Service composition and optimal selection in cloud manufacturing under event-dependent distributional uncertainty of manufacturing capabilities

Service composition and optimal selection in cloud manufacturing involves the allocation of available manufacturing cloud services (MCSs) derived from a diverse array of manufacturing resources to satisfy personalized demand of customers. Existing studies generally neglect the uncertainty of manufacturing capabilities for providing MCSs. To this end, we use an event-dependent hybrid ambiguity set consisting of the box support set, Wasserstein metric, mean, and expected cross-deviation, where the support is conditional on each event, to capture the uncertainty of manufacturing capabilities, and cast the problem as a two-stage distributionally robust optimization model. We provide model bound analysis with theoretical gap guarantees, including the lower and upper bounds derived from the solution of the linear relaxation of the resulting reformulation, and sensitivity bounds for varying some ambiguity-set parameters. To exactly solve the reformulation, we design a customized constraint generation algorithm incorporating some improvement strategies, a variant of classical Benders decomposition, which decomposes the reformulation into a relaxed master problem and an adversarial separation subproblem which identifies valid constraints to tighten the relaxed master problem. Importantly, we transform the bilinear separation subproblem into a 0-1 mixed-integer linear program, observing the property that the linear-relaxed solution is integer, which makes the separation subproblem more easy to solve. Ultimately, we conduct numerical studies on the case study of a group enterprise producing large cement equipment in Tianjin, China, to evaluate the effectiveness of the solution algorithm, quantify the benefits of accounting for event-dependent distributional ambiguity over its single-event counterpart and stochastic and deterministic counterparts, and verify the value of considering the event-dependent hybrid ambiguity set over the Wasserstein and moment counterparts, and measure the quality of the upper and lower bounds and sensitivity bounds.