TCX Ine, is an Indian electronics system integrator, currently developing a new product as part of their annual generational upgrades. Owing to their long business history, they intend to work with Deltic, Ine, as the supplier of the main hardware for this product. Deltic sells this component for $$(90$ Vs$)$ per unit with a lead time of $4$ months. Assume Deltic covers all transportation and related processing until delivery.

TCX$\text{'}$s demand forecast for the next year is a normal distribution with mean $360$ x $(10+$ Vs$)$ and standard deviation V$/5.$ TCX sells each unit, after integrating their proprietary software, for $ $135,$ Assume that TCX uses an annual holding cost rate of V$,\%,$ and any leftover units can be sold for $ $30$ on average. Assume also that Deltic's gross margin for this component is $45\%$ of its selling price.

$1)[16)$ Due to the long lead time, TCX is planning on a single order from Deltic for their needs in the next year.

Determine their optimal order quantity and the resulting expected annual profits for both TCX and Deltic.

Suppose the supply chain manager at TCX is considering an online electronic component supplier, ATBC, to procure this component from. ATEC's main value proposition is that they offer $100\%$ in$-$stock probability with

$5-$day delivery on all TCX orders, regardless of their quantity and time. TCX promises a $2-$week lead time to their clients, so this highly reactive capacity at ATEC would enable TCX to fulfill all their orders on time.

The downside is that ATEC's delivered unit price is $ $88.$

Concerned that they would lose some business with TCX$,$ Deltic offers two proposals. According to the first proposal, TCX and Deltic would keep working the same way, but Deltic would deliver a midseason second order with no price increase. According to the second proposal, TCX and Deltic would set up a periodic review replenishment system with a $4-$month reorder cycle.

$2)[60]$ Evaluate the alternatives below $($on the basis of annual profits$)$ and identify the best one for TCX:

a$)[6]$ Cut ties with Deltic, and procure the component only from ATEC.

b$)[18]$ Use both: A single pre$-$season order from Deltic, and then supply from ATEC.

c$)[19]$ Work only with Deltic, by using their midseason $2$nd replenishment as well. In this case, assume TCX$\text{'}$s demand forecast would not improve during the season, due to the long lead time.

d$)[17]$ Work only with Deltic, by setting up a periodic review system as described above. Note that you need to calculate annual profits for TCX$,$ not only costs.

To establish a even stronger ties, Deltic also intends to offer a supply chain coordinating contract that guarantees TCX the highest profit they would make in question $(2),$ while maximizing their own profit at the same time. According to the contract, TCX would have to use Deltic as the only supplier for this component.

$3)[13]$ What is the maximum expected profit Deltic can possibly obtain with a contract as described above.

$4)[8]$ Write the conditions for a coordinating buyback contract that achieves Deltic's goals above.

$5)[8)$ Write the conditions for a coordinating revenue$-$sharing contract that achieves Deltic's goals above.