Robust solutions and risk measures for a supply chain planning problem under uncertainty

We consider a strategic supply chain planning problem formulated as a two-stage stochastic integer programming (SIP) model. The strategic decisions include site locations, choices of production, packing and distribution lines, and the capacity increment or decrement policies. The SIP model provides a practical representation of real-world discrete resource allocation problems in the presence of future uncertainties which arise due to changes in the business and economic environment. Such models that consider the future scenarios (along with their respective probabilities) not only identify optimal plans for each scenario, but also determine a hedged strategy for all the scenarios. We

1. 1)
   exploit the natural decomposable structure of the SIP problem through Benders’ decomposition,
    
2. 2)
   approximate the probability distribution of the random variables using the generalized lambda distribution, and
    
3. 3)
   through simulations, calculate the performance statistics and the risk measures for the two models, namely the expected-value and the here-and-now.