Sustainable multi-echelon inventory control with shipment consolidation and volume dependent freight costs

This paper provides exact analysis of a model for sustainable control of a one-warehouse-N-retailer inventory system with time based shipment consolidation. The model is motivated by discussions with industry, and involves the possibility to reserve intermodal transportation capacity in combination with truck transports available on demand. Inventories are reviewed continuously while shipments from the warehouse are consolidated for groups of retailers and dispatched periodically. A key result is the derivation of the probability mass functions for the number of units on each shipment. This allows for realistic volume dependent freight cost structures and transportation emissions to be included in the model. We show how to jointly optimize the reorder levels, shipment intervals and capacity reservation quantities to minimize the total expected costs. Transportation emissions are taken into consideration by use of a side constraint or by introducing emissions costs. A numerical example illustrates how the model can be used for evaluating the cost impact of reducing transportation emissions. The analysis is applicable to both single- and multi-item systems.