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We study the operations scheduling problem encountered in the process of making and distributing emergency supplies. The lead times of a multi-echelon process, including shipping time, assembly time, and waiting time for raw materials must be explicitly modeled. The optimization problem is to find an inventory allocation and a production/assembly plan together with a shipping schedule for inbound supplies and outbound deliveries so that the total tardiness in customer order fulfillment is minimized. We define the problem as a mixed integer programming model, perform a structure analysis of the problem, and then propose a new search heuristic for the problem. This proposed heuristic finds a feasible solution to the problem by solving a series of linear programming relaxation problems, and is able to terminate quickly. Observations from an extensive empirical study are reported.