Mobile edge-cloud computing environments appear as a novel computing paradigm to offer effective processing and storage solutions for delay sensitive applications. Besides, the container based virtualization technology becomes solicited due to its natural lightweight and portability as well as its small migration overhead that leads to seamless service migration and load balancing. However, with the mobility property, the users’ demands in terms of the backhaul bandwidth is a critical parameter that influences the delay constraints of the running applications. Accordingly, a Binary Integer Programming (BIP) optimization problem is formulated. It minimizes the users’ perceived backhaul delays and enhances the load-balancing degree in order to offer more chance to accept new requests along the network. Also, by introducing bandwidth constraints, the available user backhaul bandwidth after the placement are enhanced. Then, the adopted methodology to design two heuristic algorithms based on Ant Colony System (ACS) and Simulated Annealing (SA) is presented. The proposed schemes are compared using different metrics,and the benefits of the ACS-based solution compared to the SA-based as well as a genetic algorithm (GA) based solutions are demonstrated. Indeed, the normalized cost and the total backhaul costs are given by more optimal values using the ACS algorithm compared to the other solutions.