Orateur
Description
We address the Multi-Item Capacitated Lot-Sizing Problem (MCLSP) under decision-dependent uncertainty through a new probing-enhanced stochastic programming framework. In this setting, the demand is strongly correlated with another random vector and the decision-maker can strategically acquire partial information about uncertain demand by selecting component of the correlated random vector to probe, conditioning production decisions on observed covariates. This approach generalizes classical stochastic models by embedding endogenous information acquisition within a three-stage optimization framework. We introduce a compact reformulation that eliminates traditional non-anticipativity constraints, resulting in a stronger linear relaxation and improved computational tractability. We extend classical $(k,U)$ inequalities to the decision-dependent setting and introduce a new class of value-function-based inequalities that strengthen the LP relaxation by capturing the structural relationship between probing and expected recourse costs. These enhancements are embedded within a branch-and-cut algorithm, which also integrates a primal heuristic to accelerate convergence. Computational experiments demonstrate the effectiveness of our proposed methodology. The new formulation together with value-function inequalities consistently outperforms classical approaches, reducing optimality gaps by up to 85%. The full-featured branch-and-cut algorithm achieves optimality gaps below 1.5% on average, even under tight capacity constraints and large scenario sets. These results highlight the critical role of structured reformulation, valid inequalities, and heuristic guidance in solving complex decision-dependent stochastic programs. Our findings display the value of proactive information acquisition and offer scalable tools for production planning under uncertainty.
