A location-inventory-pricing model in a supply chain distribution network with price-sensitive demands and inventory-capacity constraints

• This paper incorporates pricing into a supply chain location-inventory problem.
• Demands are price-sensitive and distribution centers have limited inventory capacities.
• The supply chain has market power and uses markup pricing to determine retail prices.
• The problem is solved by an efficient Lagrangian relaxation algorithm.

This paper presents a location-inventory-pricing model for designing the distribution network of a supply chain with price-sensitive demands and inventory-capacity constraints. The supply chain has market power and uses markup pricing. An efficient Lagrangian relaxation algorithm is proposed to solve the model. Our numerical study shows that by moderately increasing the number of possible values for pricing decisions, the model can be used to find near-optimal solutions of a similar location-inventory-pricing problem with continuous pricing decisions. The approach used here to incorporate pricing decisions can be applied to other supply-chain design and planning problems with price-sensitive demands.