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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