Search results for: mixed integer linear programming (MILP) optimization

Authors: Ebert Brea

Abstract:

We propose a novel direct search algorithm for identifying at least a local minimum of mixed integer nonlinear unconstrained optimization problems. The Mixed Integer Randomized Pattern Search Algorithm (MIRPSA), so-called by the author, is based on a randomized pattern search, which is modified by the MIRPSA for finding at least a local minimum of our problem. The MIRPSA has two main operations over the randomized pattern search: moving operation and shrinking operation. Each operation is carried out by the algorithm when a set of conditions is held. The convergence properties of the MIRPSA is analyzed using a Markov chain approach, which is represented by an infinite countable set of state space λ, where each state d(q) is defined by a measure of the qth randomized pattern search Hq, for all q in N. According to the algorithm, when a moving operation is carried out on the qth randomized pattern search Hq, the MIRPSA holds its state. Meanwhile, if the MIRPSA carries out a shrinking operation over the qth randomized pattern search Hq, the algorithm will visit the next state, this is, a shrinking operation at the qth state causes a changing of the qth state into (q+1)th state. It is worthwhile pointing out that the MIRPSA never goes back to any visited states because the MIRPSA only visits any qth by shrinking operations. In this article, we describe the MIRPSA for mixed integer nonlinear unconstrained optimization problems for doing a deep study of its convergence properties using Markov chain viewpoint. We herein include a low dimension case for showing more details of the MIRPSA, when the algorithm is used for identifying the minimum of a mixed integer quadratic function. Besides, numerical examples are also shown in order to measure the performance of the MIRPSA.

Keywords: direct search, mixed integer optimization, random search, convergence, Markov chain

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Authors: Mohammadali Abedini Sanigy, Jiangang Fei

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In this paper, a mathematical optimization model was developed to maximize the profit in a vegetable production planning problem. It serves as a decision support system that assists farmers in land allocation to crops and harvest scheduling decisions. The developed model can handle different rotation rules in two consecutive cycles of production, which is a common practice in organic production system. Moreover, different production methods of the same crop were considered in the model formulation. The main strength of the model is that it is not restricted to predetermined production periods, which makes the planning more flexible. The model is classified as a mixed integer programming (MIP) model and formulated in PYOMO -a Python package to formulate optimization models- and solved via Gurobi and CPLEX optimizer packages. The model was tested with secondary data from 'Australian vegetable growing farms', and the results were obtained and discussed with the computational test runs. The results show that the model can successfully provide reliable solutions for real size problems.

Keywords: crop rotation, harvesting, mathematical model formulation, vegetable production

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Authors: Mohammad Mehdi Mazarei, Ali Asghar Behroozpoor

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In this paper, we define an optimization problem corresponding to smooth and nonsmooth functions which its optimal solution is the first derivative of these functions in a domain. For this purpose, a linear programming problem corresponding to optimization problem is obtained. The optimal solution of this linear programming problem is the approximate generalized first derivative. In fact, we approximate generalized first derivative of nonsmooth functions as tailor series. We show the efficiency of our approach by some smooth and nonsmooth functions in some examples.

Keywords: general derivative, linear programming, optimization problem, smooth and nonsmooth functions

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Authors: Paffrath Meinhard, Zhou Yayun, Guo Yiqing, Ertl Harald

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Winding geometry design is an important part of power transformer electrical design. Conventionally, the winding geometry is designed manually, which is a time-consuming job because it involves many iteration steps in order to meet all cost, manufacturing and electrical requirements. Here a method is presented which automatically generates the winding geometry for given user parameters and allows the user to interactively set and change parameters. To achieve this goal, the winding problem is transferred to a mixed integer nonlinear optimization problem. The relevant geometrical design parameters are defined as optimization variables. The cost and other requirements are modeled as constraints. For the solution, a stochastic ant colony optimization algorithm is applied. It is well-known, that an optimizer can get stuck in a local minimum. For the winding problem, we present efficient strategies to come out of local minima, furthermore a reduced variable search range helps to accelerate the solution process. Numerical examples show that the optimization result is delivered within seconds such that the user can interactively change the variable search area and constraints to improve the design.

Keywords: ant colony optimization, mixed integer nonlinear programming, power transformer, winding design

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Authors: Z. Babic, I. Veza, A. Balic, M. Crnjac

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The linear programming model is sometimes difficult to apply in real business situations due to its assumption of proportionality. This paper shows an example of how to use De Novo programming approach instead of linear programming. In the De Novo programming, resources are not fixed like in linear programming but resource quantities depend only on available budget. Budget is a new, important element of the De Novo approach. Two different production situations are presented: increasing costs and quantity discounts of raw materials. The focus of this paper is on advantages of the De Novo approach in the optimization of production plan for production company which produces souvenirs made from famous stone from the island of Brac, one of the greatest islands from Croatia.

Keywords: business process, De Novo programming, optimizing, production

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Authors: Andrés I. Ávila, Patricia Aros, César San Martín, Elizabeth Kehr, Yovana Leal

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We consider a linear programming model to help farmers to decide if it is convinient to choose among three kinds of export fruits for their future investment. We consider area, investment, water, productivitiy minimal unit, and harvest restrictions and a monthly based model to compute the average income in five years. Also, conditions on the field as area, water availability and initia investment are required. Using the Chilean costs and dollar-peso exchange rate, we can simulate several scenarios to understand the possible risks associated to this market.

Keywords: mixed integer problem, fruit production, support decision model, fruit tree farms

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Authors: Farhood Rismanchian, Seong Hyeon Park, Young Hoon Lee

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During the recent years, demand for healthcare services has dramatically increased. As the demand for healthcare services increases, so does the necessity of constructing new healthcare buildings and redesigning and renovating existing ones. Increasing demands necessitate the use of optimization techniques to improve the overall service efficiency in healthcare settings. However, high complexity of care processes remains the major challenge to accomplish this goal. This study proposes a method based on process mining results to address the high complexity of care processes and to find the optimal layout of the various medical centers in an emergency department. ProM framework is used to discover clinical pathway patterns and relationship between activities. Sequence clustering plug-in is used to remove infrequent events and to derive the process model in the form of Markov chain. The process mining results served as an input for the next phase which consists of the development of the optimization model. Comparison of the current ED design with the one obtained from the proposed method indicated that a carefully designed layout can significantly decrease the distances that patients must travel.

Keywords: Mixed Integer programming, Facility layout problem, Process Mining, Healthcare Operation Management

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Authors: Ahmed Al-Sultan

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The check-in area of airport terminal is one of the busiest sections at airports at certain periods. The passengers are subjected to queues and delays during the check-in process. These delays and queues are due to constraints in the capacity of service facilities. In this project, the airport terminal is decomposed into several check-in areas. The airport check-in scheduling problem requires both a deterministic (integer programming) and stochastic (simulation) approach. Integer programming formulations are provided to minimize the total number of counters in each check-in area under the realistic constraint that counters for one and the same flight should be adjacent and the desired number of counters remaining in each area should be fixed during check-in operations. By using simulation, the airport system can be modeled to study the effects of various parameters such as number of passengers on a flight and check-in counter opening and closing time.

Keywords: airport terminal, integer programming, scheduling, simulation

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Authors: K. -H. Yang

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Supplier selection problem is one of the important issues of supply chain problems. Two categories of methodologies include qualitative and quantitative approaches which can be applied to supplier selection problems. However, due to the complexities of the problem and lacking of reliable and quantitative data, qualitative approaches are more than quantitative approaches. This study considers operational cost and supplier’s reliability factor and solves the problem by using a quantitative approach. A mixed integer programming model is the primary analytic tool. Analyses of different scenarios with variable cost and reliability structures show that the effectiveness of this approach to the supplier selection problem.

Keywords: mixed integer programming, quantitative approach, supplier’s reliability, supplier selection

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Authors: David Muyise

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Mixed Integer Programming (MIP) is an approach that involves the optimization of a range of decision variables in order to minimize or maximize a particular objective function. The main objective of this study was to apply the MIP approach to optimize the deployment of waste plastic to fuel oil processing plants in Uganda. The processing plants are meant to reduce plastic pollution by pyrolyzing the waste plastic into a cleaner fuel that can be used to power diesel/paraffin engines, so as (1) to reduce the negative environmental impacts associated with plastic pollution and also (2) to curb down the energy gap by utilizing the fuel oil. A programming model was established and tested in two case study applications that are, small-scale applications in rural towns and large-scale deployment across major cities in the country. In order to design the supply chain, optimal decisions on the types of waste plastic to be processed, size, location and number of plants, and downstream fuel applications were concurrently made based on the payback period, investor requirements for capital cost and production cost of fuel and electricity. The model comprises qualitative data gathered from waste plastic pickers at landfills and potential investors, and quantitative data obtained from primary research. It was found out from the study that a distributed system is suitable for small rural towns, whereas a decentralized system is only suitable for big cities. Small towns of Kalagi, Mukono, Ishaka, and Jinja were found to be the ideal locations for the deployment of distributed processing systems, whereas Kampala, Mbarara, and Gulu cities were found to be the ideal locations initially utilize the decentralized pyrolysis technology system. We conclude that the model findings will be most important to investors, engineers, plant developers, and municipalities interested in waste plastic to fuel processing in Uganda and elsewhere in developing economy.

Keywords: mixed integer programming, fuel oil plants, optimisation of waste plastics, plastic pollution, pyrolyzing

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Authors: Muhammed Ordu, Eren Demir, Chris Tofallis

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The number of inpatient admissions in the UK has been significantly increasing over the past decade. These increases cause bed occupancy rates to exceed the target level (85%) set by the Department of Health in England. Therefore, hospital service managers are struggling to better manage key resource such as beds. On the other hand, this severe demand pressure might lead to confusion in wards. For example, patients can be admitted to the ward of another inpatient specialty due to lack of resources (i.e., bed). This study aims to develop a simulation-optimization model to reallocate the available number of beds in a mid-sized hospital in the UK. A hospital simulation model was developed to capture the stochastic behaviours of the hospital by taking into account the accident and emergency department, all outpatient and inpatient services, and the interactions between each other. A couple of outputs of the simulation model (e.g., average length of stay and revenue) were generated as inputs to be used in the optimization model. An integer linear programming was developed under a number of constraints (financial, demand, target level of bed occupancy rate and staffing level) with the aims of maximizing number of admitted patients. In addition, a sensitivity analysis was carried out by taking into account unexpected increases on inpatient demand over the next 12 months. As a result, the major findings of the approach proposed in this study optimally reallocate the available number of beds for each inpatient speciality and reveal that 74 beds are idle. In addition, the findings of the study indicate that the hospital wards will be able to cope with 14% demand increase at most in the projected year. In conclusion, this paper sheds a new light on how best to reallocate beds in order to cope with current and future demand for healthcare services.

Keywords: bed occupancy rate, bed reallocation, discrete event simulation, inpatient admissions, integer linear programming, projected usage

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Authors: S. H. Nasseri, A. Ebrahimnejad

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Fuzzy set theory has been applied to many fields, such as operations research, control theory, and management sciences. In this paper, we consider two classes of fuzzy linear programming (FLP) problems: Fuzzy number linear programming and linear programming with trapezoidal fuzzy variables problems. We state our recently established results and develop fuzzy primal simplex algorithms for solving these problems. Finally, we give illustrative examples.

Keywords: fuzzy linear programming, fuzzy numbers, duality, sensitivity analysis

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Authors: Abu Hashan Md Mashud, M. Sharif Uddin, Aminur Rahman Khan

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In this paper, we formulate a new problem as a linear programming and Integer Programming problem and maximize profit within the limited budget and limited resources based on the construction of a tea garden problem. It describes a new idea about how to optimize profit and focuses on the practical aspects of modeling and the challenges of providing a solution to a complex real life problem. Finally, a comparative study is carried out among Graphical method, Simplex method and Branch and bound method.

Keywords: integer programming, tea garden, graphical method, simplex method, branch and bound method

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Authors: Ruben Lopez-Rodriguez

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In a microgrid, diverse energy sources (both renewable and non-renewable) are combined with energy storage units to form a localized power system. Microgrids function as independent entities, capable of meeting the energy needs of specific areas or communities. This paper introduces a Model Predictive Control (MPC) approach tailored for grid-connected microgrids, aiming to optimize their operation. The formulation employs Mixed-Integer Programming (MIP) to find optimal trajectories. This entails the fulfillment of continuous and binary constraints, all while accounting for commutations between various operating conditions such as storage unit charge/discharge, import/export from/towards the main grid, as well as asset connection/disconnection. To validate the proposed approach, a microgrid case study is conducted, and the simulation results are compared with those obtained using a rule-based strategy.

Keywords: microgrids, mixed logical dynamical systems, mixed-integer optimization, model predictive control

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Authors: Tunjo Perić, Franjo Bratić

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In this paper the goal programming methodology for solving multiple objective problem of the technological variants and production plan optimization has been applied. The optimization criteria are determined and the multiple objective linear programming model for solving a problem of the technological variants and production plan optimization is formed and solved. Then the obtained results are analysed. The obtained results point out to the possibility of efficient application of the goal programming methodology in solving the problem of the technological variants and production plan optimization. The paper points out on the advantages of the application of the goal programming methodolohy compare to the Surrogat Worth Trade-off method in solving this problem.

Keywords: goal programming, multi objective programming, production plan, SWT method, technological variants

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Authors: Vincenzo Capalbo, Gianpaolo Ghiani, Emanuele Manni

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Global e-commerce sales have reached unprecedented levels in the past few years. As this trend is only predicted to go up as we continue into the ’20s, new challenges will be faced by companies when planning and controlling e-commerce logistics. In this paper, we survey the related literature on Optimization and Machine Learning as well as on combined methodologies. We also identify the distinctive features of next-generation planning algorithms - namely scalability, model-and-run features and learning capabilities - that will be fundamental to cope with the scale and complexity of logistics in the next decade.

Keywords: e-commerce, hardware acceleration, logistics, machine learning, mixed integer programming, optimization

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Authors: Younghoon Kim, Seoung Bum Kim

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One-class classification plays an important role in detecting outlier and abnormality from normal observations. In the previous research, several attempts were made to extend the scope of application of the one-class classification techniques to statistical process control problems. For most previous approaches, such as support vector data description (SVDD) control chart, the design of the control limits is commonly based on the assumption that the proportion of abnormal observations is approximately equal to an expected Type I error rate in Phase I process. Because of the limitation of the one-class classification techniques based on convex optimization, we cannot make the proportion of abnormal observations exactly equal to expected Type I error rate: controlling Type I error rate requires to optimize constraints with integer decision variables, but convex optimization cannot satisfy the requirement. This limitation would be undesirable in theoretical and practical perspective to construct effective control charts. In this work, to address the limitation of previous approaches, we propose the one-class classification algorithm based on the mixed integer programming technique, which can solve problems formulated with continuous and integer decision variables. The proposed method minimizes the radius of a spherically shaped boundary subject to the number of normal data to be equal to a constant value specified by users. By modifying this constant value, users can exactly control the proportion of normal data described by the spherically shaped boundary. Thus, the proportion of abnormal observations can be made theoretically equal to an expected Type I error rate in Phase I process. Moreover, analogous to SVDD, the boundary can be made to describe complex structures by using some kernel functions. New multivariate control chart applying the effectiveness of the algorithm is proposed. This chart uses a monitoring statistic to characterize the degree of being an abnormal point as obtained through the proposed one-class classification. The control limit of the proposed chart is established by the radius of the boundary. The usefulness of the proposed method was demonstrated through experiments with simulated and real process data from a thin film transistor-liquid crystal display.

Keywords: control chart, mixed integer programming, one-class classification, support vector data description

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Authors: Thomas Weber, Nina Strobel, Thomas Kohne, Eberhard Abele

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In context of the energy transition in Germany, the importance of so-called virtual power plants in the energy supply continues to increase. The progressive dismantling of the large power plants and the ongoing construction of many new decentralized plants result in great potential for optimization through synergies between the individual plants. These potentials can be exploited by mathematical optimization algorithms to calculate the optimal application planning of decentralized power and heat generators and storage systems. This also includes linear or linear mixed integer optimization. In this paper, procedures for reducing the number of decision variables to be calculated are explained and validated. On the one hand, this includes combining n similar installation types into one aggregated unit. This aggregated unit is described by the same constraints and target function terms as a single plant. This reduces the number of decision variables per time step and the complexity of the problem to be solved by a factor of n. The exact operating mode of the individual plants can then be calculated in a second optimization in such a way that the output of the individual plants corresponds to the calculated output of the aggregated unit. Another way to reduce the number of decision variables in an optimization problem is to reduce the number of time steps to be calculated. This is useful if a high temporal resolution is not necessary for all time steps. For example, the volatility or the forecast quality of environmental parameters may justify a high or low temporal resolution of the optimization. Both approaches are examined for the resulting calculation time as well as for optimality. Several optimization models for virtual power plants (combined heat and power plants, heat storage, power storage, gas turbine) with different numbers of plants are used as a reference for the investigation of both processes with regard to calculation duration and optimality.

Keywords: CHP, Energy 4.0, energy storage, MILP, optimization, virtual power plant

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Authors: Abdolsalam Ghaderi

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In this paper, the single-depot capacitated location-routing problem under uncertainty is presented. The problem aims to find the optimal location of a single depot and the routing of vehicles to serve the customers when the parameters may change under different circumstances. This problem has many applications, especially in the area of supply chain management and distribution systems. To get closer to real-world situations, travel time of vehicles, the fixed cost of vehicles usage and customers’ demand are considered as a source of uncertainty. A combined approach including robust optimization and stochastic programming was presented to deal with the uncertainty in the problem at hand. For this purpose, a mixed integer programming model is developed and a heuristic algorithm based on Variable Neighborhood Search(VNS) is presented to solve the model. Finally, the computational results are presented and future research directions are discussed.

Keywords: location-routing problem, robust optimization, stochastic programming, variable neighborhood search

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Authors: Sanat Ramesh, Tarun Dutt, Abhilasha Aswal, Anushka Chandrababu, G. N. Srinivasa Prasanna

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Optimal Schedule Generation for a large national railway network operating thousands of passenger trains with tens of thousands of kilometers of track is a grand computational challenge in itself. We present heuristics based on a Mixed Integer Program (MIP) formulation for local optimization. These methods provide flexibility in scheduling new trains with varying speed and delays and improve utilization of infrastructure. We propose methods that provide a robust solution with hundreds of trains being scheduled over a portion of the railway network without significant increases in delay. We also provide techniques to validate the nominal schedules thus generated over global correlated variations in travel times thereby enabling us to detect conflicts arising due to delays. Our validation results which assume only the support of the arrival and departure time distributions takes an order of few minutes for a portion of the network and is computationally efficient to handle the entire network.

Keywords: mixed integer programming, optimization, railway network, train scheduling

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Authors: Darwin Castillo Huamaní, Francisco A. M. Gomes

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The aim of the multi-material topology optimization (MTO) is to obtain the optimal topology of structures composed by many materials, according to a given set of constraints and cost criteria. In this work, we seek the optimal distribution of materials in a domain, such that the flexibility of the structure is minimized, under certain boundary conditions and the intervention of external forces. In the case we have only one material, each point of the discretized domain is represented by two values from a function, where the value of the function is 1 if the element belongs to the structure or 0 if the element is empty. A common way to avoid the high computational cost of solving integer variable optimization problems is to adopt the Solid Isotropic Material with Penalization (SIMP) method. This method relies on the continuous interpolation function, power function, where the base variable represents a pseudo density at each point of domain. For proper exponent values, the SIMP method reduces intermediate densities, since values other than 0 or 1 usually does not have a physical meaning for the problem. Several extension of the SIMP method were proposed for the multi-material case. The one that we explore here is the ordered SIMP method, that has the advantage of not being based on the addition of variables to represent material selection, so the computational cost is independent of the number of materials considered. Although the number of variables is not increased by this algorithm, the optimization subproblems that are generated at each iteration cannot be solved by methods that rely on second derivatives, due to the cost of calculating the second derivatives. To overcome this, we apply a globally convergent version of the sequential linear programming method, which solves a linear approximation sequence of optimization problems.

Keywords: globally convergence, multi-material design ordered simp, sequential linear programming, topology optimization

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Authors: Cem Isik Dogru, Salih Tekin, Kursad Derinkuyu

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Electric vehicle (EV) carsharing is an alternative method to tackle urban transportation problems. This method can be applied by several options. One of the options is the one-way carsharing, which allow an EV to be taken at a designated location and leaving it on another specified location customer desires. Although it may increase users’ satisfaction, the issues, namely, demand dissatisfaction, relocation of EVs and charging schedules, must be dealt with. Also, excessive electricity has to be stored in batteries of EVs. To cope with aforementioned issues, two-step mixed integer programming (MIP) model is proposed. In first step, the integer programming model is used to determine amount of electricity to be sold to the grid in terms of time periods for extra profit. Determined amounts are provided from the batteries of EVs. Also, this step works in day-ahead electricity markets with forecast of periodical electricity prices. In second step, other MIP model optimizes daily operations of one-way carsharing: charging-discharging schedules, relocation of EVs to serve more demand and renting to maximize the profit of EV fleet owner. Due to complexity of the models, heuristic methods are introduced to attain a feasible solution and different price information scenarios are compared.

Keywords: electric vehicles, forecasting, mixed integer programming, one-way carsharing

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Authors: Glenda Marie D. Balitaan

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The branch of business management that deals with inventory planning and control is known as inventory management. It comprises keeping track of supply levels and forecasting demand, as well as scheduling when and how to plan. Keeping excess inventory results in a loss of money, takes up physical space, and raises the risk of damage, spoilage, and loss. On the other hand, too little inventory frequently causes operations to be disrupted and raises the possibility of low customer satisfaction, both of which can be detrimental to a company's reputation. The United Victorious Feed mill Corporation's present inventory management practices were assessed in terms of inventory level, warehouse allocation, ordering frequency, shelf life, and production requirement. To help the company achieve their optimal level of inventory, a mathematical model was created using Integer Linear Programming. Due to the season, the goal function was to reduce the cost of purchasing US Soya and Yellow Corn. Warehouse space, annual production requirements, and shelf life were all considered. To ensure that the user only uses one application to record all relevant information, like production output and delivery, the researcher built a Visual Basic system. Additionally, the technology allows management to change the model's parameters.

Keywords: inventory management, integer linear programming, inventory management system, feed mill

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Authors: Masoud Shahmanzari

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The aim of this paper is to present a Variable Neighborhood Search (VNS) with Tabu Search (TS) conditions for the Roaming Salesman Problem (RSP). The RSP is a special case of the well-known traveling salesman problem (TSP) where a set of cities with time-dependent rewards and a set of campaign days are given. Each city can be visited on any day and a subset of cities can be visited multiple times. The goal is to determine an optimal campaign schedule consist of daily open/closed tours that visit some cities and maximizes the total net benefit while respecting daily maximum tour duration constraints and the necessity to return campaign base frequently. This problem arises in several real-life applications and particularly in election logistics where depots are not fixed. We formulate the problem as a mixed integer linear programming (MILP), in which we capture as many real-world aspects of the RSP as possible. We also present a hybrid metaheuristic algorithm based on a VNS with TS conditions. The initial feasible solution is constructed via a new matheuristc approach based on the decomposition of the original problem. Next, this solution is improved in terms of the collected rewards using the proposed local search procedure. We consider a set of 81 cities in Turkey and a campaign of 30 days as our largest instance. Computational results on real-world instances show that the developed algorithm could find near-optimal solutions effectively.

Keywords: optimization, routing, election logistics, heuristics

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Authors: Mazura Mokhtar, Adibah Shuib, Daud Mohamad

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Portfolio optimization problem has received a lot of attention from both researchers and practitioners over the last six decades. This paper provides an overview of the current state of research in portfolio optimization with the support of mathematical programming techniques. On top of that, this paper also surveys the solution algorithms for solving portfolio optimization models classifying them according to their nature in heuristic and exact methods. To serve these purposes, 40 related articles appearing in the international journal from 2003 to 2013 have been gathered and analyzed. Based on the literature review, it has been observed that stochastic programming and goal programming constitute the highest number of mathematical programming techniques employed to tackle the portfolio optimization problem. It is hoped that the paper can meet the needs of researchers and practitioners for easy references of portfolio optimization.

Keywords: portfolio optimization, mathematical programming, multi-objective programming, solution approaches

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Authors: Sujeet Kumar Singh, Shiv Prasad Yadav

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This paper develops an approach for solving intuitionistic fuzzy linear fractional programming (IFLFP) problem where the cost of the objective function, the resources, and the technological coefficients are triangular intuitionistic fuzzy numbers. Here, the IFLFP problem is transformed into an equivalent crisp multi-objective linear fractional programming (MOLFP) problem. By using fuzzy mathematical programming approach the transformed MOLFP problem is reduced into a single objective linear programming (LP) problem. The proposed procedure is illustrated through a numerical example.

Keywords: triangular intuitionistic fuzzy number, linear programming problem, multi objective linear programming problem, fuzzy mathematical programming, membership function

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Authors: Tareq Oshan

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Facility location and size decisions are important to any company because they affect profitability and success. However, warehouses are exposed to various risks of failure that affect their activity. This paper presents a mixed-integer non-linear mathematical model that can be used to determine optimal warehouse locations and sizes, which warehouses to fortify, and which branches should be assigned to specific warehouses when there is a risk of warehouse failure. Every branch is assigned to a fortified primary warehouse or a nonfortified primary warehouse and a fortified backup warehouse. The standard method and an introduced method, based on the average probabilities, for linearizing this mathematical model were used. A Canadian case study was used to demonstrate the developed mathematical model, followed by some sensitivity analysis.

Keywords: supply chain network design, fortified warehouse, mixed-integer mathematical model, warehouse failure risk

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Authors: Onur Kaya, Ilknur Tukenmez

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In this study, we consider vehicle routing problems on networks with alternative direct links between nodes, and we analyze a multi-objective problem considering the financial, environmental and social objectives in this context. In real life, there might exist several alternative direct roads between two nodes, and these roads might have differences in terms of their lengths and durations. For example, a road might be shorter than another but might require longer time due to traffic and speed limits. Similarly, some toll roads might be shorter or faster but require additional payment, leading to higher costs. We consider such alternative links in our problem and develop a mixed integer linear programming model that determines which alternative link to use between two nodes, in addition to determining the optimal routes for different vehicles, depending on the model objectives and constraints. We consider the minimum cost routing as the financial objective for the company, minimizing the CO2 emissions and gas usage as the environmental objectives, and optimizing the driver working conditions/working hours, and minimizing the risks of accidents as the social objectives. With these objective functions, we aim to determine which routes, and which alternative links should be used in addition to the speed choices on each link. We discuss the results of the developed vehicle routing models and compare their results depending on the system parameters.

Keywords: vehicle routing, alternative links between nodes, mixed integer linear programming, triple bottom line accounting

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Authors: Abhishek Jain, Kavish Kejriwal, V. Balaji Rao, Abhigna Chavda

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Increasing environmental and social concerns are forcing companies to take a fresh view of the impact of supply chain operations on environment and society when designing a supply chain. A challenging task in today’s food industry is the distribution of high-quality food items throughout the food supply chain. Improper storage and unwanted transportation are the major hurdles in food supply chain and can be tackled by making dynamic storage facility location decisions with the distribution network. Since food supply chain in India is one of the biggest supply chains in the world, the companies should also consider environmental impact caused by the supply chain. This project proposes a multi-objective optimization model by integrating sustainability in decision-making, on distribution in a food supply chain network (SCN). A Multi-Objective Mixed-Integer Linear Programming (MOMILP) model between overall cost and environmental impact caused by the SCN is formulated for the problem. The goal of MOMILP is to determine the pareto solutions for overall cost and environmental impact caused by the supply chain. This is solved by using GAMS with CPLEX as third party solver. The outcomes of the project are pareto solutions for overall cost and environmental impact, facilities to be operated and the amount to be transferred to each warehouse during the time horizon.

Keywords: multi-objective mixed linear programming, food supply chain network, GAMS, multi-product, multi-period, environment

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Authors: Hyun Seop Uhm, Yong Ho Choi, Ji Eun Kim, Young Hoon Lee

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Weapon-target assignment (WTA) is a problem that assigns available launchers to appropriate targets in order to defend assets. Various algorithms for WTA have been developed over past years for both in the static and dynamic environment (denoted by SWTA and DWTA respectively). Due to the problem requirement to be solved in a relevant computational time, WTA has suffered from the solution efficiency. As a result, SWTA and DWTA problems have been solved in the limited situation of the battlefield. In this paper, the general situation under continuous time is considered by Time based Weapon Target Assignment (TWTA) problem. TWTA are studied using the mixed integer programming model, and three heuristic algorithms; decomposed opt-opt, decomposed opt-greedy, and greedy algorithms are suggested. Although the TWTA optimization model works inefficiently when it is characterized by a large size, the decomposed opt-opt algorithm based on the linearization and decomposition method extracted efficient solutions in a reasonable computation time. Because the computation time of the scheduling part is too long to solve by the optimization model, several algorithms based on greedy is proposed. The models show lower performance value than that of the decomposed opt-opt algorithm, but very short time is needed to compute. Hence, this paper proposes an improved method by applying decomposition to TWTA, and more practical and effectual methods can be developed for using TWTA on the battlefield.

Keywords: air and missile defense, weapon target assignment, mixed integer programming, piecewise linearization, decomposition algorithm, military operations research

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