2020/05/22 by D. V. Lebedev, Lebedev, Denis, Paul J. Goulart +3
Business, Management and Accounting · Decision Sciences · Economics, Econometrics and Finance · #Economic theories and models #FOS: Mathematics #Optimization and Control (math.OC) #Risk and Portfolio Optimization #Supply Chain and Inventory Management
paper · pdf · doi:10.48550/arxiv.2005.11213
openalex publication_date 2020/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider dynamic programming problems with finite, discrete-time horizons\nand prohibitively high-dimensional, discrete state-spaces for direct\ncomputation of the value function from the Bellman equation. For the case that\nthe value function of the dynamic program is concave extensible and submodular\nin its state-space, we present a new algorithm that computes deterministic\nupper and stochastic lower bounds of the value function similar to dual dynamic\nprogramming. We then show that the proposed algorithm terminates after a finite\nnumber of iterations. Finally, we demonstrate the efficacy of our approach on a\nhigh-dimensional numerical example from delivery slot pricing in attended home\ndelivery.\n