It's strongly needed to minimize the logistics response time for supporting military operations in wartime. In this paper, we suggest the ILP formulation for minimizing logistics response time in wartime. Main structure of this formulation is based on the traveling purchaser problem(TPP) which is a generalized form of the well-known traveling salesman problem(TSP). In the case of general TPP, objective function is to minimize the sum of traveling cost and purchase cost. But, in this study, objective function is to minimize traveling cost only. That's why it's more important to minimize traveling cost(time or distance) than purchase cost in wartime. We find out optimal solution of this problem by using ILOG OPL STUDIO(CPLEX v.11.1) and do the sensitive analysis about computing time according to number of operated vehicles.