Multi-objective optimization of a distributed energy network integrated with heating interchange

Two new continuous-time MILP (Mixed Integer Linear Programming) models are developed for resource constrained project scheduling problems in which activities can be conducted in different (multi) modes. There are efficient and flexible MILP models for this problem in which time is represented by a number of discrete time intervals. However, they require to use large numbers of binary variables as the number of activities increases and time horizon stretches. Hence efforts have been made to formulate MILP models based on continuous-time representation and therefore to speed up the solution process. We propose two novel MILP models based on the event and resource flow concepts. The models are verified by solving benchmark problems in the literature.

MILP and MINLP models for the optimal scheduling of multi-energy systems accounting for delivery temperature of units, topology and non-isothermal mixing

Passive Optical Network (PON) deployments have recently been aiming to combine the capacity of metro and access networks in the last mile of the Internet service provisioning. Deployment of PONs by running fiber to the premises introduces the advantage of huge capacity but at the same time, it calls for a robust design in order to avoid long service outage durations in case of network failures where survivable network design is mostly limited to the deployment budget. In this paper, we propose three mixed integer linear programming (MILP) models for various survivability policies to deploy reliable long-reach PONs under the budget limitations. Each MILP model aims to place the ONUs in optimal locations so that the covered area is maximized while availability requirements of the users are satisfied within the deployment budget. We solve the MILP models under the uniform and heterogeneous availability requirement scenarios and show that service availability and coverage introduce a trade-off so as the coverage and deployment cost do. Two out of the three survivability policies can guarantee 99.99% service availability while the third one is able to guarantee 99.999% by running the proposed MILP models. However, the first two schemes are able to cover larger area when compared to the third scheme which is the most reliable protection policy.

Purpose: The main purpose of the paper is to evaluate the impact of diverse personnel policies around personnel promotion in the design of the strategic staff plan for a public university. The strategic staff planning consists in the determination of the size and composition of the workforce for an organization.Design/methodology/approach: The staff planning is solved using a Mixed Integer Linear Programming (MILP) model. The MILP model represents the organizational structure of the university, the personnel categories and capacity decisions, the demand requirements, the required service level and budget restrictions. All these aspects are translated into a set of data, as well as the parameters and constraints building up the mathematical model for optimization. The required data for the model is adopted from a Spanish public university.Findings: The development of appropriate policies for personnel promotion can effectively reduce the number of dismissals while proposing a transition towards different preferable workforce structures in the university.Research limitations/implications: The long term staff plan for the university is solved by the MILP model considering a time horizon of 8 years. For this time horizon, the required input data is derived from current data of the university. Different scenarios are proposed considering different temporal trends for input data, such as in demand and admissible promotional ratios for workers.Originality/value: The literature review reports a lack of formalized procedures for staff planning in universities taking into account, at the same time, the regulations on hiring, dismissals, promotions and the workforce heterogeneity, all considered to optimize workforce size and composition addressing not only an economic criteria, but also the required workforce expertise and the quality in the service offered. This paper adopts a formalized procedure developed by the authors in previous works, and exploits it to assess the impact of various personnel policies in the staff planning for a particular university case, and this is the principal contribution of the paper.

In this paper we study how to trade off the economic and ecological effects in the remanufacturing closed-loop logistics network design in the context of low-carbon economy. We establish a multi-objective mixed integer linear programming model to find the optimal facility locations and materials flow allocation. In the objective function, we set three minimum targets: economic cost, CO2 emission and waste generation. Through an iterative algorithm, we get the Pareto Frontier of our problem. In the numeric study, we find that in order to achieve a Pareto improvement over an original system, three of the critical rates (i.e. return rate, recovery rate, and cost substitute rate) should be increased. Also, to meet the need of low-carbon dioxide, we plot an iso-CO2 emission curve in which decision makers have a series of optimal choices with the same CO2 emission but different cost and waste generation. Each choice may have different network design but all of these are Pareto optimal solutions, which provide a comprehensive evaluation of both economics and ecology for the decision making.

Profit allocation analysis among the distributed energy network participants based on Game-theory

This paper aims to design a sustainable stochastic electricity production network where fossil fuels-based, biomass-based, and co-firing-based production strategies are simultaneously considered in order to take advantage of all the three production strategies. A multi-objective stochastic mixed integer linear programming model is proposed to achieve economic feasibility, as well as environmental and social benefits under multiple uncertainties. The model is solved by using the improved augmented epsilon constraint method. A case study is used to illustrate the effectiveness of the proposed model. Pareto optimal analysis is conducted to understand the trade-off between economic, environmental, and social aspects of sustainability.

Mixed integer linear programming for the design of solar thermal energy systems with short-term storage

To support the selection of food items for FFQs in such a way that the amount of information on all relevant nutrients is maximised while the food list is as short as possible. Selection of the most informative food items to be included in FFQs was modelled as a Mixed Integer Linear Programming (MILP) model. The methodology was demonstrated for an FFQ with interest in energy, total protein, total fat, saturated fat, monounsaturated fat, polyunsaturated fat, total carbohydrates, mono- and disaccharides, dietary fibre and potassium. The food lists generated by the MILP model have good performance in terms of length, coverage and R 2 (explained variance) of all nutrients. MILP-generated food lists were 32-40 % shorter than a benchmark food list, whereas their quality in terms of R 2 was similar to that of the benchmark. The results suggest that the MILP model makes the selection process faster, more standardised and transparent, and is especially helpful in coping with multiple nutrients. The complexity of the method does not increase with increasing number of nutrients. The generated food lists appear either shorter or provide more information than a food list generated without the MILP model.

This paper proposes a comprehensive framework for strategic power system decarbonization planning that integrates the William Newman method (diagnosis–options–forecast–decision) with a multi-objective Mixed-Integer Linear Programming (MILP) model. The approach simultaneously minimizes (i) generation cost, (ii) expected cost of energy not supplied (Value of Lost Load, VoLL), (iii) demand response cost, and (iv) CO₂ emissions, subject to power balance, technical limits, and binary unit commitment decisions. The methodology is validated on the IEEE RTS 24-bus system with increasing demand profiles and representative cost and emission parameters by technology. Three transition pathways are analyzed: baseline scenario (no environmental restrictions), gradual transition (−50% target in 20 years), and accelerated transition (−75% target in 10 years). In the baseline case, the oil- and coal-dominated mix concentrates emissions (≈14 ktCO₂ and ≈12 ktCO₂, respectively). Under gradual transition, progressive substitution with wind and hydro reduces emissions by 15.38%, falling short of the target, showing that renewable expansion alone is insufficient without storage and demand-side management. In the accelerated transition, the model achieves −75% by year 10 while maintaining supply, with a cost–emissions trade-off highly sensitive to the carbon price. Results demonstrate that decarbonization is technically feasible and economically manageable when three enablers are combined: higher renewable penetration, storage capacity, and policy instruments that both accelerate fossil phase-out and valorize demand-side flexibility. The proposed framework is replicable and valuable for outlining realistic, verifiable transition pathways in power system planning.

Mixed Integer Linear Programming Model for Vehicle Routing Problem for Hazardous Materials Transportation

Modeling side slopes in vertical alignment resource road construction using convex optimization

Owing to its interconnections and open characteristics, Physical Internet (PI) has the potential to help companies meet the sustainability challenges. In this paper, to investigate the sustainability performance of the PI in an integrated production-inventory-distribution system, we propose a multi-objective mixed integer linear programming model (MOMILP) that encompasses all three dimensions of sustainability. The economic and environmental objectives are measured through the total cost and greenhouse gas (GHG) emissions, respectively. The social objective is captured by the impact of accident risk. Then, we solve the model by using the augmented ϵ-constraint method and compare the sustainability performance of the PI-enabled model with that of models enabled by the traditional (TR) and horizontal collaboration (HC) networks. The results show that the PI can not only improve the economic and environmental performance by increasing vehicle utilisation, but also alleviate the impacts of accident risks by avoiding risky routes. More interestingly, good compromise solutions featuring the PI can further improve the sustainability performance while guaranteeing the performance of the TR at the ideal point—something unachievable for the HC and TR. Moreover, sensitivity analyses demonstrate that the PI can still guarantee significant sustainability performance advantages under different common retailer quantities and network structures.

An improved MILP model for scheduling crude oil unloading, storage and processing

A new MILP model and fast heuristics for the variable-sized bin packing problem with time windows