Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2302.12136

Warehouse Problem with Bounds, Fixed Costs and Complementarity Constraints

Ishan Bansal·Oktay Günlük
View original source ↗Read source document ↗Export metadata ↓

Abstract

This paper studies an open question in the warehouse problem where a merchant trading a commodity tries to find an optimal inventory-trading policy to decide on purchase and sale quantities during a fixed time horizon in order to maximize their total pay-off, making use of fluctuations in sale and cost prices. We provide the first known polynomial-time algorithms for the case when there are fixed costs for purchases and sales, optional complementarity constraints that prohibit purchasing and selling during the same time period, and bounds on purchase and sales quantities. We do so by providing an exact characterization of the extreme points of the feasible region and using this to construct a suitable network where a min-cost flow computation provides an optimal solution. We are also able to provide polynomial extended linear formulations for the original feasible regions. Our methods build on the work by Wolsey and Yaman (Discrete Optimization 2018). We also consider the problem without fixed costs and provide a fully polynomial time approximation scheme in a setting with time-dependent bounds.

Explore related subjects

cs.DS

Keep this discovery

BibTeXRIS

Ishan Bansal, Oktay Günlük. 2023-02-23. Warehouse Problem with Bounds, Fixed Costs and Complementarity Constraints. https://arxiv.org/abs/2302.12136

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Quasi-Monte Carlo Beyond Hardy-Krause II: $(1 + \varepsilon)n$ Samples Suffice

Numerical integration studies how well one can estimate the integral of a function $f$ over $[0,1)^d$ using $n$ sample points. The two classical methods, Monte Carlo (MC) and quasi-Monte Carlo (QMC), have complementary strengths and weaknesses, and a fundamental question is to design an approach that combines the benefits of both. Recently, building on the transference principle in discrepancy theory, Bansal and Jiang~\cite{BJ25a} gave a randomized QMC method that bridges MC and QMC guarantees using only i.i.d.\ samples. Their method also goes beyond the classical Koksma--Hlawka inequality: it achieves integration error $\widetilde{O}_d(\sigma_{\mathsf{SO}}(f)/n)$, where the smoothed-out variation $\sigma_{\mathsf{SO}}(f)$ can be substantially smaller than the Hardy--Krause variation that governs the classical bound. However, their algorithm requires $n^2$ i.i.d.\ samples as input, and this quadratic blowup is inherent to any method based on the transference principle. In this work, we bypass the quadratic blowup: for any constant $\varepsilon > 0$, we show that $(1+\varepsilon)n$ i.i.d.\ samples suffice to both obtain the beyond-Hardy--Krause guarantee of~\cite{BJ25a}, resolving an open problem posed there, and to produce low-discrepancy point sequences. Our algorithms are variants of the online Haar-thinning method of Dwivedi, Feldheim, Gurel-Gurevich, and Ramdas~\cite{DFG+19}.

cs.DS↗
arXiv2026

Single-Exponential Algorithms and a Polynomial Kernel for Strong Connectivity Augmentation

Strong Connectivity Augmentation (SCA) asks whether a directed acyclic graph can be made strongly connected by adding at most $k$ prescribed links whose total weight is within a given budget. Klinkby, Misra, and Saurabh (SODA 2021) gave an $O^*(2^{O(k\log k)})$-time algorithm and asked whether the problem admits a single-exponential parameterized algorithm and a polynomial kernel. We answer both questions affirmatively: SCA can be solved in $O^*(9^k)$ time and admits a polynomial kernel with $O(k^4)$ vertices and $O(k^{16})$ bits. For unweighted SCA, we obtain $O^*(4^k)$ time and a kernel with $O(k^3)$ vertices. Our algorithms are based on a particularly simple reduction to Strongly Connected Spanning Subgraph with two edge costs.

cs.DS↗