BUS404 Management Science

**Assignment #2: Inventory Control & Simulation Question**

The annual demand for widgets is 16,000. Widgets cost $7.00 each and the holding rate is 35%. Every time an order is placed, an order cost of $52.00 is incurred. One can assume a constant lead time of four days, and that there are 250 work days in the year.

a. What is the EOQ? b. What is the annual holding cost? c. What is the re-order point? d. What is the re-order point if demand is variable with a daily standard deviation of 15 units, and

if management have a policy that stock outs can occur, at most, on 15% of cycles? What is the safety stock?

e. What is the annual holding and order costs resulting from the policy in part (d)?

Simulation

Colin’s Coal is a West Coast business specializing in the supply of high grade coal to craft metalworkers who use old fashioned blacksmiths’ forges. Because of limited space for storage, Colin orders small batches of coal, each 12.0 tons whenever he needs to place orders. Problems arise because of the long and variable lead times for delivery. Daily demand for coal can be approximated by a normal distribution with a mean of 2.0 tons and a standard deviation of 1.0 tons truncated at 0.0 tons.

Lead times can be anywhere five to fifteen days with equal likelihood (i.e. uniformly distributed – assume integral days only). Because of uncertainties regarding lead times, Colin currently orders another batch of coal when his stock levels drop below 26 tons.

Hearing that you are an avid student of BUS404, Colin has requested you (for suitable remuneration of course) to construct a time slice simulation using slices of one day, to determine to probability of being stocked out for different policies of re-order point and order quantity. Construct a simulation to achieve the above. You may assume that the opening stock of coal is 30.0 tons. You may also assume that Colin places orders at the end of the day and that arrivals also occur at the end of the day.