Dynamic compensation and contingent sourcing strategies for supply disruption

Alternative measures to deal with supply disruptions exist. We consider a make-to-order (MTO) supply chain with one manufacturer who sources from a single supplier. When a supply disruption occurs, the manufacturer can choose to satisfy some demand by either maintaining production through safety stocks or through a secondary contingent source, and turn some unmet demand into backorders on the basis of compensation. An optimal control model under consideration of the customers' dynamic reactions to the joint implementation of these strategies is formulated with the objective of minimising the cost of disruption. Through the application of Pontryagin's Maximum Principle, optimal mitigation strategies are established in closed form. They provide analytical guidance on how to dynamically and jointly adapt the quantity of contingent sourcing, the price of compensation, and the speed of safety inventory consumption. The results indicate how cost and time-related factors impact these strategies. We also demonstrate that pure strategies are only effective in tackling short supply shortages. For long disruptions, it is superior to adopt combined strategies that simultaneously incorporate two countermeasures in certain periods.