# Case Study: Supply Chain Planning Problem

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Case study background and problem formulations

Instructions for optimization with PSG Run-File, PSG MATLAB Toolbox and PSG MATLAB Subroutines.

PROBLEM: Supply Chain Planning
Minimize Avg (Recourse) (minimizing average of recourse function)
subject to
ConstVector1 ≤ Linearmulti ≤ ConstVector2 (linear constraints on the first stage variables)
Box constraints (bounds on the first stage variables)
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Avg = Average for Recourse
Linearmulti = Linear Multiple
Box constraints = constraints on individual decision variables
Recourse = Minimal value of the following second stage subproblem depending on scenarios for the given first stage variables
Minimize Linear (minimizing linear objective of the second stage subproblem)
subject to
ConstVector3 ≤ Linearmulti ≤ ConstVector4 (linear constraints on the second stage variables depending on scenarios)
Box constraints (bounds on the second stage variables)

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Problem ” problem_ Supply_Chain_Planning”
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Description # of Variables # of Scenarios Objective Value Solving Time, PC 3.14GHz (sec) Sources of Data Schütz, P., and A. Tomasgard, (2009): The impact of flexibility on operational supply chain planning. International Journal of Production Economics, doi:10.1016/j.ijpe.2009.11.004. Dataset1 5,602,526=22,676+74,398*75 75 -93456355.9873 56.32
PSG Environments
Run-File Problem Statement Data Solution
Matlab Toolbox Data
Matlab Subroutines Matlab code Data

CASE STUDY SUMMARY
A supply chain design problem is modeled as a sequence of splitting and combining processes. The problem is formulated as a two-stage stochastic program. The first-stage decisions are strategic location decisions, whereas the second stage consists of operational decisions. The objective is to maximize the expected profits over the planning horizon.
References
• Schütz, P., and A. Tomasgard (2011): The impact of flexibility on operational supply chain planning. International Journal of Production Economics 134(2), 300-311.