AbstractIn this article, we address two network design problems for a responsive supply chain that consists of make‐to‐order (make‐to‐assemble) facilities facing stochastic demand and service time. The response time to customer orders, critical to the success of the supply chain, is the sum of the flow time in the facility and the delivery time to the customers. The response time performance in our models is measured by the probability that the response time is shorter than a constant. This nonlinear performance measure makes the models less or not tractable. The objective of both problems is to minimize the expected network cost that consists of the cost of delivery to customers as a function of the time of delivery (or the mode of transportation), the fixed cost of locating facilities and the capacity cost as a linear function of the processing capacity. The main decision variables are the number and locations of facilities, the resources allocated to them and the delivery mode selected between facilities and demand. In the first problem, a constraint is imposed to ensure an acceptable response time level. In the second problem, a penalty is charged on the number of days that each unit is delivered later than the targeted response time and is incorporated into the objective function. In the first problem, the probabilistic constraint on the flow time can be linearized and the problem can be formulated as an integer linear programming model. In the second problem, we propose an approximation approach to linearize the objective function and an iterative search and cut algorithm to combine linear approximation with neighborhood search. A multi‐start meta‐heuristic is also suggested. Computational experiments are conducted to evaluate the performance of these solution procedures. Recommendations are made on the basis of the computational results. This appears to be the first study in the area of locating capacitated facilities with stochastic demand to incorporate the delivery mode choice decision and to evaluate the expected congestion cost as a function of the actual flow time in the facilities, instead of the average one. The models developed enable the decision maker to investigate the effect of a combination of facility location, capacity allocation, and delivery mode decisions on the expected network cost and the response time. In addition, the findings of the computational experiments shed light on tuning parameters of approximation algorithms.