Strengthening Supply Chains for Servicemembers and Security Act This bill addresses Department of Defense (DOD) supply chain risk management, specifically risk management related to pharmaceuticals. The bill requires the Office of the Under Secretary of Defense for Acquisition and Sustainment within DOD to develop and issue implementing guidance for risk management for DOD supply chains for materiel (e.g., pharmaceuticals) and identify supply chain information gaps regarding reliance on foreign suppliers of drugs. After such guidance is issued, the Defense Health Agency must develop and publish implementing guidance for risk management for DOD's supply chain for pharmaceuticals and establish a working group to assess risks to the pharmaceutical supply chain, identify the pharmaceuticals most critical to beneficiary care at military treatment facilities, and establish policies for allocating scarce pharmaceutical resources. Finally, the Defense Logistics Agency must modify Defense Logistics Agency Instructions 5025.03 and 3110.01 to require Defense Logistics Agency Troop Support to coordinate annually with customers in the military departments to test responsiveness of the agency's contingency contracts for pharmaceuticals and to include the results of the testing in the annual Warstopper Program reports.