A company has orders for approximately $100,000$ units of a product that it can sell at

a price of $150\mathrm{.}00$ per unit. The company operates $300$ days per year. It costs $5\mathrm{.}00$

to store one unit of the product for one month. The company wants to decide between

outsourcing the production of the product and manufacturing it in$-$house.

Outsourcing Option: The cost of placing an order with the preferred supplier is

estimated as $200$ per order placed.

In$-$house Option: The company manufactures other products, and it must set up the

manufacturing system for a production order for the product, which costs $300.$ The

product can be produced at a rate of $600$ per working day.

$[$Please turn over and answer the questions on the next page$]$

MM$485$ Operations Research Methods

August$/$Resit Examinations $2021/2022$ Page $3$ of $11$

a$)$ For each option determine:

i$.$ The Economic Order Quantity $(0)(4$ Marks$)$

ii$.$ The annual cost of producing $0$ every time an order is placed, or a

production run is started. $(4$ Marks$)$

iii. The number of orders$/$production runs required each year $(2$ Marks$)$

iv$.$ The length of the cycle $($time between orders$/$production runs$)(2$ Marks$)$

b$)$ For the in$-$house option, how many days will each production run last?

$(1$ Mark$)$

c$)$ Which option is best for the company and why is its total annual cost lower?