Distribution-dependent robust linear optimization with applications to inventory control

摘要: This paper tackles linear programming problems with data uncertainty and applies it to an important inventory control problem. Each element of the constraint matrix is subject modeled as a random variable bounded support. The classical robust optimization approach this problem yields solution guaranteed feasibility. As tends be too conservative when applications can tolerate small chance infeasibility, one would interested in obtaining less certain probabilistic guarantee A formulation literature produces such solution, but does not use any distributional information on uncertain data. In work, we show that leads equally (i.e., under same feasibility) better objective value. particular, by exploiting information, establish stronger upper bounds violation probability solution. These enable us "inject" conservatism into formulation, which turn more cost-effective (by 50% or some numerical instances). To illustrate effectiveness our methodology, consider discrete-time stochastic quality service constraints. Numerical tests demonstrate results 36%-54% cost savings, compared case where used.