TB9 - Operational Research at Africa (OR@Africa)

The Quadratic Knapsack Problem (QKP) is a complex optimization problem with applications in portfolio selection and resource allocation. It extends the classical Knapsack Problem by incorporating quadratic interactions between items, thereby increasing its complexity. A significant challenge in solving the QKP is the weak linear-programming relaxation. We introduce two new valid inequalities for the QKP by using the interaction graph to strengthen this relaxation. We provide theoretical guarantees on the strength of the inequalities. We introduce an adaptable sequence-independent lifting framework that further strengthens our inequalities. We demonstrate that our approach outperforms state-of-the-art sequence-independent lifting methods for computing strong lifted cover inequalities. Extensive computational experiments demonstrate that our inequalities substantially improve the branch-and-bound process, reducing optimality gaps by up to 50% compared to a commercial solver and consistently outperforming existing inequalities for the QKP.

We address integrated scheduling in continuous-flow process industries by coordinating production, transportation, multiproduct storage, and shared resources to minimize costs and satisfy demand. We propose a reduced mixed-integer linear programming formulation with comprehensive operational constraints. The approach is validated on large-scale phosphate mining case studies, achieving high-quality solutions within a one-hour time limit.

The fertilizer market in developing countries offers strong untapped potential driven by agricultural demand. However, it faces challenges such as limited infrastructure, high transportation costs, and delays in maritime imports, which reduce efficiency and slow adoption.

To address these issues, this presentation introduces the Simultaneous Maritime Inventory Routing, Bagging, and Inland Transportation Problem (SMIRB-ITP), an extension of the Maritime Inventory Routing Problem (MIRP). The model integrates key decisions, including fertilizer bagging at ports, storage facility selection and sizing, and inland transportation planning.

A mathematical formulation based on a Two-Step approach is proposed to decompose the problem into coordinated planning levels. The first step focuses on maritime operations, operating on a medium-to-long-term horizon (up to one year) and addressing tactical decisions related to deep-sea shipping. The second step addresses inland operations, capturing shorter-term decisions with a finer time discretization.

We discuss how a mixed week–day discretization reduces the computational complexity of the problem while maintaining solution quality. Computational experiments show improvements in delivery planning, with lower costs, better inventory control, and more timely distribution.

Predictive Maintenance (PdM) is crucial in manufacturing, enabling early detection of equipment failures and optimized maintenance to improve reliability and reduce costs. However, extracting accurate and explainable predictions from complex time-series data remains a challenge. Deep learning models such as Long Short-Term Memory (LSTM) networks offer strong predictive power but act as ‘black boxes,’ while fuzzy systems provide interpretability but lack accuracy in dynamic industrial settings. To address these limitations, recent studies have integrated fuzzy inference with LSTMs. In this paper, we propose FiLSTM (Fuzzy Rule Induction for LSTM), a hybrid model that leverages Decision Trees to generate fuzzy rules and membership functions directly from data. This approach improves both interpretability and prediction, achieving higher accuracy, faster computation, and lower execution time compared to FLSTM. FiLSTM advances PdM systems to real-time, scalable, and transparent industrial applications.