Supply chain networks design with multi-mode demand satisfaction policy

• This paper deals with a supply chain network design with multi-mode demand.
• The problem is mathematically formulated as mixed integer linear programming.
• A new iterative Lagrangian relaxation based heuristic was developed.

In supply chain network design, it is usually assumed that all customers’ demands have to be satisfied. While in some real cases, there is flexibility in final amount of demand; hence, several alternatives can be acceptable for the customers. We consider each alternative as a mode of demand. In multi-mode demand satisfaction policy, some modes are defined by the customers and one of those must be satisfied by the network; however, some customers may have only one mode while the others may have more. The major advantages of this policy rather than prefixed demand are outstanding performance in facility capacity usage, increasing the profit of the network and market share preserving. Also a network with the multi-mode demand satisfaction policy is much more robust than those with conventional policy of fixed demands. This paper deals with a supply chain network design with multi-mode demand. In this problem, in addition to location and allocation decisions, the demand satisfaction mode is also selected. First, the problem is mathematically formulated as a mixed integer linear program. Since the supply chain network design is NP-Hard, a new iterative Lagrangian relaxation based heuristic is developed to solve the problem. Numerical experiments show that the proposed approach can find a high quality near-optimal solution for the model in a reasonable computational time.