arXiv subjects

Richard Lusby

Publications and source records attributed to Richard Lusby.

5 recordsLinked to original sources

arXiv2025

Generalizable simulation framework for the request-to-order process in the procurement of onboard vessel requisitions

Procurement in maritime logistics faces challenges due to uncertainties in demand and fluctuating market conditions. To address these complexities, we introduce a flexible discrete-event simulation framework that models the request-to-order process. This framework captures critical stages, including the generation of onboard vessel requisitions, requisition handling, and order allocation. Through numerical analysis, we compare two order allocation policies: a naive practice, which relies heavily on contracts, and a dynamic supplier selection approach that explores cost opportunities in the spot market. Our findings reveal trade-offs between cost efficiency and contract compliance, particularly in meeting volume commitments to contracted suppliers. Excessive reliance on spot market opportunities can yield significant savings but at the expense of contract compliance. Additionally, when spot rates are highly sensitive to order quantities, both policies tend to overutilize contracts, highlighting the need for larger volume commitments in such cases. These results offer actionable insights for improving procurement practices, while the framework's adaptability makes it a powerful decision-support tool across diverse procurement contexts.

stat.AP↗

arXiv2025

Integrated optimization of operations and capacity planning under uncertainty for drayage procurement in container logistics

We present an integrated framework for truckload procurement in container logistics, bridging strategic and operational aspects that are often treated independently in existing research. Drayage, the short-haul trucking of containers, plays a critical role in intermodal container logistics. Using dynamic programming, we identify optimal operational policies for allocating drayage volumes among capacitated carriers under uncertain container flows and spot rates. The computational complexity of optimization under uncertainty is mitigated through sample average approximation. These optimal policies serve as the basis for evaluating specific capacity arrangements. To optimize capacity reservations with strategic and spot carriers, we employ an efficient quasi-Newton method. Numerical experiments demonstrate significant cost-efficiency improvements, including a 21.2% cost reduction in a four-period scenario. Monte Carlo simulations further highlight the strong generalization capabilities of the proposed joint optimization method across out-of-sample scenarios. These findings underscore the importance of integrating strategic and operational decisions to enhance cost efficiency in truckload procurement under uncertainty.

math.OC↗

arXiv2025

Multistage stochastic optimization for drayage procurement in container logistics using stochastic dual dynamic programming

Truckload procurement plays a vital role in integrated container logistics, particularly under the uncertainties of container flow and market conditions. We formulate the operational volume allocation problem in drayage procurement as a multistage stochastic transportation problem and solve it using stochastic dual dynamic programming (SDDP). We employ a multivariate count time series approach from the literature to model cargo flow dynamics, relaxing independence assumptions and capturing complex correlations. Our numerical experiments demonstrate the scalability of SDDP and its effectiveness in approximating high-quality policies across realistic problem instances. Sensitivity analyses highlight the significant impact of inflow uncertainties on costs, while spot market variability has a comparatively minor effect. Additionally, we propose an alternative stopping rule for SDDP iterations, balancing computational efficiency and solution fidelity.

math.OC↗

arXiv2022

Benders Decomposition for Bi-objective Linear Programs

In this paper, we develop a new decomposition technique for solving bi-objective linear programming problems. The proposed methodology combines the bi-objective simplex algorithm with Benders decomposition and can be used to obtain a complete set of extreme efficient solutions, and the corresponding set of extreme non-dominated points, for a bi-objective linear program. Using a Benders-like reformulation, the decomposition approach decouples the problem into a bi-objective master problem and a bi-objective subproblem, each of which is solved using the bi-objective parametric simplex algorithm. The master problem provides candidate extreme efficient solutions that the subproblem assesses for feasibility and optimality. As in standard Benders decomposition, optimality and feasibility cuts are generated by the subproblem and guide the master problem solve. This paper discusses bi-objective Benders decomposition from a theoretical perspective, proves the correctness of the proposed reformulation and addresses the need for so-called weighted optimality cuts. Furthermore, we present an algorithm to solve the reformulation and discuss its performance for three types of bi-objective optimisation problems.

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arXiv2021

Consistency Cuts for Dantzig-Wolfe Reformulations

This paper introduces a family of valid inequalities, that we term consistency cuts, to be applied to a Dantzig-Wolfe reformulation (or decomposition) with linking variables. We prove that these cuts ensure an integer solution to the corresponding Dantzig-Wolfe relaxation when certain criteria to the structure of the decomposition are met. We implement the cuts and use them to solve a commonly used test set of 200 instances of the temporal knapsack problem. We assess the performance with and without the cuts and compare further to CPLEX and other solution methods that have historically been used to solve the test set. By separating consistency cuts we show that we can obtain optimal integer solutions much faster than the other methods and even solve the remaining unsolved problems in the test set. We also perform a second test on instances from the MIPLIB 2017 online library of mixed-integer programs, showing the potential of the cuts on a wider range of problems.

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