arXiv subjects

Magnus Wiktorsson

Publications and source records attributed to Magnus Wiktorsson.

8 recordsLinked to original sources

arXiv2026

Toward Self-Organizing Production Logistics: A Multi-Agent Approach

Production logistics (PL) is increasingly exposed to variability, dynamic interdependencies, and operational disturbances that challenge conventional centralized planning and control. These characteristics are particularly pronounced in circular production systems, but are increasingly relevant across PL more generally. This paper addresses this challenge through the concept of Self-Organizing Production Logistics (SOPL) using the Design Science Research Methodology (DSRM) as a structuring framework. The paper identifies key technological and systemic drivers motivating SOPL, including autonomous logistics resources, distributed AI-based decision-making, and increasing operational uncertainty in circular production. Based on these drivers, system-level objectives and design requirements for SOPL are derived. Building on these requirements, an initial multi-agent architecture is proposed that combines embodied and non-embodied agents, event-driven coordination, semantic knowledge structures, and digital twins. In addition, a three-phase demonstration roadmap is presented, ranging from an initial laboratory demonstrator toward increasingly distributed and adaptive SOPL systems. The Phase I demonstrator serves as an experimental setup for investigating disturbance handling, human involvement, and supervisory coordination in an order-driven kitting and supply scenario. Overall, the paper contributes a conceptual foundation for the design, implementation, and experimental evaluation of SOPL systems.

eess.SY↗

arXiv2025

First to reach $n$ game

We consider a game with two players, consisting of a number of rounds, where the first player to win $n$ rounds becomes the overall winner. Who wins each individual round is governed by a certain urn having two types of balls (type 1 and type 2). At each round, we randomly pick a ball from the urn, and its type determines which of the two players wins. We study the game under three regimes. In the first and the third regimes, a ball is taken without replacement, whilst in the second regime, it is returned to the urn with one more ball of the same colour. We study the properties of the random variables equal to the properly defined overall net profits of the players, and the results are drastically different in all three regimes.

math.PR↗

arXiv2024

Stability in quadratic variation

Consider a sequence of cadlag processes $\{X^n\}_n$, and some fixed function $f$. If $f$ is continuous then under several modes of convergence $X^n\to X$ implies corresponding convergence of $f(X^n)\to f(X)$, due to continuous mapping. We study conditions (on $f$, $\{X^n\}_n$ and $X$) under which convergence of $X^n\to X$ implies $\left[f(X^n)-f(X)\right]\to 0$. While interesting in its own right, this also directly relates (through integration by parts and the Kunita-Watanabe inequality) to convergence of integrators in the sense $\int_0^t Y_{s-}df(X^n_s)\to\int_0^t Y_{s-}df(X_s)$. We use two different types of quadratic variations, weak sense and strong sense which our two main results deal with. For weak sense quadratic variations we show stability when $f\in C^1$, $\{X^n\}_n,X$ are Dirichlet processes defined as in \cite{NonCont} $X^n\xrightarrow{a.s.}X$, $[X^n-X]\xrightarrow{a.s.}0$ and $\{(X^n)^*_t\}_n$ is bounded in probability. For strong sense quadratic variations we are able to relax the conditions on $f$ to being the primitive function of a cadlag function but with the additional assumption on $X$, that the continuous and discontinuous parts of $X$ are independent stochastic processes (this assumption is not imposed on $\{X^n\}_n$ however), and $\{X^n\}_n,X$ are Dirichlet processes with quadratic variations along any stopping time refining sequence. To prove the result regarding strong sense quadratic variation we prove a new It\^o decomposition for this setting.

math.PR↗

arXiv2022

An optimization model with stochastic variables for flexible production logistics planning

Production logistics has an important role as a chain that connects the components of the production system. The most important goal of production logistics plans is to keep the flow of the production system well. However, compared to the production system, the level of planning, management, and digitalization of the production logistics system is not high enough, so it is difficult to respond flexibly when unexpected situations occur in the production logistics system. Optimization and heuristic algorithms have been proposed to solve this problem, but due to their inflexible nature, they can only achieve the desired solution in a limited environment. In this paper, the relationship between the production and production logistics system is analyzed and stochastic variables are introduced by modifying the pickup and delivery problem with time windows (PDPTW) optimization model to establish a flexible production logistics plan. This model, taking into account stochastic variables, gives the scheduler a new perspective, allowing them to have new insights based on the mathematical model. However, since the optimization model is still insufficient to respond to the dynamic environment, future research will cover how to derive meaningful results even in a dynamic environment such as a machine learning model.

math.OC↗

arXiv2020

Stability in quadratic variation, with applications

We show that non continuous Dirichlet processes, defined as in \cite{NonCont} are closed under a wide family of locally Lipschitz continuous maps (similar to the time-homogeneous variants of the maps considered in \cite{Low}) thus extending Theorem 2.1. from that paper. We provide an It\^o formula for these transforms and apply it to study of how $[f(X^n)-f(X)]\to 0$ when $X^n\to X$ (in some appropriate sense) for certain Dirichlet processes $\{X^n\}_n$, $X$ and certain locally Lipschitz continuous maps. We also consider how $[f_n(X^n)-f(X)]\to 0$ for $C^1$ maps $\{f_n\}_n$, $f$ when $f_n'\to f'$ uniformly on compacts. For applications we give examples of jump removal and stability of integrators.

math.PR↗

arXiv2010

Hedging Errors Induced by Discrete Trading Under an Adaptive Trading Strategy

Discrete time hedging in a complete diffusion market is considered. The hedge portfolio is rebalanced when the absolute difference between delta of the hedge portfolio and the derivative contract reaches a threshold level. The rate of convergence of the expected squared hedging error as the threshold level approaches zero is analyzed. The results hinge to a great extent on a theorem stating that the difference between the hedge ratios normalized by the threshold level tends to a triangular distribution as the threshold level tends to zero.

q-fin.RM↗

arXiv2010

Convergence of an Adaptive Approximation Scheme for the Wiener Process

The problem of approximating/tracking the value of a Wiener process is considered. The discretization points are placed at times when the value of the process differs from the approximation by some amount, here denoted by eta. It is found that the limiting difference, as eta goes to 0, between the approximation and the value of the process normalized with eta converges in distribution to a triangularly distributed random variable.

math.PR↗

arXiv2006

Fast simulated annealing in $\R^d$ and an application to maximum likelihood estimation

Using classical simulated annealing to maximise a function $\psi$ defined on a subset of $\R^d$, the probability $\p(\psi(\theta\_n)\leq \psi\_{\max}-\epsilon)$ tends to zero at a logarithmic rate as $n$ increases; here $\theta\_n$ is the state in the $n$-th stage of the simulated annealing algorithm and $\psi\_{\max}$ is the maximal value of $\psi$. We propose a modified scheme for which this probability is of order $n^{-1/3}\log n$, and hence vanishes at an algebraic rate. To obtain this faster rate, the exponentially decaying acceptance probability of classical simulated annealing is replaced by a more heavy-tailed function, and the system is cooled faster. We also show how the algorithm may be applied to functions that cannot be computed exactly but only approximated, and give an example of maximising the log-likelihood function for a state-space model.

math.PR↗