Assignment:
Let the annual demand for a certain item be 1,000 units in the planning period. The holding costs are $5 per unit, and the cost of placing an order is $36 per order. The penalty cost for stock outs is $3 per unit and stock out. There is a demand for 55 units during the lead time with a probability of 20%. The demand is 60 with a probability of 0.4, it is 65 with a probability of 0.30, and it is 70 with a probability of 0.10.
(a) Calculate the expected demand during lead time.
(b) Determine the economic order quantity and the resulting reorder point.
(c) Find the order quantity and the reorder point by simultaneous computation.
(d) What is the buffer stock?
(e) What is the minimal expected total or ordering, holding, and penalty costs?
Provide complete and step by step solution for the question and show calculations and use formulas.