Invited Session Tue.2.MA 376

Tuesday, 13:15 - 14:45 h, Room: MA 376

Cluster 22: Stochastic optimization [...]

Computational aspects of stochastic integer programming for large-scale and/or real-world problems


Chair: Jörg Rambau



Tuesday, 13:15 - 13:40 h, Room: MA 376, Talk 1

Jonas Schweiger
Multi-scenario topology optimization in gas networks


With the deregulations in the gas markets, the requirements on the network change rapidly and demand more flexibility from the network operators. Gas network operators therefore have to invest into their network infrastructure. As these investments are very cost-intensive and long-living, network extensions should not only focus on one bottleneck scenario, but should increase the flexibility to fulfill different demand scenarios.
In this presentation, we formulate a model for the network extension problem for multiple demand scenarios. That is, we search cost-optimal network extensions such that a variety of demand scenarios can be realized in the extended network. We propose a decomposition along the scenarios and solve the problem by a branch&bound-algorithm which uses the single-scenario problem as subproblem. Since the single-scenario problem itself is a challenging mixed-integer non-convex optimization problem, we solve them to global optimality only in the leaf nodes of our branch&bound-tree, but still use valid bounds and solutions in every node of the tree.



Tuesday, 13:45 - 14:10 h, Room: MA 376, Talk 2

Miriam Kießling
ISPO – Integrated size and price optimization for a fashion discounter with many branches

Coauthors: Sascha Kurz, Jörg Rambau


We present the integrated size and price optimization problem (ISPO)
for a fashion discounter with many branches.
Branches are supplied by pre-packaged bundles consisting of items of
different size and number - so-called lot-types. Our goal is to find a
revenue-maximizing supply strategy.
Based on a two-stage stochastic programming model including the effect of markdowns as recourse, we developed an exact branch-and-bound
algorithm where dual bounds are obtained by combinatorial bounds
combined with LP-relaxations. For practical purposes we developed a
production-compliant heuristic, the so-called ping-pong-heuristic, that uses
the special structure of the problem by alternately solving price and size
optimization. In all tested cases we obtain very small optimality gaps
(< 0.03,%).
In a field study we show that a distribution of supply over branches
and sizes based on ISPO solutions leads to better results in terms of realized return than a one-stage
optimization of the distribution ignoring the possibility of optimal pricing.



Tuesday, 14:15 - 14:40 h, Room: MA 376, Talk 3

Jörg Rambau
The stochastic guaranteed service model

Coauthor: Konrad Schade


Order policies are crucial in supply chain management. This talk is about the stochastic-guaranteed-service-model (SGSM) and its use in finding cost-minimizing orderpoints within a multi-echelon inventory system applying the (s,S)-strategy. The guaranteed-service-model (GSM) provides such orderpoints under the assumption of reliable internal lead times and bounded total demand. We introduce the SGSM - a two-stage stochastic MILP - that extends the GSM and enables recourse actions. To solve the SGSM we generate scenarios with the sample average approximation. We reduce the number of scenarios considered in the solution algorithm through a scenario reduction technique, the fast forward selection. We get the best results using an asymmetric distance based on the objective function of the SGSM we want to solve between the scenarios.
Simulation based on real world data of a large german car manufacturer show the improvement of applying the SGSM. The results are compared to the GSM, a decentral solution without optimization within the network and another stochastic optimization method.


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