# “ grg nonlinear ” B u s i n e s s F i n a n c e

“ grg nonlinear ” B u s i n e s s F i n a n c e

1. Consider the LL Bean example from the past two lectures. LL Bean is supplied by a manu- facturer to stock turtlenecks, and these turtlenecks are exclusively sold to LL Bean. For LL Bean, each turtleneck sells at the retail price \$25, and the salvage value is \$5. The manufacturer sells each item to LL Bean at a wholesale price (call this quantity w) and it costs the manufacturer \$7 to make each item. Instead of the standard wholesale contract, let us look at how the revenue sharing contract compares.
(a) Set the wholesale price to be \$8 and suppose LL Bean shares 20% of its revenue with the manufacturer (this revenue sharing includes both revenue from sales and revenue from salvage). What is the optimal order quantity for LL Bean?
(b) Set the wholesale price to be \$8 and suppose LL Bean shares 51% of its revenue with its manufacturer. What is the optimal order quantity for LL Bean?
(c) What conclusions can you draw about the performance of the supply chain in (a) and (b), compared to the wholesale contract when the wholesale price is set to maximize (i) the manufac- turer’s profit, (ii) the total supply chain profit?
Here is a guide on how to solve (a) and (b). You will need to set up an optimization problem to decide how many items LL Bean orders. The standard newsvendor model does not suffice be- cause the payment structure is different. LL Bean’s objective is to maximize its profit, its decision is the order quantity. Open up “newsvendorCalculator.xls”, and clearly define these items. Make sure that “Is the order quantity user-defined” is set to 1 (yes), and set user-defined order quantity to be 12000 (this part just gives the computer a place to start searching). Finally open up Solver, enter in your objective and decision variables, and under solving method make sure that “GRG Nonlinear” is selected.