Variables recourse

Stochastic Recourse Variables (Second-Stage Decision Variables)... 

Risk is modeled in terms of variance in both prices of imported cmde oil CrCosta and petroleum products Pry/, represented by first stage variables, and forecasted demand DRef, yr, represented by the recourse variables. The variability in the prices represents the solution robustness in which the model solution will remain close to optimal for all scenarios. On the other hand, variability ofthe recourse term represents the model robustness in which the model solution will almost be feasible for all scenarios. This technique gives rise to a multiobjective optimization problem in which... 

The two-stage mixed-integer stochastic program with recourse that includes a total number of200 scenarios for each random parameter is considered in this section. All random parameters were assumed to follow a normal distribution and the scenarios for all random parameters were generated simultaneously. Therefore, the recourse variables account for the deviation from a given scenario as opposed to the deviation from a particular random number realization. 

Considering risk in terms of variations in both projected benefits and recourse variables provided a more robust analysis of the problem. As explained earlier, the problem will have a more robust solution as the results will remain close to optimal for all given scenarios through minimizing the variations of the projected benefit. On the other hand, the model will be more robust as minimizing the variations in the recourse variables leads to a model that is almost feasible for all the scenarios... 

The above formulation is an extension of the deterministic model explained in Chapter 5. We will mainly explain the stochastic part of the above formulation. The above formulation is a two-stage stochastic mixed-integer linear programming (MILP) model. Objective function (9.1) minimizes the first stage variables and the penalized second stage variables. The production over the target demand is penalized as an additional inventory cost per ton of refinery and petrochemical products. Similarly, shortfall in a certain product demand is assumed to be satisfied at the product spot market price. The recourse variables V [ +, , V e)+ and V e[ in... 

The stochastic problem is characterised by two essential features the uncertainty in the problem data and the sequence of decisions. In our case, the demand is considered as a random variable with a certain probability distribution. The binary variables associated to the opening of a plant/warehouse as well as the continuous variables that represent the capacity of plants/warehouses are considered as first stage decisions. The fluxes of materials and the sales of products are taken as second stage or recourse variables. The objective hinctions are therefore the expected net present value and the expected consumer satisfaction. 

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