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We study a two-stage hybrid flow shop problem arising from a fine chemicals production facility, where the first stage is a continuous chemical reaction process and the second stage is a discrete filling-packaging process. The objective is to minimise the total weighted completion time through batching of the jobs and scheduling of the batches at first stage and scheduling of the jobs at second stage. We formulate the problem as a mixed integer programming model and develop a Lagrangian relaxation-based framework for solving it, where the original problem is decomposed into family-level subproblems, and each subproblem is transformed into a set-partitioning problem. The subproblems are solved to optimality via branch and price algorithm. We also propose two heuristic algorithms for reducing computational efforts without much loss of solution quality. Finally, we conduct computational experiments with both randomly generated and real data sets to test the performance of the three proposed algorithms and demonstrate that the algorithms perform efficiently. [ABSTRACT FROM AUTHOR]

Drone delivery is expected to improve operations by enhancing flexibility and reducing congestion effects induced by lastmile deliveries. With rising digitalization and urbanization, however, flight routing of drones is constantly grappling with the challenge of uncertain demand. In this study, an opportunity-constrained model that considered both the endurance and payload capacity of drones and stochastic customer demand was developed to solve the drone delivery planning problem for E-commerce in urban areas. Considering the challenging solvability of the model, historical customer demand data were leveraged to linearly transform opportunity constraints with unknown true distribution. In addition, a constructive heuristic algorithm was used to solve the established opportunity-constrained model, and an effective strategy was developed to generate the quality of initial flight paths. The experimental results based on various scales of classic cases demonstrate that an effective drone delivery route scheme can be generated by the proposed heuristic algorithm compared to traditional savings algorithm, allowing drones to complete tasks in shorter flight distances at the same payload rate, thus reducing overall costs. Compared to deterministic models, more robust flight path schemes for addressing continuously changing customer demands can be obtained. The model and insights in this study could be used as a reference for the application of drone delivery in urban areas to promote logistics efficiency. [ABSTRACT FROM AUTHOR]

• A new dynamic lot-sizing problem was defined for remanufacturing systems. • The previous studies were extended by considering multi-level structured products with components commonality. • A mixed integer programming model was developed to represent the problem mathematically. • Two types of bi-directional move based heuristics, individual-and cluster-moves, were proposed. • The cluster-move based heuristic outperformed the other and gave near optimal solutions for small-sized test instances. This study addresses dynamic lot-sizing for remanufacturing systems in which end-of-use/life products are disassembled into their components on a disassembly workstation, each recoverable part is reprocessed on one of parallel reprocessing workstations and the reprocessed and newly purchased ones, if required, are reassembled into remanufactured products on a reassembly workstation. The problem is to determine disassembly, reprocessing, reassembly lot-sizes as well as the reprocessing workstation to reprocess each recoverable part while satisfying dynamic remanufactured product demands and workstation capacities in each period of a planning horizon. As an extension of the previous studies, multi-level structured products with components commonality are considered for the objective of minimizing the sum of setup, operation and inventory costs. A mixed integer programming model is developed, and due to the problem complexity, two types of heuristics are proposed that obtain an initial solution using a greedy-type heuristic and improve it by two types of bi-directional moves with various priority rules for forward and backward moves, i.e. individual-moves and cluster-moves. Computational results show that the cluster-move based approach that considers components commonality explicitly outperforms the individual-move based one significantly and gave fast near optimal solutions for small sized test instances. Finally, a sensitivity analysis on different multi-level product structures were done and the results are reported. [ABSTRACT FROM AUTHOR]

We address in this paper the parallel machine scheduling problem with a shared loading server and a shared unloading server. Each job has to be loaded by the loading server before being processed on one of the available machines and unloaded immediately by the unloading server after its processing. The objective function involves the minimization of the overall completion time, known as the makespan. This important problem raises in flexible manufacturing systems, automated material handling, healthcare, and many other industrial fields, and has been little studied up to now. To date, research on it has focused on the case of two machines. The regular case of this problem is considered. A mixed integer programming formulation based on completion time variables is suggested to solve small-sized instances of the problem. Due to its NP -hardness, we propose two greedy heuristics based on the minimization of the loading, respectively unloading, server waiting time, and an efficient General Variable Neighborhood Search (GVNS) algorithm. In the computational experiments, the proposed methods are compared using 120 new and publicly available instances. It turns out that, the proposed GVNS with an initial solution-finding mechanism based on the unloading server waiting time minimization significantly outperforms the other approaches. [ABSTRACT FROM AUTHOR]

As a result of digitization of the economy, more and more decision makers from a wide range of domains have gained the ability to target products, services, and information provision based on individual characteristics. Examples include selecting offers, prices, advertisements, or emails to send to consumers, choosing a bid to submit in a contextual first-price auctions, and determining which medication to prescribe to a patient. The key to enabling this is to learn a treatment policy from historical observational data in a sample-efficient way, hence uncovering the best personalized treatment choice recommendation. In "Offline Policy Learning: Generalization and Optimization," Z. Zhou, S. Athey, and S. Wager provide a sample-optimal policy learning algorithm that is computationally efficient and that learns a tree-based treatment policy from observational data. In our quest toward fully automated personalization, the work provides a theoretically sound and practically implementable approach. In many settings, a decision maker wishes to learn a rule, or policy, that maps from observable characteristics of an individual to an action. Examples include selecting offers, prices, advertisements, or emails to send to consumers, choosing a bid to submit in a contextual first-price auctions, and determining which medication to prescribe to a patient. In this paper, we study the offline multi-action policy learning problem with observational data and where the policy may need to respect budget constraints or belong to a restricted policy class such as decision trees. By using the standard augmented inverse propensity weight estimator, we design and implement a policy learning algorithm that achieves asymptotically minimax-optimal regret. To the best of our knowledge, this is the first result of this type in the multi-action setup, and it provides a substantial performance improvement over the existing learning algorithms. We then consider additional computational challenges that arise in implementing our method for the case where the policy is restricted to take the form of a decision tree. We propose two different approaches: one using a mixed integer program formulation and the other using a tree-search based algorithm. Funding: This work was supported by the National Science Foundation [Grants CCF-2106508 and DMS-1916163] and the Office of Naval Research [Grant N00014-17-1-2131]. [ABSTRACT FROM AUTHOR]

We examine a coordinated capacitated lot-sizing problem for multiple product families, where demand is deterministic and time-varying. The problem considers set-up and holding costs, where capacity constraints limit the number of individual item and family set-up times and the amount of production in each period. Using a strong reformulation and relaxing the demand constraints, we improve both the upper and lower bounds using a combination of Benders decomposition and an evolutionary algorithm, followed by subgradient optimisation. Through computational experiments, we show that our method consistently achieves better bounds, reducing the duality gap compared to other single-family methods studied in the literature. [ABSTRACT FROM AUTHOR]

We develop algorithms to control the scope of an infection spread on a network by allocating a fixed immunization budget to edges of the graph. We assume that the infection propagates according to an independent cascade model and interventions operate by reducing the propensities of edges to transmit the infection. We formulate this problem as a constrained min-max optimization problem with respect to the placements of interventions and the location of the worst-case seed nodes. However, the result is a challenging bilevel mixed integer optimization problem. Furthermore, gradients of the objective function with respect to the continuous variables are unavailable in closed form. We employ tools from derivative-free optimization and stochastic optimization to optimize the objective by iterating between the outer minimization and inner maximization problems. In the inner loop, we use a weighted degree discount (WDD) method to select the seed set of the influence maximization problem. In the outer loop, we utilize two methods: a sample-based simultaneous perturbation Nelder-Mead (SBSP-NM) algorithm and a simultaneous perturbation stochastic approximation (SPSA) algorithm. We perform simulations on synthetic graphs and three larger-scale real-world datasets and illustrate the computational feasibility of our algorithms and their efficacy at controlling epidemic spreads.

The pace of changes in automating cars has sped up in the last few decades. Autonomous Vehicles (AVs) will dramatically change the future of transportation, and household-level decisions will play a large role in the AV market. However, no data is readily available on household travel behavior using AVs. This study introduces a framework to assess households' adaptation to AV operations. We developed a mixed integer program, Household Activity Pattern Problem with AV (HAPPAV), to model traveler behavior under realistic conditions while using AVs. The model generates feasible activity patterns for household members under spatial and temporal constraints. The model is able to consider complete driverless operations, such as AV pick-up and drop-off, parking availability, empty trips, and carpooling. A decomposition method is developed to solve the NP-hard problem HAPPAV. The method includes two major stages; the first stage is to generate all feasible travel patterns for household members and the second stage finds the best AV route along with detailed travel patterns. We also use novel pruning rules to enhance the performance of the decomposition method. The model is applied on the California Statewide Travel Survey. The results indicate that 62% of households can perform their daily activities with only one AV in place of two or three regular vehicles. However, AV empty trips increase total VMT by 15%. The new method improves the average runtime and solution quality by 86% and 23%, respectively. [ABSTRACT FROM AUTHOR]

A distinctive feature of software‐defined networking (SDN) is a logically centralized control plane realized using multiple physical controllers. The placement of the controllers, the so‐called controller placement problem (CPP), is a crucial design issue. It influences network performance parameters such as latency, flow setup time, network availability, load balance of the controllers, and energy consumption. In this article, we illustrate the formulation of these CPP objectives. We categorize the CPP design solutions as either static or adaptive. In adaptive CPP, the solutions proposed dynamically adapt to the number of controllers required and the switch to controller mapping to varying network traffic. We further differentiate adaptive CPP as wired or wireless. The optimization strategies adopted by the papers are analyzed and grouped into five categories: exact, heuristic, meta‐heuristic, clustering, and game theory. The merits and demerits of each approach are discussed. In conclusion, we outline the research challenges worth investigating. [ABSTRACT FROM AUTHOR]

Growing competition in the world enforces the need for an efficient design of transportation networks. Furthermore, a competitive transportation network should also be eco-friendly. As road transportation is responsible for the largest quantities of CO 2 emissions, Intermodal Transportation (IT) might be a potential alternative. From this perspective, intermodal terminals location is a cornerstone for building a sustainable transportation network. The purpose of this paper is to study and efficiently solve the Intermodal Terminal Location Problem on incomplete networks. We model this problem as a mixed integer linear program and develop a simulated annealing algorithm to tackle medium and large instances. The computational results show that the obtained solutions using simulated annealing are competitive and close to the exact solutions found by CPLEX solver for small and medium instances. The same developed algorithm outperforms the best found solutions from the literature using heuristics for larger instances. [ABSTRACT FROM AUTHOR]

Mathematical programming (MP) is a widespread approach to depict production and investment decisions of agents in agent-based models (ABM) related to agriculture. However, introducing dynamics and indivisibilities in MP models renders their solution computing time intensive. We present a meta-modeling approach as an alternative to directly integrating MP in an ABM. Specifically, we estimate a dual symmetric normalized quadratic (SNQ) value function from a set of MP solutions. The approach allows us to depict relationships between key attributes, like the farm endowment with (quasi-) fixed factors and discounted farm household incomes, without modeling the technology in detail. The estimated functions are integrated in the ABM to derive agents’ decisions. The meta-modeling approach relaxes computational restrictions such that spatial interactions in large regions can be simulated improving our understanding of structural change in agriculture. It can also be used to extrapolate to farming populations where data availability might be restricted.

This paper presents a new mathematical programming model and a solution approach for a special class of graph partitioning problem. The problem studied here is in the context of distributed web search, in which a very large world-wide-web graph is partitioned to improve the efficiency of webpage ranking (known as PageRank). Although graph partitioning problems have been widely studied and there have been several computational algorithms and mathematical programming models in the literature, the graph partitioning problem for PageRank imposes unique constraints on the density balance. This problem is called the min-cut density-balanced partitioning problem. In this paper, we propose a new mathematical programming model and a solution approach to efficiently solve this min-cut density-balanced partitioning problem. As the objective on the minimum cut and the constraint on the density balance are not the direct performance measure of PageRank, we also investigate the performance of the solutions obtained from a MIP solver and our approach on the ranking's accuracy and the local ranking's computation times. The experiment results show both solutions are comparable in terms of the ranking's accuracy and the local ranking's computation times whereas it is much faster to obtain the partitioning solutions using our approach. [ABSTRACT FROM AUTHOR]

Having traceable stock price movements and predictable market trends can always benefit investors. Considering specific irrational investor behaviors that may collectively affect a stock's price movement, we identified the cause-and- effect return patterns of affected stocks (behavioral-stocks) with their corre- sponding time-to-effects and likelihood-of-effects. Considering different indi- vidual investor perceptions on future market performances, we transformed investor perceptions into probability weights on future market performances, wherein the weights are also consistent with the estimated likelihood-of-effects of behavioral-stocks. Utilizing a scenario-based mixed-integer behavioral-stocks portfolio optimization program embedded with a new two-dimensional weight- ings on scenarios and behavioral-stocks, we obtained portfolios that statisti- cally outperform the market. [ABSTRACT FROM AUTHOR]

This paper focuses on the problem of designing a material flow network for a given block layout. For an efficient design of a network, we simultaneously consider locations of input and output points, flow paths, and the smoothness of material flow paths. A mixed integer programming formulation is given for the problem with the objective of minimising the sum of transportation cost, cost related to flow paths, and penalty cost for non-smooth flows, i.e., flows with many turns. We suggest two heuristic algorithms based on the linear programming relaxation and the Lagrangian relaxation techniques. To evaluate performance of the suggested algorithms, a series of computational experiments is performed on well-known problem instances as well as randomly generated test problems. Results show that the suggested algorithms give good solutions in a reasonable amount of computation time. [ABSTRACT FROM AUTHOR]

In this paper, we consider the material flow network design problem in which locations of input and output points of departments and flow paths are determined concurrently on a given block layout. The objective of the problem is to minimize the sum of transportation cost, flow paths construction cost and penalty cost for non-smooth material flows, i.e., flows with turns. A mixed integer programming model is given for the problem and a three-phase heuristic algorithm is developed to solve the problem. In the suggested algorithm, we generate an initial flow network by determining locations of input/output points and flow paths sequentially in the first and second phases, respectively, and then improve it by changing locations of input/output points and flow paths iteratively in the third phase. To evaluate the performance of the suggested algorithms, a series of computational experiments are performed on well-known problem instances as well as randomly generated test problems. Results of computational experiments show that the suggested algorithm gives good solutions in a short computation time. [ABSTRACT FROM AUTHOR]

Growing competition in the world enforces the need for an efficient design of transportation networks. Furthermore, a competitive transportation network should also be eco-friendly. As road transportation is responsible for the largest quantities of CO2 emissions, Intermodal Transportation (IT) might be a potential alternative. From this perspective, intermodal terminals location is a cornerstone for building a sustainable transportation network. The purpose of this paper is to study and efficiently solve the Intermodal Terminal Location Problem on incomplete networks. We model this problem as a mixed integer linear program and develop a simulated annealing algorithm to tackle medium and large instances. The computational results show that the obtained solutions using simulated annealing are competitive and close to the exact solutions found by CPLEX solver for small and medium instances. The same developed algorithm outperforms the best found solutions from the literature using heuristics for larger instances.

While most linear programming (LP) problems can be solved in polynomial time, pure and mixed integer problems are NP-hard and there are no known polynomial time algorithms to solve these problems. A characteristic equation (CE) was developed to solve a pure integer program (PIP). This paper presents a heuristic that generates a feasible solution along with the bounds for the NP-hard mixed integer program (MIP) model by solving the LP relaxation and the PIP, using the CE.

We study the covering-type k-violation linear program where at most k of the constraints can be violated. This problem is formulated as a mixed integer program and known to be strongly NP-hard. In this paper, we present a simple (k + 1) -approximation algorithm using a natural LP relaxation. We also show that the integrality gap of the LP relaxation is k + 1 . This implies we can not get better approximation algorithms when we use the LP-relaxation as a lower bound of the optimal value. [ABSTRACT FROM AUTHOR]

In this paper, we develop a model to assign airplane seats to ordinary passengers to minimize their boarding time while some seats have been reserved earlier by high priority passengers. Our proposed mixed integer programming model assigns ordinary passengers to seats based on the amount of their carry-on bags and results in the minimum time to complete boarding of the airplane. The proposed model can result in 5% to 20% reductions in the average boarding time compared to the situation when passengers' luggage is not considered. [ABSTRACT FROM AUTHOR]

This paper investigates the classical preemptive parallel-machine scheduling problem of maximizing number of on-time jobs. While the problem is known to be NP-hard, no theoretical analysis of approximation algorithms exists in the literature. As part of the analysis, a new non-standard mixed integer formulation is developed. We propose heuristics based on different design strategies. These heuristics have asymptotically tight relative errors of 1/2. Experimental tests evaluate the computational performance of the procedures. [ABSTRACT FROM AUTHOR]

A battery charging dispatch model is proposed in this letter for a battery swap station to maximize the total profit over the given time horizon by finding the optimal dispatch of the batteries, while guaranteeing the corresponding power and energy constraints. To address the uninterrupted discrete charging rate, this problem is skillfully formulated as a two-dimensional-rectangle packing problem that can be solved by a mixed-integer linear program. Numerical results suggest that the rectangle packing problem can efficiently coordinate the dispatch of the multi-type batteries. [ABSTRACT FROM AUTHOR]

The handling of symmetries in mixed integer programs in order to speed up the solution process of branch-and-cut solvers has recently received significant attention, both in theory and practice. This paper compares different methods for handling symmetries using a common implementation framework. We start by investigating the computation of symmetries and analyze the symmetries present in the MIPLIB 2010 instances. It turns out that many instances are affected by symmetry and most symmetry groups contain full symmetric groups as factors. We then present (variants of) six symmetry handling methods from the literature. Their implementation is tested on several testsets. On very symmetric instances used previously in the literature, it is essential to use methods like isomorphism pruning, orbital fixing, or orbital branching. Moreover, tests on the MIPLIB instances show that isomorphism pruning, orbital fixing, or adding symmetry breaking inequalities allow to speed-up the solution process by about 15% and more instances can be solved within the time limit. [ABSTRACT FROM AUTHOR]

Highlights • A trajectory-based traffic management model is proposed for an exclusive AV zone. • The base model can be easily extended to include the scheduling and entry decisions. • The model is further extended to accommodate side constraints such as enforcing equity. • The model is solved by a solver and a specialized rolling horizon algorithm. • Numerical experiments validate the proposed model and algorithm. Abstract This paper studies a trajectory-based traffic management (TTM) problem for the purpose of managing traffic in a road facility reserved exclusively for autonomous vehicles (AV). The base TTM model aims to find optimal trajectories for multiple AVs while resolving inter-vehicle conflicts in the most generic way. The model is formulated as a mixed integer program (MIP) that can be solved using off-the-shelf solvers. To improve computational efficiency, a specialized algorithm based on the rolling horizon approach is also developed. We then show that the base TTM model can be easily extended to first accommodate scheduling decisions (the TTMS model) and to further impose equity constraints (the TTMSE model). For the simplest network and homogeneous users, solutions to TTMS and TTMSE are similar, respectively, to system optimal (SO) and user equilibrium (UE) solutions of Vickrey's bottleneck model. Numerical experiments highlight TTM's ability to simultaneously generate optimal trajectories for multiple vehicles. They also show that, while solving TTM exactly is computationally demanding, obtaining good approximate solutions can be accomplished efficiently by the rolling horizon algorithm. [ABSTRACT FROM AUTHOR]

When a multifactor experiment is carried out over a period of time, the responses may depend on a time trend. Unless the tests of the experiment are conducted in proper order, the time trend has a negative impact on the precision of the estimates of the main effects, the interaction effects, and the quadratic effects. A proper run order, called a trend-robust run order, minimizes the confounding between the effects' contrast vectors and the time trend's linear, quadratic, and cubic components. Finding a trend-robust run order is essentially a permutation problem. We develop a multistage approach based on integer programing to find a trend-robust run order for any given design. The multistage nature of our algorithm allows us to prioritize the trend robustness of the main-effect estimates. In the literature, most of the methods used are tailored to specific designs and are not applicable to an arbitrary design. Additionally, little attention has been paid to trend-robust run orders of response surface designs, such as central composite designs, Box-Behnken designs, and definitive screening designs. Our algorithm succeeds in identifying trend-robust run orders for arbitrary factorial designs and response surface designs with two up to six factors. [ABSTRACT FROM AUTHOR]

Mathematical programming (MP) is a widespread approach to depict production and investment decisions of agents in agent-based models (ABM) related to agriculture. However, introducing dynamics and indivisibilities in MP models renders their solution computing time intensive. We present a meta-modeling approach as an alternative to directly integrating MP in an ABM. Specifically, we estimate a dual symmetric normalized quadratic (SNQ) value function from a set of MP solutions. The approach allows us to depict relationships between key attributes, like the farm endowment with (quasi-) fixed factors and discounted farm household incomes, without modeling the technology in detail. The estimated functions are integrated in the ABM to derive agents' decisions. The meta-modeling approach relaxes computational restrictions such that spatial interactions in large regions can be simulated improving our understanding of structural change in agriculture. It can also be used to extrapolate to farming populations where data availability might be restricted. [ABSTRACT FROM AUTHOR]

In this paper, we present a new formulation of the robust counterpart of the mixed integer programming model correspond to a closed loop supply chain problem given in [10]. Our formulation has significantly less constraints than the one in [10]. Finally, we compare the new model with the one in [10] for several examples showing that both of them give the same solution but the new one is faster.