A company requires raw iron at a constant rate of 10,000 tonnes per year. Each time an order is placed, the order cost is K60.00. it cost K0.04/year to store a tonne of raw iron. Storages are not allowed. The actual cost of raw iron is K25 per tonne.
Part A
i. How large should each order be?
Q = NB; D=demand per period, C_{o }= ordering cost, C_{h} = unit holding cost over the period.
Data; D=10,000tonnes/year; C_{o}=K60.00; C_{h}=C*H = K0.04/year*K25/t = K1/t
H= holding cost = K0.04/yr
Q = = 1095.45 tonnes size of order.
ii. What should be the interval between each order?
Interval refers to the cycle time. So , T = = = 0.11 years
Nb; T=cycle time; Q=order size; D=demand
iii. How many orders are placed in each year?
N= = = 9 /year NB: N=number of orders. So 9 orders in a year.
iv. Calculate the total annual cost.
Total Annual Inventory Cost

Total Annual Holding Cost

Total Annual Ordering Costs

Total Procurement Costs

TC(Q) = + + D*C
NB; C = unit cost of raw iron.
TC(Q) = + + 10000t*K25/t
=K251,095.45
Part B
i. Illustrate part A inventory size model by a diagram.
Part C
i. It is learnt that the costs given in part (A) are incorrect. The true order cost is K30.0 and inventory cost is realy K0.05. compute the size of each order using these correct costs.
Ch = C*H = K0.05*25 = K1.25/t
Q = = = 692.82 tonnes
Part D
i. How much is the company losing due to imperfect cost information?
[this should be the difference between Part A and this part]. You really need calculated the total inventory costs for both parts.
Total Annual Inventory Cost

Total Annual Holding Cost

Total Annual Ordering Costs

Total Procurement Costs

TC(Q) = + + D*C
NB; C = unit cost of raw iron.
TC(Q) = + + 10000t*K25/t
= K250,866.03
Loss = incorrect cost information inventory costs – correct cost information inventory cost.
= K251,095.45 – K250,866.03
= K229.42
So the company makes a loss of K229.42 due to imperfect cost information.
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