Integer Nonlinear Programming Model Research Articles

Fleet deployment and speed optimization of container ships considering bunker fuel consumption heterogeneity

The bunker fuel consumption cost takes up the largest percentage of the total operating cost of a container ship. How to control bunker fuel consumption is one of the important problems to be solved by the shipping companies. Especially nowadays, shipping companies have to reduce emissions to meet the regulations of the international maritime organization (IMO) and local governments. Bunker consumption is impacted by the sailing speed of ships, which also influences the round-trip time and the number of ships deploying on the specific routes. In addition, the ships deployed in the same route may have different consumption rates due to different construction techniques, waring out, etc. This paper considers two situations where bunker consumption functions are the same and different on different legs of the shipping route and establishes two mixed integer nonlinear programming models to adjust the fleet deployment with heterogenous ships and optimize ship sailing speed while maintaining the weekly service frequency to reduce the total operating cost which consists of bunker consumption cost and ship operation cost. Then two tailored exact algorithms are developed to obtain the global optimal solutions for the two models. Finally, numerical experiments are conducted to verify the validity of the two models.

Track Utilization Optimization Method for Arrival Yard of Marshalling Station Considering Arrival and Break-Up Coordination Operation

The efficiency of track utilization is one of the important factors for train operation in marshalling stations, and it can not only affect the turnover efficiency of trains, but also determine the capacity of railway stations. This paper presents an optimization method for track utilization in the arrival yard of a marshalling station considering Arrival and Break-up Coordination Operation (ABCO). The interaction between the push operation of trains and track utilization efficiency is investigated. First, the case of crossing the running route for shunting locomotives is analyzed. Whether the shunting route crosses or not can greatly affect the duration of trains occupying tracks in the station. Then, a nonlinear integer programming model (NLPM) is established based on the above analysis. The ultimate goal is to minimize the number of crossovers of the shunting route by adding a constraint condition for ensuring traffic safety. A track assignment algorithm based on ABCO for solving the NLPM is proposed. Train operations in the downlink arrival yard of station A are simulated with the proposed method. The results after applying the optimization method show that the average duration of trains on the tracks is reduced by 49.1%, and the degree to which tracks utilization is balanced is also significantly improved. The proposed method optimizes and extends the current achievements that have been reported in the literature.

Two dimensional guillotine cutting stock and scheduling problem in printing industry

We address a two-dimensional cutting stock problem combined with production scheduling that arises in paper printing industry where printing orders arrive daily, together with their specifications and desired delivery dates The planner has to decide the printing patterns, their quantities to be printed, and their production dates. The printing pattern should comply with guillotine cuts having three stages. The objective is to minimize the total printing cost composed of paper and plate costs. For plates containing orders with print on both sides, two printing options exist. With the printing options and the option of placing copies of orders in only one pattern, the problem differs from previous studies and becomes challenging to be solved by a mathematical model. We develop a nonlinear integer programming (NIP) model to obtain exact solutions for small-sized instances and an efficient Genetic Algorithm (GA) to solve real-sized problems. We design packing routines that generate balanced printing patterns by putting multiple copies of items in one pattern. The GA also takes advantage of complex heuristics for production scheduling and pattern reduction. We evaluate the performance of the GA against the NIP model. Computational experiments on large-sized real-world data demonstrate the efficiency of the GA.

Optimizing communication network geodiversity for disaster resilience through shielding approach

The communication network is the critical infrastructure and backbone of modern society. On the other hand, regional failures, including natural disasters and malicious attacks, pose a major threat to its capacity and quality of service. Therefore, it is important to design a communication network that is resilient enough to withstand disasters. A key factor of network resilience is diversity, as multiple unrelated elements prevent them from sharing the same fate. This paper focuses on the geodiversity of the network and takes it as the resilience metric for the network under geographically highly correlated regional failures. The communication networks with high geodiversity are designed by shielding critical components, where the shielded ones can survive disasters. One of the attractive advantages of the approach is its implementability, more than just a theoretical technique. Meanwhile, we develop an integer nonlinear programming (INLP) model to obtain the minimum cost shielding for communication networks with desired geodiversity. Since the problem is difficult to solve in polynomial time, a genetic-based heuristic algorithm is applied to get a near-optimal solution in a shorter time. Finally, simulation experiments are performed to illustrate our methodology and its effectiveness, and the results highlight the collective role of network elements.

Centralized drug procurement operation scheduling with a capacitated joint replenishment and delivery strategy: Evidence from China

Due to the tremendous increases in the cost of providing health care systems, it is crucial importance to control the health spending. This study aims to explore the optimization of centralized drug procurement based on a capacitated joint replenishment and delivery strategy. A mixed integer nonlinear programming model is proposed to describe the practical operation process in China. The objective is to find a replenishment and delivery schedule, which operates in such a way that the total cost (including setup costs, storage costs, freight costs and cost of capital) is minimized under the constraints of production and distribution capacity. A novel hybrid optimization, composed of an ingenious memetic algorithm and a well-designed bound heuristic, is developed to solve the proposed model. The memetic algorithm includes a modified genetic operation and a local search procedure, and the bound heuristic is used to reduce the decision space substantially. The experimental results demonstrated that the proposed optimization can effectively obtain high-quality solutions, as illustrated by a comparative numerical study.

Two-echelon inventory location model with response time requirement and lateral transshipment

This study presents a new model for a two-echelon location-inventory system with response time constraints. This system controls inventory with a (S-1, S) policy and comprises of a finite collection of customers, a finite collection of service facilities and a single plant. This paper's main novelty is the incorporation of lateral transshipment into a two-echelon location-inventory system with response time requirement. By using a continuous-time Markov process approach, we determine expected on-hand inventory level in steady state, expected lateral transshipment level in steady state and expected backorder level in steady state. We utilize these steady state levels to formulate a mixed integer nonlinear programming model which incorporates lateral transshipment into an integrated location-inventory system with response time constraint. The model minimizes the total system cost and simultaneously determines: optimal location and number of service facilities, the optimal assignment of customers and base-stock level. We exploit the model's properties using Lagrange decomposition and we show that the model is convex. The model is tested on a real-world scenario using GAMS and our model returned lower costs following comparisons with a model without lateral transshipment. We also establish that lateral transshipment results to consistency of expected cost with varying response time requirement.

Heterogeneous donor circles for fair liver transplant allocation.

The United States (U.S.) Department of Health and Human Services is interested in increasing geographical equity in access to liver transplant. The geographical disparity in the U.S. is fundamentally an outcome of variation in the organ supply to patient demand (s/d) ratios across the country (which cannot be treated as a single unit due to its size). To design a fairer system, we develop a nonlinear integer programming model that allocates the organ supply in order to maximize the minimum s/d ratios across all transplant centers. We design circular donation regions that are able to address the issues raised in legal challenges to earlier organ distribution frameworks. This allows us to reformulate our model as a set-partitioning problem. Our policy can be viewed as a heterogeneous donor circle policy, where the integer program optimizes the radius of the circle around each donation location. Compared to the current policy, which has fixed radius circles around donation locations, the heterogeneous donor circle policy greatly improves both the worst s/d ratio and the range between the maximum and minimum s/d ratios. We found that with the fixed radius policy of 500 nautical miles (NM), the s/d ratio ranges from 0.37 to 0.84 at transplant centers, while with the heterogeneous circle policy capped at a maximum radius of 500 NM, the s/d ratio ranges from 0.55 to 0.60, closely matching the national s/d ratio average of 0.5983. Our model matches the supply and demand in a more equitable fashion than existing policies and has a significant potential to improve the liver transplantation landscape.

Data-driven robust optimization for cyclic scheduling of ethylene cracking furnace system under uncertainty based on kernel learning

For an ethylene cracking furnace system (ECFS), the cyclic scheduling is significant for increasing the benefit. However, the scheduling period is always more than three hundred days, the frequently changed prices of raw materials and products may lead to suboptimal results. This paper proposes a data-driven robust optimization (DDRO) approach to handle price uncertainty. The uncertainty set is constructed from historical data by the multiple kernel learning-based one-class support vector machine. With introducing the uncertainty set in the deterministic model, a tractable mixed integer nonlinear programming model is derived by the dual approach for robust optimization. An actual case study shows that the proposed approach is better hedged against uncertainties with less conservatism than the classical methods. The robust cyclic schedule obtained by the DDRO approach increases the net profit by 3.8% than the schedule generated by the deterministic model when the price system deteriorates.

Computationally efficient train timetable generation of metro networks with uncertain transfer walking time to reduce passenger waiting time: A generalized Benders decomposition-based method

With more and more interchange stations in a large-scale metro network, passengers tend to transfer between different metro lines from origination to destination, sometimes even more than once. Passenger waiting time is one of the critical standards for measuring the quality of urban public transport services. To support high service quality, this paper proposes a mixed integer nonlinear programming (MINLP) model for the train timetable generation problem of a metro network that minimizes the transfer waiting times and access passenger waiting times. In the mathematical formulation of the model, the transfer walking times at the interchange stations between two connected lines are treated as uncertain parameters. The robust train timetable generation model is formulated to optimize timetables by adjusting arrival and departure times of each train in the metro network to reduce access and transfer passenger waiting times. A robust counterpart is further derived that transforms the formulated robust model into a deterministic one. Moreover, a generalized Benders decomposition technique based approach is developed to decompose the robust counterpart into a subproblem and a master problem. The subproblem is a convex quadratic programming problem that can be solved efficiently. Finally, two sets of numerical examples, consisting of a small case and a large-scale case based on a real-world portion of the Beijing metro network, are performed to demonstrate the validity and practicability of the proposed model and solution approach.

Managing production and inventory in a remanufacturing supply chain with two classes of cores under consignment stock agreement

AbstractThis paper addresses the production scheduling and inventory management in a closed‐loop supply chain that recycles both high‐quality and low‐quality cores and makes products using cores and new raw materials. The manufacturing/remanufacturing supply chain consists of a vendor and a buyer, and they collaborate under a consignment stock (CS) agreement. We investigate and compare three operation policies under the CS agreement, covering continuous and intermittent production manners and shipments of equal and unequal batch sizes. For each operation policy, we develop a mixed integer nonlinear programming model to jointly optimize the production sequence of two classes of cores, production cycle length, shipment frequency, and shipment batch sizes, with the objective of minimizing the cost rate. By analyzing the respective decisions and conducting an extensive numerical study with various scenarios, we explore the advantages and applications of each operation policy. Based on our research findings, we provide general guidelines and criteria for operation policy selection.

A Scatter Search Algorithm for Multi-Criteria Inventory Classification considering Multi-Objective Optimization

Inventory management requires thousands or millions of individual transactions each year. Classification of the items influences the results of inventory management. Traditionally, this is usually classified with considering an annual dollar usage criterion but maybe other criteria such as lead time, criticality, perishability, inventory cost, and demand type can be affected on that classification. Inventory items that have more than one criterion are discussed under multi-criteria inventory classification (MCIC) methods in the literature. In this paper, the MCIC problem is considered with two objectives as follows: (1) minimization of total inventory relevant cost and (2) minimization of the dissimilarity index. The proposed Mixed Integer Nonlinear Programming (MINLP) model of the MCIC problem is formulated using Scatter Search Algorithm (SSA). The suggested multi-objective optimization problem is solved using LP-metric, ɛ-constraint and weighted sum method. Pareto optimal solutions are obtained according to these different methods and selected best method by using deviation index. Scatter Search Algorithm provides high-quality solutions within reasonable computation times. The proposed model generated a Pareto frontier solution with the maximum satisfaction level and minimum distance from ideal point. Finally, the proposed model is implemented with two numerical datasets to show the performance of its efficiency and compared our results with other studies in the previous literature.

Consignment inventory management in a closed-loop supply chain for deteriorating items under a carbon cap-and-trade regulation

This paper studies an inventory management problem for a closed-loop supply chain that is operated under a consignment stock policy and subject to a cap-and-trade regulation. The supply chain makes both new products and remanufactured products, considering that new raw materials (NRMs), cores, and finished goods (FGs) suffer from deterioration. Mixed integer nonlinear programming models are established to jointly optimize the production sequence of new products and remanufactured products, number of shipments, shipment interval, batch size of FGs, and production cycle length to minimize the total of production, shipment, inventory, deterioration, and carbon emission costs per unit time. Exploring and using the structural properties of the models, a Taylor-series based method is designed to solve the models. Finally, numerical examples and sensitivity analysis are provided to show the effects of key factors on the operational decisions and on both the economy and environment. Results indicate that the deterioration of NRMs, cores, and FGs triggers the supply chain to run short production cycles while making more frequent shipments under the consignment stock policy. Both the economic and environmental costs increase with the deterioration rates. In addition, raising the carbon-trading price can reduce carbon emissions but increase the economic cost of the supply chain, rendering the urgency in reasonably determining carbon cap and trading price.

Multi-objective superstructure optimization of a microalgae biorefinery considering economic and environmental aspects

The increasing consumption of fossil fuels has many destructive effects on the environment. The development of a microalgae-based biorefinery is one of the most promising solutions to reduce these adverse effects. In the present study, a superstructure has been proposed to optimize different processing pathways for microalgae-based biofuels production. The proposed multi-objective mixed integer nonlinear programming (MINLP) model was solved in such a way as to minimize the total annualized cost (TAC) and environmental impacts simultaneously. The bi-objective optimization model was converted into a problem with a single objective using the augmented ε-constraint method. The optimal solution ranges were from 20.98 to 154.63 $MM/year for TAC, corresponding to 7.45 × 106 to 1.056 × 107 Points for the environmental impacts of the system. In the present study, the negative environmental impacts have been reduced by 42 percent compared to a base study using more environmentally friendly technological pathways.

The optimisation research of Blockchain application in the financial institution-dominated supply chain finance system

As an information technology that could significantly improve supply chain visibility and process automation, blockchain has been extensively applied in the field of supply chain finance (SCF). However, tradeoffs among the security, the operation cost, and the efficiency of the blockchain system may cause the SCF system dominated by a financial institution to inevitably fall into the dilemmas of risky or un-economic if the blockchain technology is applied inappropriately. Therefore, the objective of this paper is to optimise the blockchain application in the financial institution-based SCF system. We first analyse the application of blockchain security in SCF, and then the performance tradeoffs of blockchain and its impact on the performance of the supported SCF system. Based on the analysis above, an optimisation approach has been proposed and a corresponding non-linear integer programming (NIP) model has been constructed to select the best blockchain design schemes for the SCF system to achieve overall optimal in terms of security, cost, and efficiency. A designed ant colony algorithm is used to solve the optimisation problem. An application case analysis is used to verify the feasibility and effectiveness of the optimisation model.

Optimal plate design problem in steel production

In this paper, we address a new optimal plate design problem in steel production, in which slab selection is jointly considered. On the basis of the underlying features, the problem is formulated as a mixed integer nonlinear programming (MINLP) model with generalized disjunctive programming (GDP) constraints. A logic-based outer approximation (L-OA) algorithm is proposed to solve the problem. Specifically, a two-stage heuristic method is designed to initialise the L-OA algorithm. Numerical results are presented to demonstrate that the proposed L-OA algorithm and the heuristic method are effective and computationally efficient.

First-Train Timetable Synchronization in Metro Networks under Origin-Destination Demand Conditions

This paper focuses on how to synchronize network-wide timetables of first trains in an urban metro system, in which the train-connection-based route can be exactly determined for each first-train-attached origin-destination (OD) demand pair. With the help of even headway scheduling on each line, the problem is actually to adjust the departure times of first trains and connecting trains from their origin stations and the departure interval on each line. Subjected to train operation and connection constraints, a biobjective nonlinear integer programming model is formulated to minimize the total travel time of OD-dependent passenger demands and the deviation between the known and expected schedules. Then, the Nondominated Sorted Genetic Algorithm-II (NSGA-II) is adopted to solve the proposed model, and an improved technique is elaborated to reduce the alternative route choices. Finally, numerical experiments are conducted to demonstrate the effectiveness and availability of the proposed model and methods.

Nonpre-Emptive Integer Nonlinear Goal Programming Model for Multi-Item Inventory Problem: Case Study of a Car Retail Centre in Lagos State.

Most of the real-world optimization problems involve multiple objectives with constraint resources. Retailers oftentimes anticipate demand, they stock, and maintain warehouses with different variety of products at high cost to meet prospecting customers' demand. In this paper, a Non-preemptive Integer Nonlinear Goal Programming (NINGP) model was developed for obtaining Economic Order Quantities (EOQ) of multi-item inventory problems that satisfy the multiple and conflicting objectives of the Decision Maker (DM). The particular case considered was that of a motor vehicle dealer who sells 10 brands of Tokunbo vehicles and wants to determine the EOQ for each brand such that the deviations from the aspiration level are minimized. Using LINGO 17.0 Software to solve the NINGP model, the EOQ allocated to each brand type from 1 through 10 are 2, 2, 5, 2, 2, 3 3, 3, 3, and 3 cars respectively. The optimal number of cars was 28 with the associated cost of ₦53,825,915. Compared to the estimated budget of ₦60,000,000, the NINGP approach was able to achieve a 10% (₦6,174,085) below budget. With proper modifications considering the associated constraints, related inventory problems can be solved using the NINGP model.

Passenger Flow-Oriented Metro Operation without Timetables

Unpredictable fluctuant passenger flow usually exists in urban metro operations. In this situation, traditional predetermined metro timetables cannot always meet the variation of passenger flow, and thus the service quality of the metro system could be affected profoundly. In this paper, by introducing an innovative metro operation method without timetables, we develop a nonlinear integer programming model to continually optimise the train operation to deal with detected real-time passenger flow variations. We aim to minimise the total passenger waiting time in the research time horizon under the vehicle number constraint. A modified genetic algorithm integrated with a macroscopic metro simulator is adopted to solve the proposed model. A case study based on the Beijing Metro Line 19 is implemented to provide a quantitative result for evaluating the proposed passenger flow-oriented metro operation method without timetables. Compared to traditional timetable-based metro operation, the method could significantly improve the metro operation’s flexibility and the quality of services.

A note on integrated disassembly line balancing and routing problem

This note comments on the study of [Diri Kenger, Zülal, Çağrı Koç, and Eren Özceylan. 2020. “Integrated Disassembly Line Balancing and Routing Problem.” International Journal of Production Research 58 (23): 7250–7268.] which studies an integrated disassembly line balancing and routing problem and develops two mixed integer linear programming (MILP) models and three mixed integer nonlinear programming (MINLP) models to handle five different scenarios, respectively. The purpose is twofold. First, we demonstrate that the two MILP models can be separated into two parallel subproblems whose optimal solutions can be combined to obtain the optimal solution of the original models. Second, we show that the three MINLP models can be linearised and propose two different linearisation techniques to reformulate them as equivalent MILP models. Computational results indicate that the linearised model outperforms the original nonlinear model in most cases.

A new mathematical model for the optimization of block aggregation in open pit mines

ABSTRACT The open-pit production planning is one of the most important steps of mine design which becomes a hard and challenging optimization problem in large-scale mineral deposits. A common approach in such a situation is to cluster mining blocks (smallest mining units) into larger units. In this paper, an integer non-linear programming model of the constrained block clustering is developed with the objective of minimizing grade deviations while blocks are geometrically connected within a cluster and the shape and size of individual clusters are in the pre-defined range. Then, a population-based iterated local search algorithm is presented to solve this nonlinear model and find a near-optimum solution. The proposed model and the solution approach were applied to a case study of a gold and silver deposit with 40,947 blocks. The mining blocks are grouped into 1966 clusters which then mine planner can solve production scheduling in less computational time.