Assessment and Future Directions of Nonlinear Model Predictive ...

Distributed MPC for Dynamic Supply Chain Management 613By this algorithm, each stage initially computes an optimal order rate policyassuming neighboring stages employ a nominal constant order rate. For everysubsequent update, each stage computes an optimal order rate policy, assumingthat the MDs are based on the remainder of the previously computed policiescomputed of neighboring stages.4 Numerical ExperimentsThe simulations were carried out in MATLAB 7.0, using Simulink 6.2 and theModel Predictive Control Toolbox 2.2. The nominal and distributed MPC approachesare compared on the full three stage problem, given a step increase anddecrease in the customer demand rate at the retailer. For simulation purposes,we choose d R r (t) = 200 cases/day for t ∈ [0, ∞) \ [5, 15) and d R r (t) = 300 fort ∈ [5, 15). The response for the three stages under the nominal control policy(k 1 =1/15, k 2 =1/30) is shown in Figure 2. To implement the distributed MPCcasescasescaseso udRetailer State ResponseRetailer Order Rate and Demand Rate4001000so rs d350d ro u30050025020001500 10 20 30 40 500 10 20 30 40 50daysdays15001000Manufacturer State Responsess do udo u50030020000 10 20 30 40 500 10 20 30 40 50daysdaysSupplier State ResponseSupplier Order Rate and Demand Rate20001500ss d600500o rd r1000o uo ud40030050020000 10 20 30 40 500 10 20 30 40 50daysdayscases/daycases/daycases/day500400Manufacturer Order Rate and Demand Rateo rd rFig. 2. Nominal response to step increase at 5 days and decrease at 15 days in retailercustomer demand rate d R rAlgorithm 1, the anticipative action of the MPC Toolbox is employed so thateach entire assumed prediction can be used. Recall that the assumed predictionsare not the actual predictions, although the move suppression terms (W δuweighted) in the cost are used to ensure that these predictions are not too farapart. The forecasted demand rate at the retailer is also used with the anticipationoption turned on. A more “apples-to-apples” comparison would be toincorporate internal models with the nominal approach that use the forecastedcustomer demand rate. The response for the three stages under the distributedMPC policy with anticipation is shown in Figure 3. The weights used in MPCfor each stage are (W u ,W δu ,W s ,W ou )=(1, 5, 5, 1). The stock and unfulfilled