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An appliance manufacturer has a plant near Toronto that receives small electric motors from a manufacturer located in Winnipeg. The demand for motors is 126,000 units per year. The cost of each motor is $130. The motors are purchased in lots of 3,700 units. The ownership of motors transfers to the appliance manufacturer in Winnipeg. The question is which mode of transportation, truck or train, the appliance manufacturer should use to bring the motors from Winnipeg to Toronto. The railroad company charges $3 per motor, and it takes approximately seven days by train. The trucking company charges $6 per motor, but it takes only three days. The appliance manufacturer will keep 1,300 units as safety stock if a truck is used and 3,000 units as safety stock if a train is used for transportation. Assume 365 days per year. If the holding cost rate is 22 percent of unit cost per year, which mode of transportation will minimize total transportation and in-transit and safety holding cost? Hint: The value of a motor in Toronto for calculating the safety stock holding cost is $130 plus cost of freight per unit.

Question

An appliance manufacturer has a plant near Toronto that receives small electric motors from a manufacturer located in Winnipeg. The demand for motors is 126,000 units per year. The cost of each motor is 130.Themotorsarepurchasedinlotsof3,700units.TheownershipofmotorstransferstotheappliancemanufacturerinWinnipeg.Thequestioniswhichmodeoftransportation,truckortrain,theappliancemanufacturershouldusetobringthemotorsfromWinnipegtoToronto.Therailroadcompanycharges130. The motors are purchased in lots of 3,700 units. The ownership of motors transfers to the appliance manufacturer in Winnipeg. The question is which mode of transportation, truck or train, the appliance manufacturer should use to bring the motors from Winnipeg to Toronto. The railroad company charges 3 per motor, and it takes approximately seven days by train. The trucking company charges 6permotor,butittakesonlythreedays.Theappliancemanufacturerwillkeep1,300unitsassafetystockifatruckisusedand3,000unitsassafetystockifatrainisusedfortransportation.Assume365daysperyear.Iftheholdingcostrateis22percentofunitcostperyear,whichmodeoftransportationwillminimizetotaltransportationandintransitandsafetyholdingcost?Hint:ThevalueofamotorinTorontoforcalculatingthesafetystockholdingcostis6 per motor, but it takes only three days. The appliance manufacturer will keep 1,300 units as safety stock if a truck is used and 3,000 units as safety stock if a train is used for transportation. Assume 365 days per year. If the holding cost rate is 22 percent of unit cost per year, which mode of transportation will minimize total transportation and in-transit and safety holding cost? Hint: The value of a motor in Toronto for calculating the safety stock holding cost is 130 plus cost of freight per unit.

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Solution

To solve this problem, we need to calculate the total cost for both modes of transportation, including the transportation cost, in-transit holding cost, and safety stock holding cost.

  1. Calculate the transportation cost:

    • For the train: 3/motor126,000motors/year=3/motor * 126,000 motors/year = 378,000/year
    • For the truck: 6/motor126,000motors/year=6/motor * 126,000 motors/year = 756,000/year
  2. Calculate the in-transit holding cost:

    • The in-transit holding cost is the cost of holding inventory while it is being transported. This is calculated by multiplying the unit cost (including freight), the holding cost rate, and the transit time divided by the number of days in a year.
    • For the train: (130/motor+130/motor + 3/motor) * 22% * (7 days / 365 days) * 126,000 motors/year = $25,358/year
    • For the truck: (130/motor+130/motor + 6/motor) * 22% * (3 days / 365 days) * 126,000 motors/year = $12,679/year
  3. Calculate the safety stock holding cost:

    • The safety stock holding cost is the cost of holding extra inventory as a buffer against variability in demand and lead time. This is calculated by multiplying the unit cost (including freight), the holding cost rate, and the number of units in safety stock.
    • For the train: (130/motor+130/motor + 3/motor) * 22% * 3,000 motors = $87,780/year
    • For the truck: (130/motor+130/motor + 6/motor) * 22% * 1,300 motors = $39,286/year
  4. Add up all the costs to get the total cost for each mode of transportation:

    • For the train: 378,000/year+378,000/year + 25,358/year + 87,780/year=87,780/year = 491,138/year
    • For the truck: 756,000/year+756,000/year + 12,679/year + 39,286/year=39,286/year = 807,965/year

Therefore, the appliance manufacturer should use the train to minimize total transportation and in-transit and safety holding cost.

This problem has been solved

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