  We study the inbound supply mode and inventory management decision making for
a company that sells an assortment of products. Stochastic demand for each
product arrives periodically and unmet demand is backlogged. Each product has
two distinct supply modes that may be different suppliers or different
transport modes from the same supplier. These supply modes differ in terms of
their carbon emissions, speed, and costs. The company needs to decide when to
ship how much using which supply mode such that total holding, backlog, and
procurement costs are minimized while the emissions associated with different
supply modes across the assortment remains below a certain target level. Since
the optimal policy for this inventory system is highly complex, we assume that
shipment decisions for each product are governed by a dual-index policy. This
policy dynamically prescribes shipment quantities with both supply modes based
on the on-hand inventory, the backlog, and the products that are still
in-transit. We formulate this decision problem as a mixed integer linear
program that we solve through Dantzig-wolfe decomposition. We benchmark our
decision model against two state-of-the-art approaches in a large test-bed
based on real-life carbon emissions data. Relative to our decision model, the
first benchmark lacks the flexibility to dynamically ship products with two
supply modes while the second benchmark makes supply mode decisions for each
product individually rather than holistically for the entire assortment. Our
computational experiment shows that our decision model can outperform the first
and second benchmark by up to 15 and 40 percent, respectively, for realistic
targets for carbon emission reduction.
