Managing Risks of Supply-Chain Disruptions: Dual ... - CiteSeerX

investment costs are denotedIMainSupplier− > DualSourcing, ILocalSupplier− > DualSourcing, IMainSupplier−> LocalSupplierandILocalSupplier− > MainSupplier.5.2.4 Other assumptionsIn the model we can easily add some assumptions to make it more real.For example, as just defined the model doesn’t take into account the loss of market share that canhappen when the firm is not supplied anymore. We can therefore improve the model by assumingthat the supplier looses x% of his market share each year of disruption if ever he relies on singlesourcing.5.3 Valuation ModelThe goal of the firm is to maximize its profits. In order to choose the best sourcing strategy, thefirm needs to evaluate the different solutions. This valuation is to be done in an uncertainenvironment, and must integrate a flexible decision process along time. This can be done usingReal Options.We will use Dynamic Programming and Bellman equations, as Contingent Claim Analysis is notadapted in our case. Disruptions occur according to a Poisson Process and as a result it isimpossible to find an asset that duplicates the stochastic dynamics of the firm’s profits.The state and the control at time t affect the firm’s immediate profit flow, which we denote byπ X , U ) .t(t tThe aim is to choose the optimal vector of control variables { U t} as a function of time such thatthe total value of the payoffs at the initial time is maximized.The basic idea of dynamic programming is to split the decision sequence into two parts, theimmediate period and the whole continuation beyond that.Suppose that the current date is t and the state isX . Let us denote by F X ) the value of all thett(tfuture payoffs when the firm follows the optimal decision process from this state.54