arXiv subjects

Poulad Moradi

Publications and source records attributed to Poulad Moradi.

4 recordsLinked to original sources

arXiv2026

Risk or Replace: Efficient Asymptotics for Data-Driven Maintenance

Condition-based maintenance (CBM) is an approach that plans interventions for deteriorating systems according to their observed operational state. CBM reduces unplanned downtime and extends usable lifetime. We study a heterogeneous population of components that degrade over time according to a stochastic processes with non-negative and i.i.d. increments that are characterized by component-specific parameters that remain unobservable to the decision maker. We rely on degradation data to estimate these parameters and determine replacement actions at equidistant epochs. The goal is to minimize the long-run average cost, which incorporates fixed replacement costs, failure costs, and operating costs. This problem can be formulated as a high-dimensional partially observable Markov decision process (POMDP), which is generally intractable. We develop a tractable, data-driven CBM policy that estimates the optimal policy of a hypothetical Oracle that has full information of the underlying degradation parameters and call this policy the Estimated Oracle's Optimal Policy (EOP). We introduce a scaling regime where both the failure thresholds and cost parameters increase proportionally, reflecting practical settings in which component lifetimes and maintenance costs are large relative to the time between two consecutive CBM decision moments. We show that the regret of the EOP, defined as the difference between its long-run average cost and that of the Oracle, converges to zero in the scaling regime when the parameter estimator is consistent. Across extensive experiments using both real and simulated data, the EOP achieves very low regret and, whenever the optimal POMDP policy can be computed exactly, a negligible optimality gap.

math.OC↗

arXiv2025

Asymptotic Optimality of Projected Inventory Level Policies for Lost Sales Inventory Systems with Large Leadtime and Penalty Cost

We study the canonical periodic review lost sales inventory system with positive leadtime and independent and identically distributed (i.i.d.) demand under the average cost criterion. We demonstrate that the relative value function under the constant order policy satisfies the Wiener-Hopf equation. We employ ladder processes associated with a random walk featuring i.i.d. increments, to obtain an explicit solution for the relative value function. This solution can be expressed as a quadratic form and a term that grows sublinearly. Then we perform an approximate policy iteration step on the constant order policy and uniformly bound the gap relative to the otimal cost rate for large lead times. This leads to our main result that projected inventory level policies are asymptotically optimal as the leadtime grows when the cost of losing a sale is sufficiently large and demand has a finite second moment.

math.PR↗

arXiv2025

Load Asymptotics and Dynamic Speed Optimization for the Greenest Path Problem: A Comprehensive Analysis

We study the effect of using high-resolution elevation data on the selection of the most fuel-efficient(greenest) path for different trucks in various urban environments.We adapt a variant of the Comprehensive Modal Emission Model(CMEM) to show that the optimal speed and the greenest path are slope dependent (dynamic).When there are no elevation changes in a road network, the most fuel-efficient path is the shortest path with a constant (static) optimal speed throughout.However, if the network is not flat, then the shortest path is not necessarily the greenest path, and the optimal driving speed is dynamic.We prove that the greenest path converges to an asymptotic greenest path as the payload approaches infinity and that this limiting path is attained for a finite load.In a set of extensive numerical experiments, we benchmark the CO2emissions reduction of our dynamic speed and the greenest path policies against policies that ignore elevation data.We use the geospatial data of 25major cities across 6continents.We observe numerically that the greenest path quickly diverges from the shortest path and attains the asymptotic greenest path even for moderate payloads.Based on an analysis of variance, the main determinants of the CO2emissions reduction potential are the variation of the road gradients along the shortest path as well as the relative elevation of the source from the target.Using speed data estimates for rush hour in New York City, we test CO2emissions reduction by comparing the greenest paths with optimized speeds against the fastest paths with traffic speed.We observe that selecting the greenest paths instead of the fastest paths can significantly reduce CO2emissions.Additionally,our results show that while speed optimization on uphill arcs can significantly help CO2reduction,the potential to leverage gravity for acceleration on downhill arcs is limited due to traffic congestion.

math.OC↗

arXiv2023

Efficient Emission Reduction Through Dynamic Supply Mode Selection

We study the inbound supply mode and inventory management decision making for a company that sells an assortment of products. Stochastic demand for each product arrives periodically and unmet demand is backlogged. Each product has two distinct supply modes that may be different suppliers or different transport modes from the same supplier. These supply modes differ in terms of their carbon emissions, speed, and costs. The company needs to decide when to ship how much using which supply mode such that total holding, backlog, and procurement costs are minimized while the emissions associated with different supply modes across the assortment remains below a certain target level. Since the optimal policy for this inventory system is highly complex, we assume that shipment decisions for each product are governed by a dual-index policy. This policy dynamically prescribes shipment quantities with both supply modes based on the on-hand inventory, the backlog, and the products that are still in-transit. We formulate this decision problem as a mixed integer linear program that we solve through Dantzig-wolfe decomposition. We benchmark our decision model against two state-of-the-art approaches in a large test-bed based on real-life carbon emissions data. Relative to our decision model, the first benchmark lacks the flexibility to dynamically ship products with two supply modes while the second benchmark makes supply mode decisions for each product individually rather than holistically for the entire assortment. Our computational experiment shows that our decision model can outperform the first and second benchmark by up to 15 and 40 percent, respectively, for realistic targets for carbon emission reduction.

math.OC↗