Question

1. (Inventory Policy) Please determine an optimal inventory policy for following demand and cost parameters.

• Planning horizon                           One year
• Expected total annual demand 560,275 Units
• Fixed ordering cost                       700 USD
• Holding cost                                   20% of product cost
• Product cost                                   20 USD per unit
• Retail price                                     38 USD per unit
• Salvage value                                 15 USD per unit
• Lead time (fixed)                           3 days

1. What is the optimal order size Q?
2. Assuming the daily demand is constant and known, what is the reorder point?
3. Assuming the daily demand is uncertain with the standard deviation of 200, what is the optimal service level during the lead time?
4. In continuation of problem 3, then, what is the optimal reorder point and the safety stock? (note: this problem does not give an arbitrary target service level, you either need to assume your own or need to find out what is the optimal service level that will minimize the total cost)[1].
5. * If the planner totally disregards the uncertain nature of the daily demand and do not prepare the safety stock at all, then what will be the service level?
6. * During one week in November, due to the shipper’s company had a driver work strike, the “used to be very accurate and constant” lead time experienced a delay by additional two days. Of course, the inventory planner did not foresee this. In this case, with the typical safety stock level that is calculated in problem 4, how many percentage points will be dropping in the service level (due to the delay)? (hint: with the increased lead time, what changed?)

[1] Preferably, I hope that you can come up with the total cost minimizing service level based on the cost parameters provided. But if you have no clue, you can just assign your own arbitrary service level. It won’t impact following questions no matter what service level you choose.

Answer 1

ANSWER

Annual demand, D = 560,275
Fixed ordering cost, K = $700
Product cost, C = $20
Unit carrying cost, h = 20% of C = $4
Retail price, S = $38
Salvage Value, V = $15
Lead time, L = 3 days

1)

Optimal order size, Q = (2.D.K / h)^1/2 = SQRT(2*560275*700/4) = 14,003 units

2)

Average demand, d = 560275 / 365 = 1535 per day

Reorder point with no variability in demand = d.L = 1535 * 3 = 4,605 units

3)

Cost of underage, C_u = S - C = 38 - 20 = 18
Cost of overage, C_o = C - V = 20 - 15 = 5

So, optimal service level, F(z) = C_u / (C_o + C_u) = 18 / (5+18) = 0.7826

4)

Std. deviation of daily demand, σ = 200

F(z) = 0.7826; z = NORMSINV(0.7826) = 0.78

So, safety stock = z.σ.√L = 0.78*200*√3 = 270 units

Reorder point = d.L + Safety stock = 4605 + 270 = 4,875 units

5)

For safety stock = 0, z = 0 which means the service level is 50%.

6)

L = 5 days

Safety stock = 270 as before

So, z.σ.√L = 270

or, z = 270 / (200*√5) = 0.604

So, the service level, F(z) = NORMS DIST(0.604) = 0.7271, so the service level reduces from 78.25% to 72.71% i.e. 5.54%

_____________________________________________

If you have any query or any Explanation please ask me in the comment box, i am here to helps you.please give me positive rating.

*****************THANK YOU**************