a) Economic order quantity

Economic order quantity refers to the order quantity which minimizes the total inventory holdings and ordering costs. Economic Order Quantity is utilized only when demand for a product is regular over the year. New orders are only delivered fully when inventory comes to zero. There are a fixed costs for every order placed, not considering the number of units ordered. Also there is a cost associated with each unit held in storage. The required parameters to determine the solution of Economic Order Quantity are: purchase cost for each item, yearly demand, storage cost for each item per year and fixed cost to place an order. The number of times an order is placed affects the total cost.

Where A- demand for the cost

Cp – cost to place an order

Ch is cost to hold one unit

Therefore Economic Order Quantity = (((2*15000*75)/25))^{½}

= 90000^{½}

= 300

Therefore, EOQ= 300 units per order.

b) Annual Holding Cost

Holding cost refers to money that is spent to maintain and keep a stock of goods in the store. The holding cost include; materials, equipment, labor to operate the space, security, interest on money invested, insurance, and other direct expenses. Holding costs sometimes also incorporates opportunity cost, slowed introduction of improved items, and direct expenses.

Annual holding cost = Q/2*H

Where Q – number of pieces per order

Holding cost per unit

Therefore, Annual holding cost = (300/2)*25

Annual holding cost is = £3750

c) Annual Ordering cost

Ordering costs refers to costs which are associated when preparing a purchase order. These costs entail; telephone, cost of preparing purchase invoice, stationery, and salaries of purchasing clerks.

Annual Ordering Cost = C*D/Q

Where C – cost per order

D – Annual Demand

Q – Order size

Therefore

Annual Ordering Cost = 75 *15000/300

Annual Ordering cost =£3750

d) Reorder point

Reorder point refers to the level of inventory when an order has to be made with the usual suppliers to bring the inventory to the Economic Order Quantity. This occurs when the inventory level goes to zero. Reorder point is calculated as,

Reorder point = (2(annual usage units*order cost))/annual carrying cost per unit

=£ (2(15000*75)/25

=£2250000/25

= £90000

12.17

a) Optimal size of the production run

Production run refers to a group of good which are related or similar and are produced and are produced by specific group of processes, conditions or procedures.

Optimal production =√ ((2SD)/H) √P/ (p-u)

Where S – setup cost

D – Yearly demand

H – Holding cost

P – Production per day

U – Demand per day

= √ ((2*50*12000)/0.10) * √ (100)/(100-40)

=3464.10 * 1.29

= 4468.69

Optimal production size = 4468

b) Average Holding cost per year

Ordering costs refers to costs which are associated when preparing a purchase order. These costs entail; telephone, cost of preparing purchase invoice, stationery, and salaries of purchasing clerks.

Holding cost = (Q/2)H[1 – (d/p)

Where H, Q and P are as stated above and d is the demand rate

d = 12000/300

= 40

Therefore Holding cost = (4468/2)*0.1)[1 – 40/100]

= 223.4*0.6 =£ 134.04

c) Average setup cost per year

Setup cost refers to costs involved in setting up equipment required to manufacture the product or the costs involved in placing an order.

Setup cost per year = D*S/Q

=£12000*50/4468

Setup cost per year =£134.29

d) Total cost per year including cost of the lights

Total costs per year refer to all costs the company incurred during the annual production period.

Where TC -Total cost

TC = ((SD)/Q) + (HI_{max})/2

I_{MAX}= (p-u) d_{1}

d_{1 }= Q/P

d_{1= }4468/100

=44.68

I_{MAX} = (100 – 40)*44.68

=2680.8

Therefore

TC = 12000*50/4468 + 0.10*2680.8/2

=4468 + 134.04

=4602.04