of steel i.e., they have two products they purchase and must have shipped to the
ID: 2578849 • Letter: O
Question
of steel i.e., they have two products they purchase and must have shipped to them). Over the course of a year, the company uses 3,285,000 Ibs of Grade 1 steel and 365,000 lbs of Grade 2 steel. Grade 1 steel costs $0.01 per lb and Grade 2 steel costs $10 per lb. NOTE: These are the costs to purchase the steel, NOT transportation cost. Holding costs at the production facility are 25% of the purchase cost per lb (i.e., each grade of steel has its own holding cost). As per their contract with the supplier, the production facility owns the steel in transport and therefore the company assesses these holding costs during transportation as well. Finally, assume that any shipment you receive contains a % of grade 1 and 2 steel that is equal to their respective %s of annual demand. The production facility is reviewing a few options of transport for their steel Option 1: Ship by rail with carrier 1 In this option, one train consists of a minimum of 30 cars up to a maximum of 90 cars. Each car has a capacity of 10,000 lbs. Given the distance from the production facility to the supplier, to ship steel, it will cost $15,000 as a fixed fee for each train plus $400 per car that is on the train. This method results in a 15 day lead time. Option 2: Ship by truck with carrier 2 With this carrier, you have 2 choices - Use their fleet of small trucks and ship 10,000-40,000 lbs at a time for S0.09 per lb. In addition, you will be assessed a cost of S600 per truck used. - Use their fleet of large trucks and ship 40,000 to 60,000 lbs at a time for $0.06 per lb. In addition, you will be assessed a cost of $900 per truck used. a. What is the minimum cost that Option 1 can provide (include cost to transport and cost to hold inventory)? b. What is the minimum cost that Option 2 can provide with the small fleet of trucks (include cost to transport and cost to hold inventory)? c. What is the minimum cost that Option 2 can provide with the large fleet of trucks (include cost to transport and cost to hold inventory)? d. What is your overall recommendation to minimize total cost? (Include mode of transport, size details of each shipment and total cost) e. Assume that you must hold enough safety stock to cover demand over the lead time. What is the cheapest option now? (Include total cost, size details of the shipment and mode) f. In this problem, it is necessary to check both the minimum and maximum for all the weight ranges Why must we check both here?Explanation / Answer
Given
Grade 1 steel
3285000
lbs
$ 0.01
Grade 2 steel
365000
lbs
$ 10.00
(i)
Minimum cost that option I can provide
Purchase Cost
Grade 1 steel
$ 32,850
Grade 2 steel
$ 3,650,000
$ 3,682,850
Transportation Cost
(working Notes)
$ 221,000
Holding Cost(purchases)
(3682850*25%)
$ 920,713
Holding Cost(transportation)
(221000*15/365)*25%
$ 2,271
Total Cost
$ 4,826,833
Assumed that the holding cost in respect of transportation cost @25%
Working Notes: Transportation Cost
Total demand of steel in Lbs
Grade 1 steel
3,285,000
Grade 2 steel
365,000
3,650,000
No. of Cars required
365
(3650000/10000)
No. of Trains required
5
(365/90)
Transportation cost
Fixed cost
(5*15000)
$ 75,000
variable costs - Cars
(365*400)
$ 146,000
$ 221,000
(ii)
Minimum cost that option 2 can provide with small fleet of trucks
Purchase Cost
Grade 1 steel
$ 32,850
Grade 2 steel
$ 3,650,000
$ 3,682,850
Transportation Cost
(working Notes)
$ 383,700
Holding Cost(purchases)
(3682850*25%)
$ 920,713
Holding Cost(transportation)
(383700*15/365)*25%
$ 3,942
Total Cost
$ 4,991,205
Assumed that the holding cost in respect of transportaion cost @25%
Working Notes: Transportation Cost
Total demand of steel in Lbs
Grade 1 steel
3,285,000
Grade 2 steel
365,000
3,650,000
No. of Trucks required
91.25
(3650000/40000)
Transportation cost
Fixed cost
(92*600)
$ 55,200
variable costs - lbs
(3650000*0.09)
$ 328,500
$ 383,700
(iii)
Minimum cost that option 2 can provide with large fleet of trucks
Purchase Cost
Grade 1 steel
$ 32,850
Grade 2 steel
$ 3,650,000
$ 3,682,850
Transportation Cost
(working Notes)
$ 365,100
Holding Cost(purchases)
(3682850*25%)
$ 920,713
Holding Cost(transportation)
(365100*15/365)*25%
$ 3,751
Total Cost
$ 4,972,414
Assumed that the holding cost in respect of transportation cost @25%
Working Notes: Transportation Cost
Total demand of steel in Lbs
Grade 1 steel
3,285,000
Grade 2 steel
365,000
3,650,000
No. of Trucks required
60.83
(3650000/60000)
Transportation cost
Fixed cost
(61*600)
$ 36,600
variable costs - lbs
(3650000*0.09)
$ 328,500
$ 365,100
(iv)
Recommendation to minimize total cost: Since the total cost is lower for Option 1 i.e., Ship by rail, hence Option 1 shall be exercised
Mode of Transport
Size Details
Total Cost
Option 1
Rail
10000 lbs
$ 4,826,833
Option 2 small fleet
Trucks
10000-40000 lbs
$ 4,991,205
Option 2 large fleet
Trucks
40000-60000 lbs
$ 4,972,414
(v)
Cheapest Option where there is a need to hold safety stock to cover the demand during lead time
Mode of Transport
Size Details
Cost
Holding cost for keeping safety stock
Total Cost
Option 1
Rail
10000 lbs
$ 4,826,833
$ 37,838
$ 4,864,671
Option 2 small fleet
Trucks
10000-40000 lbs
$ 4,991,205
$ -
$ 4,991,205
Option 2 large fleet
Trucks
40000-60000 lbs
$ 4,972,414
$ -
$ 4,972,414
Since the total cost is lower for Option 1 i.e., Ship by rail, hence Option 1 shall be exercised
(vi)
It is necessary to check Minimum and Maximum weight ranges, since the there are two types of transportation costs
i.e., Fixed cost per Truck or Rail and Variable cost per car / Lbs
In order to minimise the number of trucks or rails, maximum capacity shall be taken for each truck/rail and
Minimum weight is useful to determine whether a perticular Rail or Truck can be run
Given
Grade 1 steel
3285000
lbs
$ 0.01
Grade 2 steel
365000
lbs
$ 10.00
(i)
Minimum cost that option I can provide
Purchase Cost
Grade 1 steel
$ 32,850
Grade 2 steel
$ 3,650,000
$ 3,682,850
Transportation Cost
(working Notes)
$ 221,000
Holding Cost(purchases)
(3682850*25%)
$ 920,713
Holding Cost(transportation)
(221000*15/365)*25%
$ 2,271
Total Cost
$ 4,826,833
Assumed that the holding cost in respect of transportation cost @25%
Working Notes: Transportation Cost
Total demand of steel in Lbs
Grade 1 steel
3,285,000
Grade 2 steel
365,000
3,650,000
No. of Cars required
365
(3650000/10000)
No. of Trains required
5
(365/90)
Transportation cost
Fixed cost
(5*15000)
$ 75,000
variable costs - Cars
(365*400)
$ 146,000
$ 221,000
(ii)
Minimum cost that option 2 can provide with small fleet of trucks
Purchase Cost
Grade 1 steel
$ 32,850
Grade 2 steel
$ 3,650,000
$ 3,682,850
Transportation Cost
(working Notes)
$ 383,700
Holding Cost(purchases)
(3682850*25%)
$ 920,713
Holding Cost(transportation)
(383700*15/365)*25%
$ 3,942
Total Cost
$ 4,991,205
Assumed that the holding cost in respect of transportaion cost @25%
Working Notes: Transportation Cost
Total demand of steel in Lbs
Grade 1 steel
3,285,000
Grade 2 steel
365,000
3,650,000
No. of Trucks required
91.25
(3650000/40000)
Transportation cost
Fixed cost
(92*600)
$ 55,200
variable costs - lbs
(3650000*0.09)
$ 328,500
$ 383,700
(iii)
Minimum cost that option 2 can provide with large fleet of trucks
Purchase Cost
Grade 1 steel
$ 32,850
Grade 2 steel
$ 3,650,000
$ 3,682,850
Transportation Cost
(working Notes)
$ 365,100
Holding Cost(purchases)
(3682850*25%)
$ 920,713
Holding Cost(transportation)
(365100*15/365)*25%
$ 3,751
Total Cost
$ 4,972,414
Assumed that the holding cost in respect of transportation cost @25%
Working Notes: Transportation Cost
Total demand of steel in Lbs
Grade 1 steel
3,285,000
Grade 2 steel
365,000
3,650,000
No. of Trucks required
60.83
(3650000/60000)
Transportation cost
Fixed cost
(61*600)
$ 36,600
variable costs - lbs
(3650000*0.09)
$ 328,500
$ 365,100
(iv)
Recommendation to minimize total cost: Since the total cost is lower for Option 1 i.e., Ship by rail, hence Option 1 shall be exercised
Mode of Transport
Size Details
Total Cost
Option 1
Rail
10000 lbs
$ 4,826,833
Option 2 small fleet
Trucks
10000-40000 lbs
$ 4,991,205
Option 2 large fleet
Trucks
40000-60000 lbs
$ 4,972,414
(v)
Cheapest Option where there is a need to hold safety stock to cover the demand during lead time
Mode of Transport
Size Details
Cost
Holding cost for keeping safety stock
Total Cost
Option 1
Rail
10000 lbs
$ 4,826,833
$ 37,838
$ 4,864,671
Option 2 small fleet
Trucks
10000-40000 lbs
$ 4,991,205
$ -
$ 4,991,205
Option 2 large fleet
Trucks
40000-60000 lbs
$ 4,972,414
$ -
$ 4,972,414
Since the total cost is lower for Option 1 i.e., Ship by rail, hence Option 1 shall be exercised
(vi)
It is necessary to check Minimum and Maximum weight ranges, since the there are two types of transportation costs
i.e., Fixed cost per Truck or Rail and Variable cost per car / Lbs
In order to minimise the number of trucks or rails, maximum capacity shall be taken for each truck/rail and
Minimum weight is useful to determine whether a perticular Rail or Truck can be run
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