2025/01/02 by Sumin Kang, Kang, Sumin, Manish Bansal +1
Business, Management and Accounting · Engineering · #90C11 #90C15 #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Mathematical Programming #Scheduling and Optimization Algorithms #Supply Chain and Inventory Management
paper · pdf · doi:10.48550/arxiv.2501.01081
openalex publication_date 2025/01/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce two-stage stochastic min-max and min-min integer programs with bi-parameterized recourse (BTSPs), where the first-stage decisions affect both the objective function and the feasible region of the second-stage problem. To solve these programs efficiently, we introduce Lagrangian-integrated L-shaped (L2) methods, which guarantee exact solutions when the first-stage decisions are pure binary. For mixed-binary first-stage programs, we present a regularization-augmented variant of this method. Our computational results for a stochastic network interdiction problem show that the L2 method outperforms a benchmark method, solving all instances in 23 seconds on average, while the benchmark method failed to solve any instance within 3600 seconds. The L2 method also achieves optimal solutions, on average, 18.4 times faster for a stochastic facility location problem. Furthermore, we show that the L2 method can effectively address distributionally robust optimization problems with decision-dependent ambiguity sets that may be empty for some first-stage decisions, achieving optimal solutions, on average, 5.3 times faster than existing methods.