Optimization Models

Optimization Model for Inventory Deployment

A large Canadian retailer has a nation-wide supply chain network. There is a national distribution centre (DC) with a number of smaller, regional DCs. Of the tens of thousands of distinct inventory items (SKUs), some will be carried at every DC. Others may be kept at only the national DC, or there plus one or two of the regional DCs.

Shipment of a mixture of SKUs to a given set of retail stores will then be a complicated logistical operation. The associated costs will combine several relevant parameters involving inventory and transportation.

The preceding total cost can be estimated and calculated. But how does the above deployment relate to the optimal locations for the stocking of each product? To decide, WATMIMS employed the technique of inverse optimization.

The present choices to stock or not stock each SKU at specific location(s) are clearly feasible. However, those inventory decisions are probably not optimal, for the current values of the transportation and inventory cost parameters. By how much would those parameter values need to change, in order that the present stocking decisions be optimal with respect to the revised cost parameters? That question is answered by the technique of "inverse optimization."

After formulating the model in this way, and running and experimenting with it, the WATMIMS researchers determined that particular transportation-cost parameters were in greatest need of revision, in order that the current feasible solution would become optimal. Thus, it would be well worth some time and effort to carefully re-evaluate those parameters. And by this proposal, the client was able to choose the appropriate strategies for inventory stocking or deployment.