We study stochastic mixedinteger programs where both first-stage and recourse decisions can be mixedintegers. A new family of Lagrangian cuts, termed "ReLU Lagrangian cuts," is introduced by reformulating ...
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We propose an extension of two-player zero-sum games, where one player may select available actions for themselves and the opponent, subject to a budget constraint. We present a mixed-integer linear programming (MILP)...
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We propose an extension of two-player zero-sum games, where one player may select available actions for themselves and the opponent, subject to a budget constraint. We present a mixed-integer linear programming (MILP) formulation for the problem, provide analytical results regarding its solution, and discuss applications in the security and advertising domains. Our computational experiments demonstrate that heuristic approaches, on average, yield suboptimal solutions with at least a 20% relative gap with those obtained by the MILP formulation.
In the real manufacturing environment, the machining stage of the jobs and the assembly stage of the products are often completed in different workshops. In addition, automatic guided vehicle (AGV) plays an indispensa...
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In the real manufacturing environment, the machining stage of the jobs and the assembly stage of the products are often completed in different workshops. In addition, automatic guided vehicle (AGV) plays an indispensable role in the transportation of jobs from machining workshop to assembly workshop. This paper studies multi-objective three-stage flexible job shop scheduling problem (FJSP-T-A) with minimizing both the makespan and the total energy consumption. In FJSP-T-A, jobs are first machined in flexible job shop, then are transported to assembly workshop by AGVs, and finally are assembled in assembly workshop. To solve this problem, a mixed-integer linear programming model (MILP) is developed and the optimal Pareto front for small-scale instances are solved by using the $\varepsilon $ -method. FJSP-T-A is NP-hard, and an efficient multi-population co-evolutionary algorithm (MPCEA) is proposed to efficiently solve large-scale instances. In the MPCEA, we design a strategy to select relatively high-quality individuals to enhance the algorithm's convergence speed, and design a multi-objective variable-neighborhood search (MOVNS) method to improve the local search ability. Experiments are conducted to prove the effectiveness of the MILP model and the MPCEA.
Ridepooling services play an increasingly important role in modern transportation systems. With soaring demand and growing fleet sizes, the underlying route planning problems become increasingly challenging. In this c...
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Ridepooling services play an increasingly important role in modern transportation systems. With soaring demand and growing fleet sizes, the underlying route planning problems become increasingly challenging. In this context, we consider the dial-a-ride problem (DARP): Given a set of transportation requests with pickup and delivery locations, passenger numbers, time windows, and maximum ride times, an optimal routing for a fleet of vehicles, including an optimized passenger assignment, needs to be determined. We present tight mixed-integer linear programming (MILP) formulations for the DARP by combining two state-of-the-art models into novel location-augmented-event-based formulations. Strong valid inequalities and lower and upper bounding techniques are derived to further improve the formulations. We then demonstrate the theoretical and computational superiority of the new models: First, the linearprogramming relaxations of the new formulations are stronger than existing location-based approaches. Second, extensive numerical experiments on benchmark instances show that computational times are on average reduced by 53.9% compared to state-of-the-art event-based approaches.
Frequently, parameters in optimization models are subject to a high level of uncertainty coming from several sources and, as such, assuming them to be deterministic can lead to solutions that are infeasible in practic...
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Frequently, parameters in optimization models are subject to a high level of uncertainty coming from several sources and, as such, assuming them to be deterministic can lead to solutions that are infeasible in practice. Robust optimization is a computationally efficient approach that generates solutions that are feasible for realizations of uncertain parameters near the nominal value. This paper develops a data-driven robust optimization approach for the scheduling of a straight pipeline connecting a single refinery with multiple distribution centers, considering uncertainty in the injection rate. For that, we apply support vector clustering to learn an uncertainty set for the robust version of the deterministic model. We compare the performance of our proposed robust model against one utilizing a standard robust optimization approach and conclude that data-driven robust solutions are less conservative.
Fractional and Rounded capacity inequalities are two important families of valid inequalities known for the homogeneous Capacitated Vehicle Routing Problem (CVRP). Such inequalities impose the minimum number of vehicl...
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Fractional and Rounded capacity inequalities are two important families of valid inequalities known for the homogeneous Capacitated Vehicle Routing Problem (CVRP). Such inequalities impose the minimum number of vehicles required to service each and every subset of customers, be it a fractional or an integer value. In case of the Heterogeneous version of the routing problem (HCVRP), the minimum number of vehicles required for a subset of customers is not defined uniquely: it depends on the vehicle types and fleet composition that was engaged in serving the customers. This paper revises existing literature on the capacity-based valid inequalities for the HCVRP and presents new routines to separate them exactly using mixedintegerlinearprogramming (MILP). In addition, this paper proposes a new family of capacity-based valid inequalities for the HCVRP together with an exact routine to separate them. A computational study demonstrates applicability of considered inequalities in solving HCVRP instances using a standard MILP solver.
Despite the adverse impacts of occupational fatigue such as accidents and injuries in the manufacturing industry, it has not been systematically examined in the literature on production scheduling. In this paper, we i...
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Despite the adverse impacts of occupational fatigue such as accidents and injuries in the manufacturing industry, it has not been systematically examined in the literature on production scheduling. In this paper, we integrate the classic bio-mathematical fatigue prediction model from the brain science literature into the simple single machine scheduling problem with sequence-dependent setup times. Then, we formulate the problem as a mixed-integer linear programming model and propose an adaptive large neighborhood search heuristic. The effectiveness of the heuristic is numerically validated through real cases. Finally, we argue that considering bio-mathematical fatigue prediction can lead to safer production schedules, notably reducing the fatigue working hours in our real case.
We study mathematical formulations for batch-processing machine scheduling problems (BPMPs), which are the challenging issues in the machine scheduling literature where machines are capable of processing a batch of jo...
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We study mathematical formulations for batch-processing machine scheduling problems (BPMPs), which are the challenging issues in the machine scheduling literature where machines are capable of processing a batch of jobs simultaneously if jobs with non-identical sizes can be packed in a capacitated machine. In this paper, we tackle single- and parallel-machine BPMPs, and other interesting problem variants that aim at minimizing the makespan. We develop novel formulations along with valid inequalities and an algorithm framework that makes use of dual information and bounding techniques to achieve efficiency when instances are intractable. Extensive computational experiments on benchmark instances show that our approaches achieve state-of-the-art results and prove the optimality of intractable instances in the literature.
The proposed study introduces a joint optimal control strategy for automated bus trajectories and signal priority to enhance transit corridor reliability, where the operations of multiple bus lines are hindered by dif...
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The proposed study introduces a joint optimal control strategy for automated bus trajectories and signal priority to enhance transit corridor reliability, where the operations of multiple bus lines are hindered by differing control strategies. The optimization of bus acceleration maneuvers and signal priority schemes is performed concurrently to minimize bus schedule deviations. The nonlinear optimization model is reformulated as a mixed-integer linear programming (MILP) problem and solved using a branch-and-bound solver, with an event-based re-computation scheme tailored for real-time operations. Sensitivity and computational efficiency analyses confirm the model's effectiveness under varying road geometries, signal parameters, and traffic conditions. Simulation results demonstrate that the proposed model improves bus punctuality by 57.2%, with only a 3.7% increase in private vehicle delays compared to the trajectory control-only strategy. Furthermore, it reduces private vehicle delays by 14.7% compared to the signal priority-only strategy, while achieving similar reductions in bus schedule deviations.
In this paper, we consider an oilfield planning problem with decisions about where and when to invest in wells and facilities to maximize profit. The model, in the form of a mixed-integerlinear program, includes an o...
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In this paper, we consider an oilfield planning problem with decisions about where and when to invest in wells and facilities to maximize profit. The model, in the form of a mixed-integerlinear program, includes an option to expand capacity for existing facilities, annual budget constraints, well closing decisions, and fixed production profiles once wells are opened. While fixed profiles area novel and important feature, they add another set of time-indexed binary variables that makes the problem difficult to solve. To find solutions, we develop a three-phase sequential algorithm that includes (1) ranking, (2) branching, and (3) refinement. Phases 1 and 2 determine which facilities and wells to open, along with well-facility assignments. Phase 3 ensures feasibility with respect to budget constraints and adjusts construction times and facility capacities to increase profit. We first demonstrate how our algorithm navigates the problem's complex features by applying it to a case study parameterized with realistic production profiles. Then, we perform computational experiments on small instances and show that our algorithm generally achieves the same objective function values as CPLEX but in much less time. Lastly, we solve larger instances using our three-phase algorithm and several variations to demonstrate its scalability and to highlight the roles of specific algorithmic components.
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