Lagrangian Relaxation Bounds for a Production-Inventory-Routing Problem
We consider a single item Production-Inventory-Routing problem with a single producer/supplier and multiple retailers. Inventory management constraints are considered both at the producer and at the retailers, following a vendor managed inventory approach, where the supplier monitors the inventory at retailers and decides on the replenishment policy for each retailer. We assume a constant production capacity. Based on the mathematical formulation we discuss a classical Lagrangian relaxation which allows to decompose the problem into four subproblems, and a new Lagrangian decomposition which decomposes the problem into just a production-inventory subproblem and a routing subproblem. The new decomposition is enhanced with valid inequalities. A computational study is reported to compare the bounds from the two approaches.
KeywordsInventory routing Lagrangian relaxation Lagrangian decomposition Lower bounds
The research of the first and third authors was supported through CIDMA and FCT, the Portuguese Foundation for Science and Technology, within project UID/MAT/ 04106/2013. The research of the second author was financed by the ERDF - European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation - COMPETE 2020 Programme within project “POCI-01-0145-FEDER-006961”, and by FCT within project UID/EEA/50014/2013.
- 6.Agra, A., Christiansen, M., Ivarsoy, K., Solhaug, I., Tomasgard, A.: Combined ship routing and inventory management in the salmon farming industry. Ann. Oper. Res. (in press)Google Scholar
- 11.Christiansen, M., Fagerholt, K.: Maritime Inventory Routing Problems. In: Floudas, C., Pardalos, P. (eds.) Encyclopedia of Optimization, 2nd edn, pp. 1947–1955. Springer, New York (2009)Google Scholar
- 14.FICO Xpress Optimization SuiteGoogle Scholar
- 20.Ruokokoski, M., Solyali, O., Cordeau, J.-F., Jans, R., Süral, H.: Efficient formulations and a branch-and-cut algorithm for a production-routing problem. GERAD Technical report G-2010-66. HEC Montréal, Canada (2010)Google Scholar
- 23.Solyali, O., Süral, H.: A relaxation based solution approach for the inventory control and vehicle routing problem in vendor managed systems. In: Neogy, S.K., Das, A.K., Bapat, R.B. (eds.) Modeling, computation and Optimization, pp. 171–189. World Scientific, Singapore (2009)Google Scholar