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

to reserve for the future, by maximizing the expected value of the portfolio.The paper of Martinez-de-Albeniz presents two types of result. First it characterizes the optimalreplenishment policies and then it provides structural properties of the portfolio. In case of a singleperiod model, it even derives closed form expressions that can be easily solved.Martinez-de-Albeniz, in particular, expands its study to disruption management. Improving hismodel, he defined a random variable A in [0,1] so that the amount that can be ordered by themanufacturer from the contract is no more than Ax (where x is the maximum capacity, defined aspreviously). To model disruption, A is such that it takes the value 0 with probability p, and 1otherwise. He defines new optimality equations, and in the particular case of a single period and anexponentially distributed demand he derives n closed form equations that permit to determineeasily the optimal n-uplet x , x ,..., x ) .(1 2 nIn particular he solves the problem posed in Sheffi (2001). A high technology company sellsmedical devices made by a contract manufacturer in Malaysia. The Malaysian supplier delivers thedevices at $100 a piece and the devices are sold by the US company at $400 each. Fixed costs,including marketing and setup, have been estimated at $200 per device. The company estimatedthat there is a 1% probability that the Malaysian supplier will not be able to deliver for an extendedperiod (that was modeled as a single period in Albeniz’s paper). A local supplier can deliver thesame devices for $150 each.Using the previous notations we have:vv12= 100, w1= 150, w2= 0, A1= 0, A⎧0 w.p. α ⎫= ⎨ ⎬⎩1 w.p.1-α⎭2= 1 w.p.1Assuming that the demand is exponential with probability 1, Figure A.1 presents the optimalcapacities to reserve toward each supplier, according to the disruption probability.82