An important aspect of customer order supply systems in supplier firms is to manage the processes of "order picking in the warehouses, packing and preparing the shipments for being loaded into the vehicles and transported to the customers". In this regard, two major issues should be considered under resource restrictions: 1) On time customer delivery (meeting deadline) and 2) preparing and shipping the orders with the minimum cost. In this paper, a discrete simulation method is applied to study the processes and analyzing the performance of the customer order supply system of a supplier of spare parts for automobile. Alternative configurations have also been investigated for its operations using time-cost trade-off approach. Nine scenarios were simulated to evaluate the effect of 5, 10, 15, 30, 60, 90, 120, 150 and 180-minute waiting periods (base scenario was 10-minute waiting period), for receiving orders and afterwards planning to both picking them and providing vehicles for delivering the shipments to customers. The data (60000 records) have been collected during a typical period of 118 days of performance of the system under consideration. The study shows that the total shipment cost will be reduced considerably by implementing the optimal scenario. This research is also useful for similar order supply systems in various industries, especially in spare part ones.