| The supply chain disruption occurs with very low probability, but imposes a firm to negative financial
impacts and recovering from such shocks is typically very slow. In this paper, we propose a capacitated supply
chain network design (SCND) model under random disruption in facility and transportation, in which two tiers of
decision makers of distribution centers (DC) and customers seek to determine their optimal plans. Unlike other
studies in the extent literature, we use new concepts of reliability to model the strategic behavior of DCs and
customers at the network: (1) each DC might be partially failed, but could still support serving with a portion of
its capacity. (2) The capacity loss in disrupted DC will be provided from non-disrupted DC, and (3) a fraction of
the capacity that DCs lose in disruption time depends on the amount of investment for opening and operating.
We formulate the problem as a mixed-integer non-linear program and a modified version of Benders
decomposition (BD) is proposed to optimally solve the model, which itself has a contribution in the SCND under
random disruption problems. The most difficulty related to the BD is the solution time of master problem. The
classical BD in some cases results in low density cuts. Covering Cut Bundle (CCB) generation addressed this
issue in a way of generating a bundle of cuts which could cover more decision variables of the master problem
than the classical Benders cut. Our inspiration to improve the CCB generation led to a new method, namely
Maximum Density Cut (MDC) generation. MDC is based on the observation that in some cases CCB generation
is cumbersome to be solved to cover all decision variables of the master problem than to cover part of them. Thus
MDC method addresses this issue by generating the cut that includes the remaining of the decision variables of
the master problem which are not covered yet. The numerical experiment demonstrates the practicability of the
proposed model which is promising in the SCND area, and with a significant decreasing in the number of
iterations of the BD, the CPU times improve. |