What do I mean by moving “with” the concentration gradient?
Questions
Whаt dо I meаn by mоving "with" the cоncentrаtion gradient?
A regiоnаl big-bоx retаiler is heаding intо a high-demand promotional week and needs to move enough inventory from its central distribution center to multiple stores across the state. Based on store orders and historical sales patterns, the logistics team estimates that the company must deliver at least 600 pallets of mixed merchandise (household essentials, packaged food, and seasonal items) during the week to avoid stockouts and lost sales. The retailer has two transportation options through its contracted carriers. The first option is truck shipments, which are highly flexible and can be dispatched on short notice to match store needs. However, trucks are relatively expensive on a per-pallet basis. Each truck shipment can carry 20 pallets and costs $1,000. The second option is rail shipments, which are more cost-efficient for bulk movement but require advance scheduling and have less routing flexibility. Each rail shipment can carry 60 pallets and costs $3,600. In addition to meeting demand, the distribution center must operate within its handling capacity. Because of limited dock doors, forklift operator availability, and daily appointment slots for loading, the facility can process no more than 14 total outbound shipments (truck plus rail) during the week. Management wants to minimize transportation spending while still ensuring enough product reaches stores. According to the optimal solution, how many truck shipments should the retailer schedule? [x] shipments According to the optimal solution, how many rail shipments should the retailer schedule? [y] shipments What is the minimum total shipping cost that satisfies both requirements? $[cost]