Objective Mixed Integer Linear Programming Research Articles

Efficient and sustainable closed-loop supply chain network design: A two-stage stochastic formulation with a hybrid solution methodology

In recent years, consumers and legislators have pushed companies to design their supply chain networks to consider environmental and social impacts as an important performance outcome. Due to the role of resource utilization as a key component of logistics network design, another primary goal of design is ensuring available scarce resources are used as efficiently as possible across all facilities. To address efficiency issues in a sustainable closed-loop supply chain network, a stochastic integrated multi-objective mixed integer nonlinear programming model is developed in this paper, in which sustainability outcomes as well as efficiency of facility resource utilization are considered in the design of a sustainable supply chain network. In doing so, efficiency is assessed using a bi-objective output-oriented data envelopment analysis model. A hybrid three-step solution methodology is presented that creates a linear form of the original mixed integer nonlinear programming problem using piecewise McCormick envelopes approach. In the second step, an aggregated single objective programming model is derived by exploiting the multi-choice goal programming. Finally, a Lagrangian relaxation algorithm is developed to effectively solve the latter stochastic single objective mixed integer linear programming problem. The application of the proposed approach is investigated with data drawn from a case study in the electronics industry. This case study illustrates how firms may balance sustainability and efficiency in the supply chain network design problem. Further, it demonstrates the integration of efficiency results in improving economic aspects of sustainability as well as social responsibility outcomes, but also highlights the trade-offs that exist between efficiency and environmental impacts.

Optimal scheduling of gas and electricity consumption in a smart home with a hybrid gas boiler and electric heating system

Space and water heating are two major components of household energy consumption, and a number of work has been done to combine multiple residential heating technologies to develop hybrid heating solutions that are more flexible, efficient and economical. This paper studied and modelled a smart home with a novel hybrid heating system, which consists of a wall-hung gas boiler (for both space and water heating) that is connected to a water tank with an auxiliary electric resistance heater (for water heating), and auxiliary split air conditioners (for space heating). A multi-objective optimization was further formulated to optimally schedule the gas and electricity consumption of a smart home equipped with the hybrid heating system as well as an onsite photovoltaic (PV) system, a battery energy storage system, an electric vehicle and various types of flexile loads. Two objectives, i.e. the minimization of operating energy cost (including both electricity and gas payment) and the maximization of thermal comfort, were considered. The optimization problem was finally transformed to a single objective mixed integer linear programming problem that can be solved by existing optimization solvers. Simulation results verified the operational performance of the studied hybrid heating system and the effectiveness of the proposed scheduling method. Sensitivity analysis was conducted considering various levels of electricity/gas prices, onsite PV capacity, battery capacity and outdoor air temperature, and it shows that in all the scenarios the operating energy cost of the smart home with the hybrid heating system was always lower than that with the pure electricity or pure gas heating systems. The performance under various uncertainties and the benefits of adopting model predictive control were also demonstrated. It is noted that this paper only focuses on the optimal scheduling and operation costs of the hybrid heating system. Optimal configuration and sizing of the heating system with the initial investment (i.e. capital expenditures) considered are identified as research directions in the future.

Multi-objective particle swarm optimisation based integrated production inventory routing planning for efficient perishable food logistics operations

Sustainable and efficient food supply chain has become an essential component of one’s life. The model proposed in this paper is deeply linked to people's quality of life as a result of which there is a large incentive to fulfil customer demands through it. This proposed model can enhance food quality by making the best possible food quality accessible to customers, construct a sustainable logistics system considering its environmental impact and ensure the customer demand to be fulfilled as fast as possible. In this paper, an extended model is examined that builds a unified planning problem for efficient food logistics operations where four important objectives are viewed: minimising the total expense of the system, maximising the average food quality along with the minimisation of the amount of CO2 emissions in transportation along with production and total weighted delivery lead time minimisation. A four objective mixed integer linear programming model for intelligent food logistics system is developed in the paper. The optimisation of the formulated mathematical model is proposed using a modified multi-objective particle swarm optimisation algorithm with multiple social structures: MO-GLNPSO (Multi-Objective Global Local Near-Neighbour Particle Swarm Optimisation). Computational results of a case study on a given dataset as well as on multiple small, medium and large-scale datasets followed by sensitivity analysis show the potency and effectiveness of the introduced method. Lastly, there has been a scope for future study displayed which would lead to the further progress of these types of models.

Towards a comprehensive model of a biofuel supply chain optimization from coffee crop residues

Biofuel production from agricultural waste has been identified as a promising strategy in the field of renewable energy. This topic involves complex mathematical modeling tasks such as feedstock characteristics, biorefinery location, capacity strategy and material flows. This paper proposes a Multiple Objective Mixed Integer Linear Programming model (MOMILP) for the design of a sustainable supply chain using multiple agricultural residues. The proposed comprehensive model is utilized in a case study in Colombia, using coffee crop residues. Computational results show the model’s robustness as a decision-making tool, which allows the projection of a flexible supply chain structure in the long term.

A Method for Generating a Well-Distributed Pareto Set in Multiple Objective Mixed Integer Linear Programs Based on the Decision Maker’s Initial Aspiration Level

This paper attempt to generate a representative subset of the Pareto optimal set for multiple objective mixed integer linear programming problem using the weighted L1 norm distance. The procedure presented in this paper is somewhat similar to the one used in the ideal-point methods and its aim is to generate at each iteration the closest-points to the ideal vector corresponding to the decision maker’s initial aspiration level for a new tradeoff parameter. Unlike most of the known algorithms for generating a discrete representation of the Pareto optimal set, the procedure generates at each iteration a nondominated point by solving only one mixed integer linear programming problem. The obtained solution minimizes the weighted L1 norm distance to the ideal vector with respect to the distance between the ideal vector and previously found vectors. More generally, this approach is able to generate all Pareto optimal solutions, where all of the decision variables are restricted to be integer. In order to explain the presented details, several illustrative examples are provided.

Project cost–quality–risk tradeoff analysis in a time-constrained problem

One of the main issues in any scheduling of projects is the difficulty of convincing customer on total project makespan. There are many occasions where customer informs the contractor that the schedule must be shortened. This action could lead to increase in total cost as well as risk, which may also end of having lower quality project. This paper proposes a multi objective mixed integer linear programming for minimizing “project total extra cost”, “project total risk enhancement” and “project total quality reduction” subject to time constraint. In other words, the proposed study provides a tradeoff between the three mentioned objectives to shorten the overall project duration. Goal attainment method is used for solving the multi objective model and obtaining the Pareto-optimal solutions. The computational experiments are also applied to evaluate the efficiency of the proposed model.

Multiple Objective Fuzzy Sourcing Problem with Multiple Items in Discount Environments

The selection of proper supply sources plays a vital role to maintain companies’ competitiveness. In this study a multiple criteria fuzzy sourcing problem with multiple items in discount environment is considered as a multiple objective mixed integer linear programming problem. Fuzzy parameters are demand level and/or aspiration levels of objectives. Three objective functions are minimization of the total production and ordering costs, the total number of rejected units, and the total number of late delivered units, respectively. The model is developed for the all-units discount scheme. For the incremental discount and volume discount environment, modification requirements of the model are mentioned. The previously proposed interactive fuzzy approach combined with three fuzzy mathematical models is employed to obtain most satisfactory solution which is also a nondominated one. This study provides a realistic mathematical model and promising solution strategy to multiple item-single period sourcing problem in discount environment. Consideration of fuzziness makes the obtained nondominated solution implementable for the real cases.

Multi-objective optimization for the design and synthesis of utility systems with emission abatement technology concerns

The sustainable design configuration of utility systems incorporating pollutant emission abatement technologies has an important influence on economic cost, pollutant emission, and energy consumption of the process industry. In this paper, four typical cogeneration systems that address different emission reduction technologies are proposed as candidate structures for utility system design. The proposed systems are a gas boiler-based cogeneration system firing clean natural gas, circulating fluidized bed boiler-based cogeneration system incorporating SO2 abatement during combustion, pulverized coal boiler-based cogeneration system encompassing desulfurization and denitration after combustion, and gas–steam combined cogeneration system firing clean natural gas. The equipment performance, energy consumption, material consumption, pollutant emission, and investment and operation cost models of these cogeneration systems, as well as the corresponding emission abatement processes, are established. A multi-objective mixed integer nonlinear programming (MOMINLP) model is formulated to determine the equipment type (or cogeneration system and emission abatement technology), equipment number, equipment design capacity, and equipment operation load while simultaneously combining the multiple objectives of minimization of economic cost, minimization of environmental effect, and maximization of exergy efficiency. The original MOMINLP model is converted into a multiple objective mixed integer linear programming (MOMILP) model through linear approximation, unit size discretization, and relaxation. The augmented ε-constraint method is applied to identify the set of Pareto optimal solutions with respect to the aforementioned objective functions. An example of industrial utility system design optimization was presented. In addition, the best combination of cogeneration system for utility system structure under different objective was introduced. The sensitivity of the solutions to the primary energy source price and power to heat ratio was conducted.

A method for finding well-dispersed subsets of non-dominated vectors for multiple objective mixed integer linear programs

We present an algorithm for generating a subset of non-dominated vectors of multiple objective mixed integer linear programming. Starting from an initial non-dominated vector, the procedure finds at each iteration a new one that maximizes the infinity-norm distance from the set dominated by the previously found solutions. When all variables are integer, it can generate the whole set of non-dominated vectors.

Analytic network process and multi-period goal programming integration in purchasing decisions

This paper presents a multi-period inventory lot sizing scenario, where there is single product and multiple suppliers. By considering multi-period planning horizon, an integrated approach of Archimedean Goal Programming (AGP) and Analytic Network Process (ANP) is suggested. This integrated approach proposes a two-stage mathematical model to evaluate the suppliers and to determine their periodic shipment allocations given a number of tangible and intangible criteria. In the evaluation stage, the suppliers are evaluated according to 14 criteria that are involved in four control hierarchies; benefit, opportunity, cost and risk (BOCR). In the shipment stage, a multi objective mixed integer linear programming (MOMILP) model is described to solve the order allocation problem. This MOMILP model is suggested to achieve target values of periodic goals: budget, aggregate quality, total value of purchasing (TVP) and demand over the planning horizon, without exceeding vendor production capacities. This multi-period model is solved by using AGP. Finally some computational experiments are conducted to test the performance of the proposed method.

04/02821 A multiple objective mixed integer linear programming model for power generation expansion planning: Antunes, C. et al. Energy, 2004, 29, (4), 613–627

04/02821 A multiple objective mixed integer linear programming model for power generation expansion planning: Antunes, C. et al. Energy, 2004, 29, (4), 613–627

A multiple objective mixed integer linear programming model for power generation expansion planning

Power generation expansion planning inherently involves multiple, conflicting and incommensurate objectives. Therefore, mathematical models become more realistic if distinct evaluation aspects, such as cost and environmental concerns, are explicitly considered as objective functions rather than being encompassed by a single economic indicator. With the aid of multiple objective models, decision makers may grasp the conflicting nature and the trade-offs among the different objectives in order to select satisfactory compromise solutions. This paper presents a multiple objective mixed integer linear programming model for power generation expansion planning that allows the consideration of modular expansion capacity values of supply-side options. This characteristic of the model avoids the well-known problem associated with continuous capacity values that usually have to be discretized in a post-processing phase without feedback on the nature and importance of the changes in the attributes of the obtained solutions. Demand-side management (DSM) is also considered an option in the planning process, assuming there is a sufficiently large portion of the market under franchise conditions. As DSM full costs are accounted in the model, including lost revenues, it is possible to perform an evaluation of the rate impact in order to further inform the decision process.

Implementing flexible automation: A multiple criteria decision making approach

This paper presents a multiple objective mixed integer linear programming model for the multiperiod flexible automation selection problem. The model includes five objectives, designed to address financial aspects, flexibility, firm disruption, and group homogeneity of new modules. The proposed model incorporates several types of flexibility. An interactive multiple criteria solution procedure is used to obtain an approximate optimal solution, based on a decision maker's implicit and unknown value function. The solution provides schedule for replacement of current machines, implementation of new modules, and production plans capitalizing on flexibility during transition and subsequent periods. A numerical example is provided to illustrate the approach. The optimal solution is then contrasted with that of a single-objective model.