This question has been troubling me as I am not used to questions without numbers as it is hard for me to visualise. I also find stochastic problems hard in general.
So far what I have come up with for part a):
Could I let xi = amount produced at plant i, tij = amount sent from plant i to retailer j
minimise: xiP+ticij
1) Production should not be exceeded plant capacity: xi<=Bi
2) Amount sent from each plant can not exceed amount produced tij<=xi
3) Amount sent to each retailer should not exceed average demand tij <= average dj
4) Non- negativity >=0
For the part b I am at a loss at how to develop the stochastic model. I know the first stage decision variables are to choose the amount to produce, and at the second stage when demands are known the variables are the amount to transport.
I would be extremely grateful for any hints for this question (or these types of questions in general). Thanks!
I would work with more equalities rather than inequalities. Beside that for the second and third constraint we have to sum up the amounts to be sent.
$\sum_{j=1}^R t_{ij}=x_i \ \ \forall \ i \in \{1,\ldots, P \}$
$\sum_{i=1}^P t_{ij}=d_j \ \ \forall \ j \in \{1,\ldots, R \}$