Distributionally robust project crashing with partial or no correlation information

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Abstract
Crashing is shortening the project makespan by reducing activity times in a project network by allocating resources to them. Activity durations are often uncertain and an exact probability distribution itself might be ambiguous. We study a class of distributionally robust project crashing problems where the objective is to optimize the first two marginal moments (means and SDs) of the activity durations to minimize the worst‐case expected makespan. Under partial correlation information and no correlation information, the problem is solvable in polynomial time as a semidefinite program and a second‐order cone program, respectively. However, solving semidefinite programs is challenging for large project networks. We exploit the structure of the distributionally robust formulation to reformulate a convex‐concave saddle point problem over the first two marginal moment variables and the arc criticality index variables. We then use a projection and contraction algorithm for monotone variational inequalities in conjunction with a gradient method to solve the saddle point problem enabling us to tackle large instances. Numerical results indicate that a manager who is faced with ambiguity in the distribution of activity durations has a greater incentive to invest resources in decreasing the variations rather than the means of the activity durations.
Funding Information
  • Ministry of Education - Singapore (T2MOE1706)

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