Question

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).

Answer 1

a) Long run average inventory shall be the average of highest and lowest level of inventory. The lowest level cannot be below 300 units and highest assuming to be 1200 So we hve,

(1200 + 300)/2 = 1500 / 2 = 750 units

b) the order quantity for each order is 500 and lead time is 9 days, each time at level 1200 in inventory 2 orders would be made so at he 9th day the inventory would go up by 1000

at t=0 we have 1400

at t=1 we have 1300

at t=2 we have 1200, therefore 2 orders placed for 500 each to be delivered on t= 10

at t=10 we have 400 + 1000 = 1400

c) No. of orders outstanding at t=10 would be 0 as both orders would be delivered at t=10

d) zero as 2 orders would be placed at once.