Question

HighMed, a manufacturer of medical equipment used in heart procedures, is located in Madison, Wisconsin, and its products are used by cardiologists all over North America. The medical equipment is not sold through purchasing agents but directly to doctors. HighMed currently divides the United States into 24 territories, each with its own sales force. All product inventories are maintained locally and replenished from Madison every four weeks using UPS. The average replenishment lead-time using UPS is one week. UPS charges at a rate of $0.60+0.40x, where x is the quantity shipped in pounds. The products sold fall into two categories - Highval and Lowval. Highval products weigh 0.20 pounds and cost $200 each. Lowval products weigh 0.06 pounds and cost $25 each. Weekly demand for Highval products in each territory is normally distributed, with a mean of H=2 with a standard deviation of H=5. Weekly demand for Lowval products in each territory is normally distributed, with a mean of L=20 with a standard deviation of L=5. HighMed maintains sufficient safety inventories in each territory to provide a cycle service level (CSL) of 0.997 for each product. Holding cost at HighMed is 20 percent. In addition to the current approach, the management team at HighMed is considering two other options:

Option A. Keep the current structure but replenish once every week rather that once every four weeks.

Option B. Eliminate inventories in the territories, aggregate all inventories in a finished-goods warehouse at Madison, and replenish the warehouse once a week. If inventories are aggregated at Madison, orders will be shipped using FedEx, which charges $5.10+0.50x per shipment, where x is the quantity shipped in pounds. The factory requires a one-week lead-time to replenish finished-goods inventories at the Madison warehouse. An average customer order is for one unit of Highval and 10 units of Lowval. What should HighMed do? (In order to analyze this, you need to compare the current situation, Option A and Option B).

Answer 1

Given :-

Average replenishment lead-time= 1 week

Quantity shipped= x pounds

L= 1 week

T=4 weeks

For HighVal products:

• Weight=0.2 pounds
• Cost= $200
• Weekly demand H=2 and H= 5

For LowVal products:

• Weight=0.06 pounds
• Cost= $25
• Weekly demand L=20 and L= 5

CSL=0.997

Holding Cost = 20%

UPS Lead time= 1 week

UPS charges=$ 0.6+0.4x

FedEx charges=$ 5.1+0.5x

Customers order 1 H + 10 L units

Solution:

Total Cost = Inventory Cost + Transportation Cost

1. For Current Scenario

Calculating Inventory Costs

A) For HighVal Product

Avg Lot size QH=Expected demand X Time = 2 unitsX 4= 8 units

Safety inventory ssH=F-1(CSL)T+L =F-1(0.997)4+1 = 30.7 units

Total HighVal inventory= QH/2+ssH =8/2+30.7=34.7 units

Total HighVal inventory for 24 territories = 24X 34.7 = 832.8 units

B) For LowVal Product

Avg Lot size QL=Expected demand X Time = 20unitsX 4= 80units

Safety inventory ssL=F-1(CSL)T+L =F-1(0.997)4+1 = 30.7 units

Total LowVal inventory= QL/2+ssL =80/2+30.7=70.7 units

Total LowVal inventory for 24 territories = 24X 70.7 = 1696.8 units

Average inventory holding cost=20% of ( HighVal inventory X $200 + LowVal inventory X $25 ) = 0.2X(832.8X200+1696.8X25) =$41796

Calculating Transportation Cost

Average weight of each order= 0.2X QH+0.06XQL=0.2 x 8 +0.06 X 80= 6.4 pounds

Shipping Cost per order= $0.6 +0.4 X 6.4 = $ 3.16

Annual Transportation Cost= $ 3.16 X 13 X 24= $ 985.92

Total Cost= $ 41796 +985.92 =$ 42781.92

Similarily for Option A and Option B

Reorder Interval= 1 week

Calculations for Option A and Option B

	Option A	Option B
HighVal Safety Inventory	466.3	95.2
HighVal Inventory	490.3	119.2
LowVal Safety Inventory	466.3	95.2
LowVal Inventory	706.3	335.2
Inventory Cost	23143.5	6444
Shipment size	2HighVal+20LowVal	1HighVal+10LowVal
Shipment weight	1.6	0.8

For Option A

Annual Transportation cost for option A =1547.52

Total Annual Cost =$ 24690.52

For Option

Average weight of each customer order=0.2*0.8+0.06*8 = 0.64 pounds

Shipping cost per customer= $ 5.1+0.5*0.64=$5.42

Number of customer orders per territory per week = 4

Total orders per year =4x52x24= 4992

Annual transportation cost=$ 5.42*4992=$27056.64

Total Cost =$27056.64+6444= $33500.64

The transportation cost increases in case of the change in shipment weight .Aggregating inventory will lead to a low transportation cost but is better option in case of large customer size in case the customer size is small disaggregartion is a better option.