Question

Lenovo uses two different types of processors for its laptops: single-core and dual-core. Lenovo sources these processors from three different suppliers. Demands for processors, purchase costs, and fixed ordering costs are as follows:

The inventory holding cost per unit per year is assumed to be 20% of the unit purchase cost for all processor types. Assume 365 days in a year.

(a) Answer the following

1. What is the optimal order quantity for each processor type?

2. What is the optimal total annual cost (inventory holding costs plus purchase costs plus fixed ordering costs) for each processor type?

(b) Supplier of the dual-core processor makes the following offer: Lenovo can order both processor types for a fixed ordering cost of 12000, of course if both processors are ordered at the same time. However purchase cost per unit for the single-core processor will increase to 81$/unit.

1. What is the optimal order quantity for each processor type?

2. What is the optimal total annual cost in this case?

3. Do you think that Lenovo should accept this offer?

Processor type	Demand (units/day)	Purchase cost ($/unit)	Fixed ordering cost ($)
Single-core	500	80	10000
Dual-core	1000	100	12000

Answer 1

a) If order separetley

The optimal order quantity for single core processor is 15105 units

The optimal order quantity for dual core processor is 20929 units

The optimum Total Annual Cost for single core processor is $14962493

The optimum Total Annual Cost for dual core processor is $36918569

The total cost of both the processor is $14962493+$36918569=$51881062

Calculation

b) If ordered together with fixed ordering cost 12000 and cost of single core is $81

The optimal order quantity for single core processor is 8691 units

The optimal order quantity for dual core processor is 17381 units

The optimum total cost of both the processor is $51778707.1

Calculation

Lenovo should accept this offer as the total annual cost is decreased by $102355 ($51881062-$51778707.1) if we order the items together