement because of a destroyed air target, breakdown of a weapon system or a new incoming air target. The objective functions are defined as the maximization of probability of no-leaker and the maximization of stability in engagement order of weapon systems. Stability is defined as assigning same air target in sequence in engagement order of a weapon system so that reacquisition and re-tracking of air target are not required by sensors. We propose a new solution procedure to generate updated assignment plans by maximizing efficiency of defense while maximizing stability through swapping weapon engagement orders. The proposed solution procedure generates non-dominated solutions from which defense can quickly choose the most-favored course of action. We solve a set of representative problems with different sizes and present computational results to evaluate effectiveness of the proposed approach.

Fuzzy bi-objective model for hazardous materials routing and scheduling under demand and service time uncertainty

We develop a fuzzy-based bi-objective optimisation model for hazardous materials (hazmat) vehicle routing and scheduling problem with time windows. The task is to find optimal links and routes to maintain a balance between safe and fast distribution of hazmats between origins and destinations through a transport network. We consider unknown probabilities for hazmat incidents along with a game-theoretic demon approach in a link-based model. Using the Nash game theory approach, an integrated routing and scheduling hazmat shipment problem is formulated. Since the formulated problem is a bi-objective model with travel time and population risk objectives, we also propose a solution method based on a hybrid Monte-Carlo simulation and fuzzy goal programming to obtain the set of Pareto optimal solutions. Computational results of a carefully crafted numerical example are also provided to illustrate the effectiveness of the developed mathematical model and the solution method in obtaining Pareto-optimal solutions.

Fuzzy bi-objective model for hazardous materials routing and scheduling under demand and service time uncertainty

We develop a fuzzy-based bi-objective optimisation model for hazardous materials (hazmat) vehicle routing and scheduling problem with time windows. The task is to find optimal links and routes to maintain a balance between safe and fast distribution of hazmats between origins and destinations through a transport network. We consider unknown probabilities for hazmat incidents along with a game-theoretic demon approach in a link-based model. Using the Nash game theory approach, an integrated routing and scheduling hazmat shipment problem is formulated. Since the formulated problem is a bi-objective model with travel time and population risk objectives, we also propose a solution method based on a hybrid Monte-Carlo simulation and fuzzy goal programming to obtain the set of Pareto optimal solutions. Computational results of a carefully crafted numerical example are also provided to illustrate the effectiveness of the developed mathematical model and the solution method in obtaining Pareto-optimal solutions.

A green closed-loop supply chain network: a bi-objective mixed integer linear programming model

The increasing level of customer awareness and application of environmental laws by governments, on the one hand, and the increasing number of competitors, on the other hand, has obliged industry owners to include green activities in the design of the supply chain network. Green activities include any type of action that reduces environmental degradation. Hence, this study seeks to develop a bi-objective, mixed integer linear programming (MILP) model for designing a green supply chain network. In the proposed model, the minimisation of costs and detrimental environmental effects are discussed. LP metric method is used to solve the bi-objective model and the proposed model is run by using simulated data in small and medium sizes in GAMS software. Finally, the model sensitivity analysis is measured in order to evaluate the validity and performance of the proposed model by using demand-driven scenarios. The results of this model indicate the effectiveness of the proposed model.

Joint optimization of production and routing master planning in mobile supply chains

Many supply chains suffer from a lack of flexibility, adaptability, and robustness, which imposes customer dissatisfaction, transportation, backlog, and rework costs on companies. The mobile supply chain (MSC) is a newly developed idea that aims to rectify this problem. In this kind of supply chain, production, distribution, and delivery of a product family are performed by a mobile factory (MF), which can be carried by truck, while stationary production sites are no longer required. The production process is completed directly at the customer's location following customer detail requirements. In this paper, a mathematical model is developed to optimize the mobile factory routing problem as well as production scheduling at each customer's site, which is inspired by a real-world application of modular production in the chemical industry. For this purpose, due dates of customers’ work orders and transportation costs should be considered simultaneously. The model results indicate that if these objective functions are taken into account separately, the results will be sub-optimal solutions causing substantial financial losses for customers and suppliers. The proposed bi-objective model using a multi-objective optimization approach proffers a Pareto frontier. Accordingly, decision-makers can choose from a range of solutions, from zero delayed orders to the lowest transportation costs. However, in many cases it is possible to reach zero delayed orders with just a small increase in transportation costs.

Designing a clothing supply chain network considering pricing and demand sensitivity to discounts and advertisement

These days, clothing companies are becoming more and more developed around the world. Due to the rapid development of these companies, designing an efficient clothing supply chain network can be highly beneficial, especially with the remarkable increase in demand and uncertainties in both supply and demand. In this study, a bi-objective stochastic mixed-integer linear programming model is proposed for designing the supply chain of the clothing industry. The first objective function maximizes total profit and the second one minimizes downside risk. In the presented network, the initial demand and price are uncertain and are incorporated into the model through a set of scenarios. To solve the bi-objective model, weighted normalized goal programming is applied. Besides, a real case study for the clothing industry in Iran is proposed to validate the presented model and developed method. The obtained results showed the validity and efficiency of the current study. Also, sensitivity analyses are conducted to evaluate the effect of several important parameters, such as discount and advertisement, on the supply chain. The results indicate that considering the optimal amount for discount parameter can conceivably enhance total profit by about 20% compared to the time without this discount scheme. When the optimized parameter is taken into account for advertisement, 12% is obtained as total profit.

A green closed-loop supply chain network: a bi-objective mixed integer linear programming model

The increasing level of customer awareness and application of environmental laws by governments, on the one hand, and the increasing number of competitors, on the other hand, has obliged industry owners to include green activities in the design of the supply chain network. Green activities include any type of action that reduces environmental degradation. Hence, this study seeks to develop a bi-objective, mixed integer linear programming (MILP) model for designing a green supply chain network. In the proposed model, the minimisation of costs and detrimental environmental effects are discussed. LP metric method is used to solve the bi-objective model and the proposed model is run by using simulated data in small and medium sizes in GAMS software. Finally, the model sensitivity analysis is measured in order to evaluate the validity and performance of the proposed model by using demand-driven scenarios. The results of this model indicate the effectiveness of the proposed model.

Flows optimisation of industrial symbiosis based on bi-objective mathematical modelling

It seems clear that industrial systems can no longer continue to operate by taking unrestricted amounts of natural resources, especially when these are non-renewable. In order to limit this over-consumption, the industrial symbiosis principle is an interesting solution. The objective here is to determine, using a mathematical bi-objective model, the optimal flow allocations within a symbiosis. Our model applies at the tactical and operational levels, i.e., when the symbiosis is already defined. The aim is to study the best possible flow distribution in order to maximise both the symbiosis overall economic and symbiotic profits (defined as the difference between internal and external flows). With this in mind, we will conduct a numerical application based on a real example with generic values before presenting an optimisation algorithm based on the ε-constraint method. Finally, simulations will be performed to study the evolution of results.

Resilient supply chain under risks: A network and structural perspective

Constant development and changes in the supply chain lead the system to meet various risks. Thus, a proper procedure should be adopted to cope with such issues. This study addresses a bi-objective model to design a resilient and robust forward supply chain under uncertainty and multiple disruptions. The investigated objective functions include minimizing the total cost and the total non-resiliency of the network that are tackled using the e-constraint method. Notably, resilience strategies and two-stage stochastic programming are respectively considered to cope with disruption and operational risks. Ultimately, some random numerical benchmarked examples are applied to the model to confirm the proposed formulation's performance. The results indicate that considering risks in the system leads to increased costs, but it would be profitable in the long term. Notably, a resilient chain can prevent system failure and enhance capabilities to reduce risk exposure costs and damages.

A Sustainable Distribution Design for Multi-Quality Multiple-Cold-Chain Products: An Integrated Inspection Strategies Approach

Cold-chain products are time-sensitive and perishable and pose the risk of failure if they are transported to a distant location. Thus, there is a need to analyze their quality during distribution so that the customers may receive optimal-quality products. To address this issue, this study integrates inspection strategies with the sustainable distribution system of multi-quality multiple-cold-chain products. A bi-objective model of cost and emission is proposed under the constraints of heterogeneous vehicle and time window. Furthermore, this study intends to address the following questions: which inspection strategy helps to ensure the potency of delivered products, and what is the impact of quality differentiation on the value of objective functions? A set of meta-heuristics is used for implementing the model using a rich panel of experiments. The results reveal that the quality conditions of different products impact the solutions of cost and emissions. Moreover, the conformity strategy is more viable, as it results in less cost and ensures that the quantity of delivered products meets the level of demand. Finally, the study provides implications for managers and practitioners to develop a sustainable distribution system to maintain the quality of cold-chain products.

Flows optimisation of industrial symbiosis based on bi-objective mathematical modelling

It seems clear that industrial systems can no longer continue to operate by taking unrestricted amounts of natural resources, especially when these are non-renewable. In order to limit this over-consumption, the industrial symbiosis principle is an interesting solution. The objective here is to determine, using a mathematical bi-objective model, the optimal flow allocations within a symbiosis. Our model applies at the tactical and operational levels, i.e., when the symbiosis is already defined. The aim is to study the best possible flow distribution in order to maximise both the symbiosis overall economic and symbiotic profits (defined as the difference between internal and external flows). With this in mind, we will conduct a numerical application based on a real example with generic values before presenting an optimisation algorithm based on the e-constraint method. Finally, simulations will be performed to study the evolution of results.

A New Method to Solve Interval Transportation Problems

transportation problem (ITP) in which the cost-coefficients of the objective function, source and destination parameters are all in the form of interval. In this paper, the single objective interval transportation problem is transformed into an equivalent crisp bi-objective transportation problem where the left-limit and width of the interval are to be minimized. The solution to this bi-objective model is then obtained with the help of fuzzy programming technique. The proposed solution procedure has been demonstrated with the help of a numerical example. A comparative study has also been made between the proposed solution method and the method proposed by Das et al.(1999) .

A Multi-objective Particle Swarm Optimization Based on Pareto Archive for Integrated Production and Distribution Planning in A Green Supply Chain

ABSTRACT This paper presents a bi-objective model for integrated production and distribution planning in a multi-period multi-product green supply chain. This paper considers many near-real-world factors, such as: normal and overtime production shifts, limited storage capacity of the finished product and raw materials, different vehicle types, direct and indirect shipping along with considering different production methods that influence the production costs and sale prices, simultaneously. Mixed integer programming model is proposed in which the profit maximization and the CO2 emission minimization are formulated. A particle swarm optimization algorithm based on Pareto archive that utilizes the genetic algorithm operators is proposed to solve the model.

Multi-objective matheuristic for minimization of total tardiness and energy costs in a steel industry heat treatment line

This research focuses on solving a scheduling problem in a heat treatment line of a multinational steel company. A bi-objective model is proposed to minimize the line total energy costs and total tardiness. The solution is carried out through a matheuristic technique that combines metaheuristics and mathematical programming. A Mixed Integer Linear Programming (MILP) model is designed to generate initial solutions to a Multi-objective Variable Neighborhood Search (MOVNS) algorithm. One benefit of this approach is the ability to handle large-scale problems, common in real production scheduling cases, with reasonable computational time and alternative quality planning. The suggested matheuristic is proven to be statistically superior to an only metaheuristic approach, taking as performance metric the final approximated Pareto solutions’ hypervolume. Tests performed with data from the industry showed improvements in the scheduling of the heat treatment line with reductions of energy costs and tardiness up to 13% and 90%, respectively. The methodology can also be extended to other similar scheduling processes.

A Bi-objective Integrated Optimization Model of High-speed Train Rescheduling and Train Control

A Bi-objective Integrated Optimization Model of High-speed Train Rescheduling and Train Control

Choice of loading clusters in container terminals

The storage allocation in the export yard of a container terminal determines the efficiency of container loading. Even if the yard manager has optimised the allocation of export containers to avoid rehandling, conflicts among loading quay cranes can still occur. Thus, all the possible handlings during loading must be considered when organising the yard space. In previous studies, the yard storage allocation has been assessed based on the subblock, which consists of several adjacent bays. However, to minimise all possible handlings in the loading process at the terminal, optimising more flexible storage clusters is also important. Thus, our aim in this research is to model the choice of loading clusters and derive a more flexible allocation strategy for organising the space in the export yard. A bi-objective model is built, which considers both the transportation distance and handling balance between blocks. A model aimed at minimising all possible handlings in the export yard for the loading process is also developed, and several of the insights derived can inform yard management in real-life operations. It is proven that the handling requirements have a significant effect on the choice of loading clusters, and yard managers should consider the various features of liner and loading processes when organising their storage space.