Operations Management: Sustainability and Supply Chain Management (12th Edition)
Operations Management: Sustainability and Supply Chain Management (12th Edition)
12th Edition
ISBN: 9780134130422
Author: Jay Heizer, Barry Render, Chuck Munson
Publisher: PEARSON
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Chapter D, Problem 12P

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••• D.12 The wheat harvesting season in the American Midwest is short, and farmers deliver their truckloads of wheat to a giant central storage bin within a 2-week span. Because of this, wheat-filled trucks waiting to unload and return to the fields have been known to back up for a block at the receiving bin. The central bin is owned cooperatively, and it is to every farmer’s benefit to make the unloading/storage process as efficient as possible. The cost of grain deterioration caused by unloading delays and the cost of truck rental and idle driver time are significant concerns to the cooperative members. Although farmers have difficulty quantifying crop damage, it is easy to assign a waiting and unloading cost for truck and driver of $18 per hour. During the 2-week harvest season, the storage bin is open and operated 16 hours per day, 7 days per week, and can unload 35 trucks per hour according to an exponential distribution. Full trucks arrive all day long (during the hours the bin is open) at a rate of about 30 per hour, following a Poisson pattern. To help the cooperative get a handle on the problem of lost time while trucks are waiting in line or unloading at the bin, find the following:

  1. a. The average number of trucks in the unloading system
  2. b. The average time per truck in the system
  3. c. The utilization rate for the bin area
  4. d. The probability that there are more than three trucks in the system at any given time
  5. e. The total daily cost to the farmers of having their trucks tied up in the unloading process
  6. f. As mentioned, the cooperative uses the storage bin heavily only 2 weeks per year. Farmers estimate that enlarging the bin would cut unloading costs by 50% next year. It will cost $9,000 to do so during the off-season. Would it be worth the expense to enlarge the storage area?
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QUESTION 3a. Delightful Coffee Limited (DCLL) purchases coffee from Hopeful Harvest Plantations (HHP)in Santa Cruz, Trinidad. HHP sells coffee at four (4) different prices, depending on the size ofthe order, as shown in Table 3 (below):Table 3. Hopeful Harvest Plantations - Coffee pricesWeight of Coffee Price ($USD)Less than 45 kilograms $18 per kilogram45 to 449 kilograms $17 per kilogram,450 to 1000 kilograms $16 per kilogramMore than 1000 kilograms $15 per kilogramThe cost to place an order at DCLL is $50. Annual demand is 4,500 units. The holding (orcarrying) cost is 20 percent of the material price. (i) Calculate the EOQ at each Price Break.
QUESTION 3a. Delightful Coffee Limited (DCLL) purchases coffee from Hopeful Harvest Plantations (HHP)in Santa Cruz, Trinidad. HHP sells coffee at four (4) different prices, depending on the size ofthe order, as shown in Table 3 (below):Table 3. Hopeful Harvest Plantations - Coffee pricesWeight of Coffee Price ($USD)Less than 45 kilograms $18 per kilogram45 to 449 kilograms $17 per kilogram,450 to 1000 kilograms $16 per kilogramMore than 1000 kilograms $15 per kilogramThe cost to place an order at DCLL is $50. Annual demand is 4,500 units. The holding (orcarrying) cost is 20 percent of the material price. (i) Calculate the EOQ at each Price Break and Indicate which EOQs are feasible and those which are not feasible. Please answer the above question

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