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algorithm allocation alternative applied assignment assume average beneﬁt branch-and-bound computational Concave Function concave minimization Condorcet consider constraints convergence cost decomposition deﬁned deﬁnition demand denote distribution dual solution due date empirical process extreme point feasible ﬁnd ﬁnding ﬁnite ﬁrst ﬁxed formulation given global optimal heuristic Horst integer inventory system iteration Journal Lemma linear program lower bound LP relaxation machine makespan Manuscript received master problem maximum maximum independent set method Naval Postgraduate School Naval Research Logistics negative binomial distribution node NP-hard objective function obtained Operations Research optimal solution ordering policy outer approximation parameters partitioning period Poisson polyhedral primal procedure PROOF random random variable rank resupply saddle point satisﬁes searchers Section sequence solve speciﬁc stochastic subproblem supply mode Table tardiness TDTSP technique Theorem tion unit University upper bound variables vertex cover Wiley & Sons