“That’s an interesting proposal, Ray, but I’ll have to compare it with several others that we’ve received recently and get back to you,” Archibald Edwards said as he escorted the freight sales representative for Banner Freightways to the door of his office.

For the first time in several weeks, Edwards, Traffic Manager for DR Corporation (DRC), had an opportunity early in March of 2009 to ponder several of the best proposals he had received for the transportation of major appliance motors to the Harrisburg, Pennsylvania manufacturing plant operated by DRC, a manufacturer of a line of major appliances for sale nationally.

Among these was a proposal from the Northeastern Railroad to haul motors in piggybacked trailers on flatcars from DRC’s sole supplier, Americon Electric in St. Louis, to Harrisburg for a rate of $13 per hundredweight with a 20,000-pound minimum on each shipment.1 This contrasted with a competing offer by Trans-Eastern Trucking Company, received several weeks earlier, to provide service on the basis of a 10,000-pound minimum and a rate of $15 per hundredweight.

Both of these offers could be compared with DRC’s current practice of shipping motors by Banner on a sliding rate basis of $16 per hundredweight for all shipments totaling less than 15,000 pounds (with a 15,000 pound minimum), $12 per hundredweight for weights over 15,000 pounds and up to 25,000 pounds, and $8 per hundredweight for weights over 25,000 and up to 40,000 pounds on a single shipment. Banner’s freight sales representative had just indicated that Banner would be willing to lower its incremental rate on larger shipments to $6 per hundredweight for weights on each shipment in excess of 25,000 pounds.

In addition, Edwards had on his desk a proposal from his transportation department advocating the creation of a private trucking operation to haul the motors, involving the acquisition and operation of a truck capable of hauling up to fifty 40,000 pound loads each per year. The tractor/trailer combination was anticipated to require total annual operating costs, including depreciation as well as additional administrative overhead, of approximately $250,000. The proposal noted that DRC could provide no backhauls for the return trip to St. Louis, but that it might be possible for DRC to solicit backhaul loads from other shippers if it were to purchase and operate its own trucks.

DRC’s motors were purchased on the basis of an annual agreement calling for a minimum volume of 100,000 motors at a price of $480 per motor. Currently, DRC’s requirements were for about 120,000 motors, averaging about 10 pounds each in weight, each year. Demand had been relatively constant for several years. During the past year, DRC’s shipments had averaged 3,000 motors each. It was estimated that unloading costs for the various carriers would be approximately comparable. DRC’s warehouse in Harrisburg could accommodate as many as 5,000 motors. The company’s purchasing department estimated that the cost to process an order to Americon was approximately $80 each, including clerical and expediting costs. The Controller had estimated that the company’s annual cost of carrying inventory, figured on the average value of product in inventory, was 12.5% (including 5% for the average cost of money and the remaining 7.5% for the costs of insurance, taxes, and product obsolescence). Typically, piggyback shipments had required five days’ total transit time from St. Louis to Harrisburg for other DRC components. All of the trucking companies offered a roughly comparable three-day service. The internal private trucking proposal assumed a three-day one-way haul.

According to the case above,

Assume the company operated 250 days per year, expects to use 120,000 units per year and uses a perpetual review inventory control system. Assume further they use Banner Freightways which has an average transit time of 3 days with a standard deviation of 2 days, and daily demand is normally distributed with a standard deviation of 50 units. The unit cost continues to be $480. The annual cost of carrying inventory has been recalculated to be 2% per month of the value of the part.

A) Calculate the Economic Order Quantity (EOQ)

B) Calculate the necessary safety stock to cover 98% of the replenishment cycles.

C) Assume North Eastern has an average lead time of 5 days with a 4 day standard deviation. How much lower should its rate be compared to Banner’s in order to offset the service differences between the two carriers?