TY - JOUR

T1 - An aggregation-based approximate dynamic programming approach for the periodic review model with random yield

AU - Voelkel, Michael A.

AU - Sachs, Anna-Lena

AU - Thonemann, Ulrich W.

N1 - This is the author’s version of a work that was accepted for publication in European Journal of Operational Research. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in European Journal of Operational Research, 281, 2, 2019 DOI: 10.1016/j.ejor.2019.08.035

PY - 2020/3/31

Y1 - 2020/3/31

N2 - A manufacturer places orders periodically for products that are shipped from a supplier. During transit, orders get damaged with some probability, that is, the order is subject to random yield. The manufacturer has the option to track orders to receive information on damages and to potentially place additional orders. Without tracking, the manufacturer identifies potential damages after the order has arrived. With tracking, the manufacturer is informed about the damage when it occurs and can respond to this information. We model the problem as a dynamic program with stochastic demand, tracking cost, and random yield. For small problem sizes, we provide an adjusted value iteration algorithm that finds the optimal solution. For moderate problem sizes, we propose a novel aggregation-based approximate dynamic programming (ADP) algorithm and provide solutions for instances for which it is not possible to obtain optimal solutions. For large problem sizes, we develop a heuristic that takes tracking costs into account. In a computational study, we analyze the performance of our approaches. We observe that our ADP algorithm achieves savings of up to 16% compared to existing heuristics. Our heuristic outperforms existing ones by up to 8.1%. We show that dynamic tracking reduces costs compared to tracking always or never and identify savings of up to 3.2%.

AB - A manufacturer places orders periodically for products that are shipped from a supplier. During transit, orders get damaged with some probability, that is, the order is subject to random yield. The manufacturer has the option to track orders to receive information on damages and to potentially place additional orders. Without tracking, the manufacturer identifies potential damages after the order has arrived. With tracking, the manufacturer is informed about the damage when it occurs and can respond to this information. We model the problem as a dynamic program with stochastic demand, tracking cost, and random yield. For small problem sizes, we provide an adjusted value iteration algorithm that finds the optimal solution. For moderate problem sizes, we propose a novel aggregation-based approximate dynamic programming (ADP) algorithm and provide solutions for instances for which it is not possible to obtain optimal solutions. For large problem sizes, we develop a heuristic that takes tracking costs into account. In a computational study, we analyze the performance of our approaches. We observe that our ADP algorithm achieves savings of up to 16% compared to existing heuristics. Our heuristic outperforms existing ones by up to 8.1%. We show that dynamic tracking reduces costs compared to tracking always or never and identify savings of up to 3.2%.

KW - Inventory

KW - Approximate dynamic programming

KW - Random yield

KW - Tracking

KW - Value of information

U2 - 10.1016/j.ejor.2019.08.035

DO - 10.1016/j.ejor.2019.08.035

M3 - Journal article

VL - 281

SP - 286

EP - 298

JO - European Journal of Operational Research

JF - European Journal of Operational Research

SN - 0377-2217

IS - 2

ER -