Consider an inventory system whereby an inventory replenishment order for Q units is placed whenever inventory reaches ROP units. The lead time for the order is LT days and daily demand is d units. Beginning on-hand inventory at time=0 is OH units.

Use these parameters:

Q = 500; ROP = 1,200; LT = 9; d = 100; OH = beginning on-hand inventory = 1,400.

and provide an answer for each of the following:

Long-run average inventory on-hand (note don't include the inventory in the first order cycle, since it depends on the beginning inventory, but determine what the long run average amount of on-hand inventory will be once order cycles and inventory amounts fall into a regular pattern): ___________

Inventory on hand at time=10: _________

Number of orders outstanding (in the pipeline but not yet received) at time=10 (your number will be 0,1,2, or 3): __________

Order cycle length (time between orders): ___________ days.

(Draw yourself a sawtooth diagram for analyzing this, like we did in class and posted in an example on Blackboard. The diagram "maps out" inventory at discrete points in time t=0, 1 day, 2 days, etc., as though demand occurs between two points in time and order placement and order receipt occur at a specific point in time. So, inventory at time 1 = starting on-hand inventory d units. If the result is equal to the reorder point (ROP), then an order for Q units should be placed at time 1 and will arrive at time 1+LT).