Mulungushi village operates 52 weeks per year, 6 days per week and uses continuous review inventory system. It purchases bath soap for $5.65 per box. The following information is available about these boxes of soap.

Demand = 132 boxes/week

Order cost = $74/order

Annual holding cost = 24 percent of cost

Desired customer service level = 95 percent

Lead time = 3 weeks

Standard deviation of weekly demand = 25 boxes

Current on hand inventory is 159 boxes with no open orders or backorders

Required:

(a) What is the EOQ? What would be the average time between orders (in weeks)?

(b) What should the reorder point be?

(c) An inventory withdraw of 18 boxes was just made. Is it time to reorder?

(d) Mulungushi Village currently uses a lot of size of 600 boxes. What is the annual holding cost of this policy? Annual Ordering costs? Without calculating the EOQ, how can you conclude from these two calculations that the current lot size is too large?

(e) What would be the annual cost saved by shifting from the 600-box lot size to the EOQ?

(f) Suppose that the weekly demand forecast of 132 boxes is incorrect and actual demand averages only 83 boxes per week. how much higher will total cost be, owing to the distorted EOQ caused by this forecast error?

(g) Supposed that actual demand is 83 boxers but the ordering costs are cut to only $25 by using the internet to automate order placing. However the purchasing agent does not tell anyone, and the EOQ is not adjusted to reflect this reduction in ordering cost. How much higher will total costs be compared to what they could be if the EOQ were adjusted?

[50 marks]