529 / 2024-04-25 19:51:42

EOQ Replenishment Policy with an Endogenous Holding Cost Based on Warehousing Optimization

Endogenous Holding Cost ;,Warehousing,replenishment policy

The inventory replenishment policy has been extensively studied, for more than 100 years, with an exogenous holding cost. However, much less is known when the holding cost is endogenously affected by warehousing optimization. In this paper, we present the first inventory model for the joint decision of replenishment policy and warehousing optimization. In particular, we incorporate the machine traveling cost that is obtained from the warehousing optimization into the holding cost. The replenishment quantities depend on the holding cost; conversely, the optimal warehousing decisions depend on the order quantities. To visualize the architecture between the total holding cost and the order quantity, we propose a non-linear function to approximate the holding cost used for replenishment policy and that results from warehouse optimization, namely (α,γ)-EOQ policy. The efficiency of the algorithm is validated through extensive experiments: near-optimal solutions by the (α,γ)-EOQ policy can be reached, within 0.1% gap over the optimal solutions. The numerical results show that our (α,γ)-EOQ policy beats a linear policy that uses a linear function to approximate the exogenous holding cost with a up to 4% cost saving. The results also show that our joint model for inventory and warehousing problem produces a considerable cost reduction of more than 8.9% compared with the inventory model ignoring the machine travel cost.