Question

A company can either produce the substrate for a semiconductor chip in-house (at its factory) or it can buy the substrate from a contractor. If the substrate is produced in-house, there is a $20 cost each time the machine is set up and each set-up requires 2.75 days. The production rate is 100 units per day. The cost of materials is $3 for each substrate produced. If the substrate is purchased from a contractor, then it will cost $3 for each substrate purchased, and an additional $15 for each order that is placed. The cost of maintaining the item in stock, whether is purchased or produced in-house, is $0.02 per substrate per day. The company estimates that it will need 26,000 substrates each year.

(c) Determine the maximum per order cost that Nave would be willing to pay so that ordering the substrate would be preferred to producing it in-house.

Answer 1

Case I - when the items are purchased in house.

demand per day =26000/365 =71.23

demand / production ratio = 71.23/100 = 0.7123

Economic production qty = [ 2 x annual demand x cost of order or set up / cost of holding per year x ( 1-d/p)]^1/2

= [ 2 x 26000 x20 / 0.02 x365 x (1 -0.723)]^1/2 = 704

number of orders = 26000/704 = 36.93

cost of ordering and storing = 20x36.93 + 704/2 x ( 1-0.7123) x 0.02 x365 = 738.6 + 739.2 = 1478

Case ii - When procured from contractor

EOQ = [ 2x 26000x15 / 0.02 x365]^1/2 = 327

Total cost = 327 /2 x0.02x365 + 26000x15 / 327 = 1193+1193 =2386

for holding cost to be 739 ( when the two costs are same) in case II, the EOQ is

739 = n/2 x ( 0.02x365) = 202.46

if cost of order is C,

(26000/203 ) x C = 739

C = 5.769