Question

The Try to Have Just One' (THJO) sunflower seed company roasts and seasons sunflower seeds (in shell). For their production, they require a specific type of oil that they source from a local supplier; the leadtime on orders is 3 days. The oil comes in a box that is lined with plastic, with each box of oil costing THJO $48. Demand averages 50 boxes per day, with a standard deviation of 24.45 (assume that they run production 365 days/year). Ordering is done by a Procurement Specialist working at THJO and requires checking with the Production department to see if there are any plans that might cause a sudden change in demand, creating a purchase order (PO), transmitting the purchase order by email and following up with the supplier, and then processing the product receipt and invoice when the product arrives-a recent study by the Procurement department estimates a total administrative cost of $40 per PO (independent of order quantity). The Accounting and Finance department has requested that a rate of 21% be used when determining holding costs of inventory (this includes cost of capital, insurance, variable storage, and other costs that vary with the amount of inventory on hand). (For the sake of this analysis, ignore seasonality in demand, and any quantity discounts or 8 transportation costs.) Currently, they order Q-300 when inventory reaches R-200 boxes. 1. 1] Diagram their current ordering policy in a "sawtooth" diagram that clearly labels the order quantity, reorder point, cycle stock, safety stock and lead time. Start time zero with 250 units on hand (so your first order will be placed at day 1).

Answer 1

Lead time (L) = 3 days

Average daily demand (d) = 50

Standard deviation of daily demand (sigmad) = 24.45

Number of working days = 365

Annual demand (D) = 365*50 = 18250

Price (P) = 48

Ordering cost (S) = 40

Inventory holding cost (H) = 0.21*48 = 10.08

1.

The sawtooth diagram is shown below

500 4 400 Order quantity ROP 200 Lead time 100 Safety stock 6 7 89 10 11 12 13 14

2.

The formulas

EOQ or Q = sqrt(2DS/H)

Annual ordering cost = DS/Q

Annual holding cost = HQ/2 + safety stock*H

Safety stock = ROP – daily demand*lead time (this means our current safety stock is 50)

Also

Ideal safety stock = z*sigmad*sqrt(L)

Now using these formulas we can calculate the values ( the two columns can be filled with the following info)

Current order quantity

Order quantity (Q)= 300

Annual ordering cost = 18250*40/300 = 2433.33

Annual holding cost = 10.08*300/2 + 50*10.08 = 2016

Total cost = 2433.33 + 2016 = 4449.33

Optimal order quantity

Order quantity (Q) = sqrt(2*18250*40/10.08) = 380.58 or 380 units

Annual ordering cost = 18250*40/380 = 1921.05

Annual holding cost = 10.08*380/2 + 50*10.08 = 2419.2 (assuming that we still maintain same safety stock)

Total cost = 1921.05 + 2419.2 = 4340.25

3.

Currently the safety stock is 50. This means the z value is

50 = z*24.45*sqrt(3)

Or, z = 1.18

This means the current service level is P(z = 1.18) = 0.8809 or 88.09%

If we want 97.5% service level then the z value will be 1.95

This means the safety stock should be 1.95*24.45*sqrt(3) = 82.57 or 83 units

At 97.5% service level the safety stock should be 83 and the reorder point should be 150+83 = 233 boxes.