An integrated inventory problem with transportation in a divergent supply chain under service level constraint

• A model is developed to integrate the production-inventory and transportation decisions in a divergent supply chain.
• The transportation decision is addressed comprehensively through a vehicle routing problem.
• The objective is to minimize the total expected cost of the system.
• A coordinated two-phase iterative approach is proposed to solve the model.

This study investigates an integrated inventory problem with transportation in a single-vendor and multi-buyer divergent supply chain. The vendor manufactures a product and delivers the product to the buyers located in different locations by a fleet of vehicles of identical capacity. The external demands per unit time on the buyers are independent and normally distributed. The lead time components of the buyers, excluding transportation time, can be reduced at an added crash cost. A model has been formulated to minimize the total expected cost of the system associated with the production, inventory, transportation and lead time reduction to find the optimal production, inventory and routing decisions while satisfying the service level constraint of the buyers. We propose a coordinated two-phase iterative approach to solve the model, which has been illustrated through a numerical example.