Question

Flex Inc., an electronic system integrator, developed a new product, which consists of a key component sourced from a supplier and the software developed in house. For the coming selling season, Flex’s demand forecast for the integrated system is normally distributed with a mean of 1000 and standard deviation of 600. Flex incurs no costs associated with software integration. It sells the integrated system at $121 per unit to several of its key customers. Flex can also dump any integrated systems in a secondary electronic market for $50 per unit.

Flex can buy the key component from Solectric at $72 per unit. However, due to long lead time and short product life cycle, Flex has only one opportunity to place order with Solectric prior to the beginning of its selling season.

Another company, XE, can also supply the key component to Flex for $83.5 per unit. XE’s main value proposition is that it offers one-day delivery on any order no matter when the orders are submitted. Since the software integration can be done in one day and Flex promises one-week of lead time for its customers, the one-day lead time from XE will allow Flex to operate with make-to-order production system (i.e., Flex can take customer order first, then order from XE).

9.    If Flex sources exclusively from Solectric, what is the optimal order quantity?

10. If Flex decide to source from Solectric first, then from XE if the demand surpass the supply from Solectric, how should Flex place its order with both suppliers?          

Answer 1

9)

Underage or shortage cost, Cu = 121 - 72 = 49

Overage or excess cost, Co = 72-50 = 22

Critical fractile = Cu/(Cu+Co) = 49/(49+22) = 0.6901

z = NORMSINV(0.6901) = 0.49625

Optimal order quantity to buy from Solectric = mean demand + z * std dev of demand

= 1000 + 0.49625*600

= 1298

10)

Underage or shortage cost, Cu = 83.5 - 72 = 11.5

Overage or excess cost, Co = 72-50 = 22

Critical fractile = Cu/(Cu+Co) = 11.5/(11.5+22) = 0.3433

z = NORMSINV(0.3433) = -0.4035

Optimal order quantity to buy from Solectric = mean demand + z * std dev of demand

= 1000 - 0.4035*600

= 758

For z=-0.4035, L(z) = 0.6327 (taken from standard normal loss table)

Expected shortage, L = std dev of demand * L(z) = 600*0.6327 = 380

Optimal order quantity to buy from XE = 380

Flex should buy 758 from Solectric and 380 from XE