Piecewise linear lower and upper bounds for the standard normal first order loss function

DOI10.1016/j.amc.2014.01.019zbMath1410.62027arXiv1307.1708OpenAlexW1543956290WikidataQ57539190 ScholiaQ57539190MaRDI QIDQ1644563

Roberto Rossi, S. Armagan Tarim, Steven Prestwich, Brahim Hnich

Publication date: 21 June 2018

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.1708

zbMATH Keywords

minimaxpiecewise linear approximationcomplementary first order loss functionEdmundson-Madanskyfirst order loss functionJensen's

Mathematics Subject Classification ID

Approximations to statistical distributions (nonasymptotic) (62E17)

Related Items (10)

A note on ``Linear programming models for a stochastic dynamic capacitated lot sizing problem ⋮ The stochastic lot sizing problem with piecewise linear concave ordering costs ⋮ A mathematical programming-based solution method for the nonstationary inventory problem under correlated demand ⋮ A mixed integer programming formulation for the stochastic lot sizing problem with controllable processing times ⋮ The stochastic inventory routing problem on electric roads ⋮ The dynamic bowser routing problem ⋮ An Extended Mixed-Integer Programming Formulation and Dynamic Cut Generation Approach for the Stochastic Lot-Sizing Problem ⋮ Heuristics for the stochastic economic lot sizing problem with remanufacturing under backordering costs ⋮ Computing non-stationary \((s, S)\) policies using mixed integer linear programming ⋮ Approximations for non-stationary stochastic lot-sizing under \((s,Q)\)-type policy

Uses Software

• Algorithm 885

Cites Work

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• Modelling and computing \((R^{n}, S^{n})\) policies for inventory systems with non-stationary stochastic demand
• Optimal approximation of convex curves by functions which are piecewise linear
• A uniform approximation to the right normal tail integral
• A sigmoid approximation of the standard normal integral
• Double precision rational approximation algorithms for the standard normal first and second order loss functions
• Double precision rational approximation algorithm for the inverse standard normal first order loss function
• Conditional value at risk and related linear programming models for portfolio optimization
• Inventory control.
• Simple Approximations for the Inverse Cumulative Function, the Density Function and the Loss Integral of the Normal Distribution
• Introduction to Stochastic Programming

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