MIP Model Research Articles

A robust multi-objective MIP model to optimize the supply chain of steel industry taking into account the sustainability approach

The construction of a steel production plant in the countries provided that they benefit from the required raw materials, and infrastructural facilities such as roads, power plants, water, etc. are considered an economic advantage. If these prerequisites exist, the next challenge in building a steel plant is to determine the number, optimal location, and flow between the supplier and the plant and also between the plant and the consumer market. On the other hand, there is always a serious challenge for environmental issues and the impact on pastures and wildlife due to the polluting nature of this industry. In addition, considering the situation in which the amount of consumption under disruptions makes the supply chain of steel inefficient, it is necessary to design a model that is close to the real world. In this study, to obtain the optimum number and location of steel factories, material flow, and considering the sustainability approach, we design a robust three-level supply chain network for the steel industry, taking into account the sustainability approach including three objective functions. The first objective function aims to minimize logistics and production costs, the second objective function maximizes the quality score of the final selected location, and the third objective function is proposed to maximize the efficiency of product production lines. In this study, a scenario-based robust optimization model is applied to overcome the uncertainty of the proposed model. Furthermore, to incorporate the score of location into the third objective function, a decision-making method based on the sustainability approach is used. Finally, the proposed model is validated within steel industry in Iran as a case study.

A sustainable modelling for solid waste management using analytical hierarchy process, Monte Carlo simulation and NSGA-III

The issue of solid waste management is one of the greatest challenges of any society. Instead of leveraging solid waste's potential to produce energy using waste-to-energy (WTE) technologies, different countries especially developing countries stick to their ineffective and inferior methods to dispose of solid wastes. To fill this gap between energy production and waste management, this paper develops a novel methodology that integrates three efficacious tools, including Monte Carlo simulation, multi-attribute decision-making, and mathematical optimisation modelling to solve the problem from the perspective of economy, energy recovery, environment (3E), and social sustainability. In this paper, a multi-attribute decision-making method, namely AHP, is investigated to select the most suitable emerging WTE technological options as well as the optimal waste collection routes, to capture solid waste as a potential renewable energy source. Monte Carlo simulation and beta-PERT distribution are also applied to reduce the uncertainty intrinsic to decision-making. After validating the proposed methodology in a real-world case study of Tehran city, we apply a novel meta-heuristic algorithm namely NSGA-III to solve the problem on large scales with a reasonable computational time. The performance of this algorithm in solving waste location-routing problems is explored by conducting several trials. Highlights Addressing an integrated waste-to-energy and transportation network for solid waste management. Developing a novel methodology for finding the best waste-to-energy technological alternatives with respect to the sustainable criteria. Finding the high-quality set of waste collection routes, in addition to the location of facilities with the consideration of waste collection in a separated manner and vehicle's fuel consumption and emission in the MIP model. Monte Carlo simulation and beta-PERT distribution are proposed to stochastically model the absence of accurate data. Application of NSGA-III algorithm to handle the solid waste location routing problem.

A column generation approach for the lexicographic optimization of intra-hospital transports

AbstractOver the last few years, the efficient design of processes in hospitals and medical facilities has received more and more attention, particularly when the improvement of the processes is aimed at relieving the workload of medical staff. To this end, we have developed a method to determine optimal allocations of intra-hospital transports to hospital transport employees. When optimizing transport plans in hospitals, there are various optimization goals to strive for. Therefore, we used a lexicographic approach to solve this multi-criteria optimization problem. To calculate optimal transport plans in a sufficiently short computation time, we have decomposed the problem at hand with the Dantzig–Wolfe reformulation and solved the resulting pricing subproblem with an enumerative column generation approach. To improve the efficiency of the column generation process, we have investigated and implemented different pruning methods, dominance rules and a column reuse mechanism for the online setting of the application at hand. In an extensive computational study, we first evaluated the efficiency of the different pruning methods before we compared our solution approach with the standard branch-and-bound column search approach, classical column generation methods and the solution of an integrated MIP model solved by a commercial solver. Finally, we present performance indicators of the transport optimization tool, which was developed from our method and is now productively used in a German hospital.

Optimal Establishments of Massive Testing Programs to Combat COVID-19: A Perspective of Parallel-Machine Scheduling-Location (ScheLoc) Problem

Massive testing to identify COVID-19-infected people is crucial in combating COVID-19. However, from the perspective of facility location problems, many current massive testing programs are not properly set, leading to unreasonable travelling distances, long makespan, unbalanced workload, and long queues. This article proposes a decision framework for developing massive testing programs. Specifically, a biobjective parallel-testing-site Scheduling-location (ScheLoc) model is formulated, simultaneously minimizing the makespan and total travelling distance. The former can help reduce the time length of potential virus spread, and the latter can help alleviate the risk of virus spread and traveler inconvenience. To solve the proposed biobjective ScheLoc problem, in addition to the standard <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\bm {\epsilon }$</tex-math></inline-formula> -constraint method, we further develop two novel strategies. The first one iteratively solves simpler approximate MIP models (IMIP). The second innovatively extends the classical logic-based Benders decomposition approach to solve biobjective problems (B-LBBD). A Hong Kong-based case study shows that the proposed decision framework can significantly reduce the makespan and travelling distance (with a mean of 13 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> and 5.1 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> , respectively) and enhance workload balancing. Besides, the developed solution methods, especially the B-LBBD, outperform the adapted <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\bm {\epsilon }$</tex-math></inline-formula> -constraint method in various aspects.

An effective approach for bi-objective multi-period touristic itinerary planning

Planning effective itineraries for tourists is a major problem that has been gaining attention over the last years. This paper proposes a new bi-objective integer linear programming model for this problem. Decisions include the choice of the best itinerary to be performed considering multi-period routing, time windows for the visited attractions and the choice of restaurants and hotels. The conflicting objectives considered are: (i) maximizing the level of service offered by the itinerary, and (ii) minimizing the total distance traveled. The problem resolution, even for small instances by exact methods, is limited. This motivated the proposition of a new customized MIP-heuristic based on decomposition, fix-and-optimize and MIP-start, to produce good-quality solutions with moderate computational effort. Tchebycheff’s scalarization method was coupled to this heuristic and multiple compromise solutions were obtained. Extensive results with problem instances of different sizes and characteristics showed a good performance of this approach, capable of producing effective solutions within short runtimes. The analysis of the solutions indicated a strong conflict between the objectives, allowing the user to quantify the losses and gains when one criterion is prioritized over the other. A brief sensitivity analysis of some model parameters revealed interesting managerial insights. Some examples include quantifying the negative impacts in terms of the level of service offered by concentrating hotels and restaurants in the center of tourist attractions, increasing visit and transfer times between attractions and reducing the planning horizon for the entire itinerary. These aspects validate the potential of using this MIP model and applying this MIP-heuristic in real situations.

Adaptive Large Neighborhood Search Metaheuristic for the Capacitated Vehicle Routing Problem with Parcel Lockers

Background: The growth of e-commerce necessitates efficient logistics management to address rising last-mile delivery challenges. To overcome some of the last-mile delivery costs, parcel lockers as a delivery option, can be an alternative solution. This study presents the Capacitated Vehicle Routing Problem with Delivery Options (CVRPDO), which includes locker delivery. Methods: this problem is solved with An Adaptive Large Neighborhood Search (ALNS). The solution suggests some specific destroy and repair operators and integrates them with various selection schemes. The proposed method results are compared with the exact solution of the MIP model of the problem for validation. Results: Objective function values improved by 25%, 30%, 7%, 5%, and 6% for 1000, 800, 600, 400, and 200 customers, respectively, when using a 120-s ALNS runtime compared to the MIP model with a 3-h runtime. Conclusions: the CVRPDO problem involves creating a set of routes for ve-hicles that visit each customer at their delivery location or deliver their parcels to one of the lockers. These routes should respect the capacity of each vehicle and locker while minimizing the total routing costs and the number of utilized vehicles. The problem is resolved by ALNS algorithm, which outperformed the MIP model.

Classification and forecasting of sustainable-resilience suppliers via developing a novel fuzzy MIP model and DEA in the presence of zero data

Classification and forecasting of sustainable-resilience suppliers via developing a novel fuzzy MIP model and DEA in the presence of zero data

Human NCF190H Variant Promotes IL-23/IL-17-Dependent Mannan-Induced Psoriasis and Psoriatic Arthritis.

Recently, a major single nucleotide variant on the NCF1 gene, leading to an amino acid replacement from arginine to histidine at position 90 (NCF1R90H), associated with low production of reactive oxygen species (ROS), was found to be causative for several autoimmune diseases. Psoriasis in the skin (PsO) and psoriatic arthritis (PsA) were induced with mannan by intraperitoneal injection or epicutaneous application, evaluated by visual and histology scoring. Immunostaining was used to identify macrophages, NCF1, and keratinocytes. The population of immune cells was quantified by flow cytometry, gene expression was analyzed by RT-qPCR, and the JAK/STAT signaling pathway was investigated by immunohistochemical staining and western blot. We found that the low ROS responder NCF190H variant promotes PsO and PsA (the MIP model). The NCF190H-expressing mice had hyperactivated macrophages, expanded keratinocytes, and dramatically increased numbers of γδT17 cells with upregulated IL-17A, IL-23, and TNF-α. In addition, the JAK1/STAT3 signaling pathway was also upregulated in cells in the psoriatic skin tissues of Ncf190H mice. To summarize, a defined SNP (NCF1-339, also named NCF190H) was found to activate the IL-23/IL-17 axis and JAK-STAT signaling pathways, leading to hyperactivation of macrophages and keratinocytes and causing mouse psoriasis and psoriatic arthritis.

Modelling and optimisation of two-sided disassembly line balancing problem with human–robot interaction constraints

The mature application of human–robot interaction technology provides a new operation method for remanufacturing waste products, especially in the disassembly process, which further exerts the respective advantages of humans and robots. Therefore, this paper proposes an innovative two-sided disassembly line balancing problem with human–robot interaction constraints (TDLBP-HRI). First, a mixed integer programming model is established for TDLBP-HRI to minimise the number of workstations and smoothness index while simultaneously optimising robot energy consumption and disassembly costs. Then, a discrete squirrel search algorithm (DSSA) is developed to efficiently solve large-scale problems caused by the NP-hard property of TDLBP-HRI. Since SSA is an algorithm that can only solve single-objective linear problems, this research attempts to discretise and improve it to solve multi-objective TDLBP-HRI. In addition, according to the characteristics of the problem, a two-layer decoding strategy is constructed to ensure the uniqueness of the solution, and a fast non-dominated sort is introduced to enhance the multi-objective optimisation capability of the DSSA. To verify the performance of the proposed DSSA, the benchmarks of two other DLBPs types are calculated, and the obtained results are found to be significantly better than those reported in the literature. The correctness of the MIP model and DSSA is verified by comparing the results of the GUROBI solver and DSSA in solving two small-scale TDLBP-HRI examples. Following this, DSSA is shown to outperform four other classical algorithms through different scales cases of TDLBP-HRI. Finally, the proposed model and algorithm are applied to a waste power battery disassembly example. The results show that the proposed model and method can improve the performance of the disassembly line and provide new insights into the application of human–robot interaction technology in the disassembly line.

E-commerce warehousing: An efficient scattered storage assignment algorithm with bulky locations

The problem of assembling a large number of heterogeneous time-critical customer orders from a wide range of products is one of the biggest challenges that E-commerce retailers are currently facing. Unlike the traditional warehouses that could hardly keep up with the surge in demands brought by the e-commerce boom, internet fulfillment warehouses (IFWs) are designed to suit such a fast-paced environment for handling sales and customer orders of online retailers, and scattered storage is one of the trending storage assignment strategies adopted by many of them. Under the scattered storage strategy, the newly arrived items are exploded into a bunch of small stocking lots and purposely scattered around the entire warehouse. Such an assignment strategy enhances the probability of always having a nearby location containing the requested item. Thus, it potentially shrinks the order fulfillment time. This paper presents a novel scattered storage assignment approach suited for IFWs operations. Compared with the existing literature, this assignment approach pays more attention to handling the inevitable quantity fluctuation of customer ordering patterns. The proposed problem is mathematically expressed as a MIP model, and a heuristic algorithm, consisting of a feasibility checking procedure and a two-stage item allocation procedure, is developed to generate a high-quality solution in a time-efficient manner. Numerical studies are then conducted to assess the computational performance of the proposed algorithm and to justify if the proposed model is efficacious and improves order-picking efficiency.

A MIP model and a hybrid genetic algorithm for flexible job-shop scheduling problem with job-splitting

In the scheduling literature, it is generally assumed that jobs are not split into sub-lots, or that the number and size of sub-lots are limited or predetermined. These assumptions make the problem more manageable. However, they may prevent more successful schedules. For many businesses, considering the splitting of jobs while scheduling them can create significant improvement opportunities. This study addresses the Flexible Job-Shop Scheduling Problem (FJSP) with job-splitting, determining how many sub-lots each job should be split into and the size of each sub-lot. A MIP model is proposed for the considered problem. In the model, the size and number of sub-lots of a job are not predefined or bounded. The objective function of the model is to minimize the makespan. Feasible solutions could not be found for large-sized problems by the mathematical model. So, a Hybrid Genetic Algorithm (HGA) is also proposed. In the proposed HGA, a Local Search Algorithm (LSA) that determines the size of sub-lots has been included in the GA to improve the efficiency. To show the success of the proposed HGA, its performance is compared with the classical GA.

A location–transportation problem under demand uncertainty for a pharmaceutical network in Brazil

We study the integrated location–transportation problem under uncertain demand, addressing the case of a pharmaceutical logistics network in Brazil. We propose a mathematical model with multi-time scales to make decisions accordingly with their timing. The model considers practical features, such as fleet sizing, safety constraints in cargo transportation, and tax issues. We address uncertainty in decision-making by developing a robust counterpart and present solution methods based on Fix-and-Optimize heuristics. We perform computational experiments using real data from a partner company and evaluate the impact of uncertainty on the problem. The heuristics outperform the MIP model by reducing the average of logistics costs and taxes by 40%. Demand uncertainty and variability significantly influence the problem decisions. Also, the robust model reduces expected solution costs. Thus, these models and solution methods can support the decision-making process on location–transportation problems in Logistics Network Planning in contexts similar to the pharmaceutical industry in Brazil.

Service network design with consistent multiple trips

We introduce and study a challenging service network design problem arising within a city logistics company based in Beijing, China. To provide cost-effective same-day delivery services, the company divides the whole urban area into regions. Within each region, a fleet of small-capacity vehicles picks up and delivers packages. A fleet of line-haul vehicles (large-capacity vehicles) executes consistent multiple trips over the regions to transport consolidated packages, during which transshipment is allowed. In this study, we focus on designing the trips of line-haul vehicles, i.e., their region visiting sequences, as the performance of the logistics system depends significantly on the coordination of line-haul vehicles. We model the trip design problem as a service network design problem with consistent multiple trips. We develop a continuous-time MIP model to formulate the problem and optimally solve small-size instances. In addition, we propose an adaptive large neighborhood search heuristic to solve larger instances. Numerical experiments on randomly generated instances as well as real-world operational data demonstrate the effectiveness and efficiency of our solution approach.

Solving a real-world nurse rostering problem by Simulated Annealing

Designing high quality nurse rostering plans is essential for health care facilities in order to guarantee efficiency, safety and quality-of-care balanced with staff well-being.We introduce a new real-world formulation for the nurse rostering problem, arising in many Italian healthcare institutions, which has been developed in collaboration with a primary software company in the field. It considers nurses with different skills, special shifts depending on the skills, time work-load limits, and different types of days-off. In addition, preferences and incompatibilities between nurses are taken into account.We propose a MIP model and a local search method, driven by a Simulated Annealing metaheuristic, based on a combination of two neighborhoods. The solution method was tested on 34 real-world instances coming from various healthcare institutions in North Italy. The dataset is available at https://bitbucket.org/satt/nrp-instances, along with our best solutions.

New MIP model for short-term planning in open-pit mines considering loading machine performance: a case study in Iran

New MIP model for short-term planning in open-pit mines considering loading machine performance: a case study in Iran

Tactical and strategic redesign of supply chains affected by delocalisation

The present research work addresses the problem of modelling and redesigning a supply chain. With that general purpose, a model is developed to minimise logistics costs, including specific considerations about provisioning, inventories, products, location, selection of supply channels, assignments between distribution centres and demand zones, and transfers between distribution centres. The solution procedure is based on the design of a linear-programming-like MIP model for large optimisation scales. The model is validated with real data from a multinational beauty product company. Simulated data are used for larger instances. The performance of the solution procedure of the model enables optimal solutions to be obtained in practical instances of the problem at excellent CPU times.

Home care routing and scheduling problem with teams’ synchronization

The demand for home care (HC) services has steadily been growing for two main types of services: healthcare and social care. If, for the former, caregivers' skills are of utter importance, in the latter caregivers are not distinguishable in terms of skills. This work focuses social care and models caregivers' synchronization as a means of improving human resources management. Moreover, in social care services, several visits need to be performed in the same day since patients are frequently alone and need assistance throughout the day. Depending on the patient's autonomy, some tasks have to be performed by two caregivers (e.g. assist bedridden patients). Therefore, adequate decision support tools are crucial for assisting managers (often social workers) when designing operational plans and to efficiently assign caregivers to tasks. This paper advances the literature by 1) considering teams of one caregiver that can synchronize to perform tasks requiring two caregivers (instead of having teams of two caregivers), 2) simultaneously modelling daily continuity of care and teams' synchronization, and 3) associating dynamic time windows to teams' synchronizations introducing scheduling flexibility while minimize service and travel times. These concepts are embedded into a daily routing and scheduling MIP model, deciding on the number of caregivers and on the number and type of teams to serve all patient tasks. The main HC features of the problem, synchronization and continuity of care, are evaluated by comparing the proposed planning with the current situation of a home social care service provider in Portugal. The results show that synchronization is the feature that most increases efficiency with respect to the current situation. It evidences a surplus in working time capacity by proposing plans where all requests can be served with a smaller number of caregivers. Consequently, new patients from long waiting lists can now be served by the “available” caregivers.

Designing the breadth and depth of distribution networks in the retail trade

Retailers whose sales volumes have changed noticeably over time or who want to expand their business to new geographical areas are faced with the question of how to improve or suitably restructure their current logistics network. These include new developments in warehouse automation or design measures to improve supply chain resilience. We examine a distribution network design problem that integrates the strategic decision of determining the number of distribution centers (DC) and the number of DC types anticipating the impact of these decisions on subsequent tactical planning. We propose a MIP modeling approach that factors in costs that result from setting up and operating the warehouses, inbound and outbound transportation, inventory holding at the DCs and instore logistics. The resulting distribution network potentially consists of several types of warehouses that store a distinct set of products each, and corresponds to structures commonly applied in grocery retailing, for example. To solve the problem we present an iterated local search that is based on a decomposition approach to facilitate practical applicability of the model. The application of our solution approach to a real-life case of a major European grocery chain highlights the improvement potential that is achievable by restructuring existing retail networks. We found that up to 15% of decision-relevant supply chain costs and even 30% to 50% of the decision-relevant instore costs can be reduced compared to the original network structure. Further sensitivity analyses provide additional insights into the problem structure, cost tradeoffs and robustness of the solutions generated.

Online joint optimization of pick order assignment and pick pod selection in robotic mobile fulfillment systems

Robotic mobile fulfillment systems is a large dynamic system where information such as backlog, inventory, pod location, and robot state will change with time during its operation. In this paper, we model the dynamic system for the online joint optimization of pick order assignment and pick pod selection considering multiple items and then propose a new MIP model to solve the decision-making in the key process. We design a heuristic based on alternate decision and order-driven to solve large-scale problems. We extend an open-source simulation framework to evaluate the results of proposed model and algorithm through different instances in the dynamic system. Experimental results show that the performance of the new MIP model is at least 13% higher than that of the different settings, and the performance of the designed heuristic is at least 57% higher than that of the state-of-the-art sequential method in the literature.

Solving the integrated bin allocation and collection routing problem for municipal solid waste: a Benders decomposition approach

The municipal solid waste system is a complex reverse logistic chain which comprises several optimisation problems. Although these problems are interdependent—i.e., the solution to one of the problems restricts the solution to the other—they are usually solved sequentially in the related literature because each is usually a computationally complex problem. We address two of the tactical planning problems in this chain by means of a Benders decomposition approach: determining the location and/or capacity of garbage accumulation points, and the design and schedule of collection routes for vehicles. Our approach manages to solve medium-sized real-world instances in the city of Bahía Blanca, Argentina, showing smaller computing times than solving a full MIP model.