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

We will describe the firm’s current status by a state variable X. At any date or period t, the currentvalue of this variableXtis known, but future variables Xt+ 1, XT + 2… are random variables.5.2.2 Control variablesAt t, the firm can decide to change its sourcing strategy and decide to use dual sourcing if ever ithas only one supplier, or on the contrary to abandon one of its supplier if it currently uses two. Thefirm can also decide to abandon its main supplier to rely only on the local supplier, or vice-versa.At last, the firm can simply decide to maintain its current sourcing policy. We represent thesedifferent choices by the control variables that can be equal to KMS(keep main supplier), KLS(keep local supplier), KDS(keep dual sourcing), TDS(change sourcing strategy to dual sourcing),TLS(change sourcing strategy to take local supplier only), T MS(change sourcing strategy to takemain supplier only). The set of control variables is denoted U.5.2.3 Profit FunctionThe firm sells devices on the US market and buys its main components from a foreignmanufacturer. This supplier delivers the components at a price of wMdollars per piece and thedevices are sold at P dollars a piece. Fixed costs including marketing and channel setup have beenestimated at c dollars per device. Thus, using only the main supplier, in the normal state thecompany can make profits of:πMain Supplier= P − w − c dollars per device (30)MThe local supplier delivers the same components at a higher priceusing these components the firm makes a profit ofw≥ wL1 M, and on productsπ1LocalSupplier= P − w − c dollars per device (31)L1andπ < (32)1LocalSuppl ierπMain SupplierUnder a dual supply arrangement the local supplier may be given a portion x of the business if it52