arXiv subjects

Morteza Davari

Publications and source records attributed to Morteza Davari.

4 recordsLinked to original sources

arXiv2025

Fairness, Travel, and Market Potential: An Optimization Framework for NBA Expansion

The National Basketball Association (NBA) is actively considering the addition of two expansion teams, raising the question of how to restructure its conferences and divisions to balance travel efficiency, fairness, and revenue opportunities. This study fills a gap at the intersection of sports operations and strategic league design by providing a quantitative framework for expansion planning. We develop two optimization models: one minimizing total travel distance and another using a Nash Bargaining framework to balance travel burdens while accounting for media market size. Using data from all 30 current franchises and six candidate cities (Seattle, Las Vegas, Montreal, Vancouver, Tampa, and Mexico City), we evaluate 15 pairwise expansion scenarios under alternative season lengths and divisional formats. Results show that while the distance-minimizing model produces geographically tight divisions, the Nash Bargaining model generates more balanced outcomes, particularly for geographically isolated franchises, with only modest efficiency losses. Our study offers a flexible decision support framework for league executives, policymakers, and sports economists. It provides evidence-based insights into how expansion decisions can balance operational efficiency, fairness in competition, and access to major media markets in a multi-billion-dollar sports league.

physics.soc-ph↗

arXiv2025

Balanced connected partitions of edge-weighted graphs: Hardness and solving methods

The balanced connected $k$-partition problem (\textsc{bcp}) is a classic problem, which consists in partitioning the set of vertices of a vertex-weighted connected graph into a collection of~$k$ classes such that each class induces a connected subgraph of \emph{roughly} the same weight. In this study, we investigate edge-weighted variants of $\textsc{bcp}$, where we are given a connected graph $G$, $k \in \Z_\ge$, and an edge-weight function $w \colon E(G)\to\Q_\ge$, and the goal is to compute a spanning $k$-forest~$\mathcal{T}$ of $G$ (i.e., a forest with exactly $k$ trees) that minimizes the weight of the heaviest tree in~$\mathcal{T}$ in the min-max version, or maximizes the weight of the lightest tree in~$\mathcal{T}$ in the max-min version. We show that both versions of this problem are $\NP$-hard on complete graphs with $k=2$, unweighted split graphs, and unweighted bipartite graphs with $k\geq 2$ fixed. Moreover, we prove that these problems do not admit subexponential-time algorithms, unless the Exponential-Time Hypothesis fails. We focus on the min-max version and devise a tight $k$-approximation algorithm, compact and non-compact integer linear programming formulations, branch and cut, and branch and price algorithms. Finally, we present the outcomes of an experimental study on the performances of different solution methods. The source code of the complete implementation of the proposed algorithms is also available.

cs.DS↗

arXiv2021

Scheduling a single parallel-batching machine with non-identical job sizes and incompatible job families

We study the scheduling of jobs on a single parallel-batching machine with non-identical job sizes and incompatible job families. Jobs from the same family have the same processing time and can be loaded into a batch, as long as the batch size respects the machine capacity. The objective is to minimize the total weighted completion time. The problem combines two classic combinatorial problems, namely bin packing and single machine scheduling. We develop three new mixed-integer linear-programming formulations, namely an assignment-based formulation, a time-indexed formulation (TIF), and a set-partitioning formulation (SPF). We also propose a column generation (CG) algorithm for the SPF, which is the basis for a branch-and-price (B&P) algorithm and a CG-based heuristic. We develop a preprocessing method to reduce the formulation size. A heuristic framework based on proximity search is also developed using the TIF. The SPF and B&P can solve instances with non-unit and unit job durations to optimality with up to 80 and 150 jobs within reasonable runtime limits, respectively. The proposed heuristics perform better than the methods from the literature.

math.OC↗

arXiv2020

Single-machine scheduling with an external resource

This paper studies the complexity of single-machine scheduling with an external resource, which is rented for a non-interrupted period. Jobs that need this external resource are executed only when the external resource is available. There is a cost associated with the scheduling of jobs and a cost associated with the duration of the renting period of the external resource. We look at four classes of problems with an external resource: a class of problems where the renting period is budgeted and the scheduling cost needs to be minimized, a class of problems where the scheduling cost is budgeted and the renting period needs to be minimized, a class of two-objective problems where both, the renting period and the scheduling cost, are to be minimized, and a class of problems where a linear combination of the scheduling cost and the renting period is minimized. We provide a thorough complexity analysis (NP-hardness proofs and (pseudo-)polynomial algorithms) for different members of these four classes.

cs.DS↗