arXiv subjects

Omar Abbaas

Publications and source records attributed to Omar Abbaas.

4 recordsLinked to original sources

arXiv2026

A Two-Stage Stochastic Optimization Model for the Equitable Deployment of Fixed and Mobile Electric Vehicle Charging Stations

A major barrier to wide adoption of Electric Vehicles (EVs) is the absence of reliable and equitable charging infrastructure. Poorly located charging stations create coverage gaps and slow down EV adoption, especially in underserved communities. This paper proposes a two-stage stochastic mixed-integer programming model for the optimal deployment of Fixed and Mobile Charging Stations (FCSs and MCSs) across multiple zones and periods. Initially, a finite dominating set of candidate locations is identified using the Edge Scanning Algorithm for a Single Refueling Station (ESS), an exact continuous-location method. We modify the ESS algorithm to incorporate existing public charging stations, thereby avoiding redundant coverage. In the first stage of our model, FCSs are allocated based on long-term traffic patterns, budgetary constraints, and socioeconomic factors to ensure stable baseline coverage. The second stage dynamically assigns MCSs in response to short-term demand fluctuations and uncertainties, aiming to minimize relocation costs while maximizing coverage. We use a scenario-based framework to capture demand variability. Numerical experiments on realistic networks demonstrate the model's capacity to enhance system resilience and reduce unmet demand. These findings offer practical insights for planners and policymakers seeking to develop accessible and demand-responsive EV charging infrastructure.

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arXiv2025

An exact pricing algorithm for revenue maximization under the logit demand function

Determining the optimal selling price is a challenge in revenue management, especially in markets characterized by nonlinear and price-sensitive demand. While traditional models, such as linear, power, and exponential demand functions, offer analytical convenience, they often fail to capture realistic purchase dynamics, leading to suboptimal pricing. The logit demand function addresses these limitations through its bounded, S-shaped curve, offering a more realistic representation of consumer behavior. Despite its advantages, most existing literature relies on heuristic approaches, such as pricing at the inflection point, which prioritizes maximum price sensitivity but does not guarantee maximum revenue. This study proposes a novel, exact pricing algorithm that analytically derives the revenue-maximizing price under the logit demand function using the Lambert W function. By providing a closed-form solution, the approach eliminates reliance on heuristic iterative methods and corrects the common practice of considering the inflection point price as market price. In fact, we demonstrate that the optimal price is consistently lower than the inflection-point price under reasonable assumptions, leading to lower prices for consumers and higher revenue for sellers. Numerical experiments illustrate the proposed algorithm and examine the changes in the optimality gap as demand function parameters vary. Results indicate that the optimal price is consistently lower than the inflection-point price, with an average 20% price reduction accompanied by a 15% increase in revenue.

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arXiv2025

A Finite Dominating Set Approach for the Multi-Item Multi-Period Order Allocation Problem under All-Unit Quantity Discounts and Blending Ratios

This study addresses the multi-item multi-period order allocation problem under all-unit quantity discounts (AUQD) and blending ratios. A manufacturer makes a single product that requires mixing/assembling multiple ingredients/components with pre-determined blending ratios. We consider a single supplier offering quantity-based discounts which introduces non-linearities to the problem. The objective is to minimize procurement cost which includes purchasing, inventory, and ordering costs. We develop a solution procedure that systematically generates a finite dominating set (FDS) of order quantities guaranteed to include an optimal solution to the problem. A Mixed Integer Linear Programming (MILP) model based on the FDS. Our procedure guarantees optimality and eliminates the need for nonlinear discount modeling. Numerical experiments demonstrate that the proposed MILP achieves optimal solutions with significantly reduced computational effort, up to 99% faster for large-scale instances compared to conventional formulations. Sensitivity analyses reveal that the model dynamically adapts to changes in holding costs, shifting between bulk-purchasing and just-in-time strategies, and identifying cost-sensitive ingredients that drive total system cost.

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arXiv2025

Finite dominating sets for the refueling station location problem in fleet operations

This study considers a set of routes used by public transportation vehicles and dedicated distribution fleets in a general network. We aim to optimally locate alternative fuel refueling stations in the network to serve these dedicated routes. Deviations from prescribed routes for refueling purposes are allowed. Unlike most related literature, our approach considers all points in the network as candidate refueling station locations. We derive coverage constraints for any candidate location to serve a given route. Then we develop an exact algorithm to establish a finite dominating set (FDS) of candidate locations guaranteed to include an optimal solution to the problem. This set can be used in a mathematical model to minimize the number of stations required to cover all flows in the network. Numerical experiments on realistic networks are presented to illustrate the proposed methodology and to demonstrate its scalability and sensitivity to changes in parameter values.

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