1.4(E) In railroad operations there is substantial debate about train length. In a particular market longer...

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1.4(E) In railroad operations there is substantial debate about train length. In a particular market longer trains reduce crew costs. On the other hand, by operating more frequent, shorter trains, "railroads incur greater crew costs, but obtain better service and improved freight car utilization. Furthermore, short trains can be handled more easily at yards, at sidings, and on the line than long trains. In some instances, however, running more short trains could cause operating delays on congested portions of the system" (Martland, Assarabowski, and Mc- Carren 1977). Consider the situation of a 200-mile segment of rail line on which the present operating policy is to run two trains per day with 90 cars each, or a total capacity of 180 cars per day: TO = (Qº, Lº) (2, 90), where = Q = frequency (trains per day), L = train length (cars per train). The cost per train in dollars is (after Martland 1977) CTRAIN (Q, L) = 2.40+ (480 + 1.334 + 0.0044²) or, for a day's schedule of Q trains, CDAY (Q, L) = QCTRAIN = 2.40L + Q(480+ 1.33L + 0.004/²). The total capacity available in cars per day, Vc, is Vc = QL. Operating management believes that the following demand function applies in this corridor (VD is demand volume): °(&)²: VD(Q, L) 180 a "best estimate" of ß is 0.5. Management's objective is to increase net revenue, INR, where /NR = /GR - CDAY and gross revenue, /GR, is a function of equilibrium volume V₁ and price P: /GR = VEP. At present P = $15 per carload for freight over this segment. a. Consider the possibility of adding 1, 2, or 3 more trains per day, maintaining the same train lengths. Predict the equilibrium flows and the corresponding costs and revenues for these strategies. Which of these strategies (Tº, T¹, T², T³) would you recommend to management, and why? b. If your objective were maximum service to users, which would you recommend, and why? Compare with your answer to part a and discuss. c. For a given frequency, what are the advantages and disadvantages of varying train lengths? If you knew that for a frequency Qi the de- mand would be Vi, what train length would you recommend? = = d. Consider these alternative strategies: T4 = (Q4 = 3, L4 :75), T5 (4, 75), T6=(5, 75), T² = (4, 70), T8 (5, 70), T⁹ = (5, 60). Which of these would you recommend from the operator's perspective? for Q = 4? for Q = 5? Which of the ten strategies Tº-T⁹ would you recommend from the operator's perspective ? from the user's perspec- tive ? Discuss. e. Using your result to part c, find the train length LOPT that is best from the operator's perspective for each frequency Q = 3, 4, 5, and predict the impacts of the corresponding strategies. Plot the results on axes defined by VD and /NR and discuss. Which would be best from the operator's perspective? from the user's perspective? Why? Which would you recommend, and why? f. How might the results change for ß = 0.2? = 0.8? (Check only for L = LOPT for this range of frequencies.) g. Critique the assumptions (implicit and explicit) of this formulation of the problem: Under what conditions, and to what extent, do you think they would be reasonable? (For example, what do you think of the explicit assumption that demand is independent of the train length ?) 1.4(E) In railroad operations there is substantial debate about train length. In a particular market longer trains reduce crew costs. On the other hand, by operating more frequent, shorter trains, "railroads incur greater crew costs, but obtain better service and improved freight car utilization. Furthermore, short trains can be handled more easily at yards, at sidings, and on the line than long trains. In some instances, however, running more short trains could cause operating delays on congested portions of the system" (Martland, Assarabowski, and Mc- Carren 1977). Consider the situation of a 200-mile segment of rail line on which the present operating policy is to run two trains per day with 90 cars each, or a total capacity of 180 cars per day: TO = (Qº, Lº) (2, 90), where = Q = frequency (trains per day), L = train length (cars per train). The cost per train in dollars is (after Martland 1977) CTRAIN (Q, L) = 2.40+ (480 + 1.334 + 0.0044²) or, for a day's schedule of Q trains, CDAY (Q, L) = QCTRAIN = 2.40L + Q(480+ 1.33L + 0.004/²). The total capacity available in cars per day, Vc, is Vc = QL. Operating management believes that the following demand function applies in this corridor (VD is demand volume): °(&)²: VD(Q, L) 180 a "best estimate" of ß is 0.5. Management's objective is to increase net revenue, INR, where /NR = /GR - CDAY and gross revenue, /GR, is a function of equilibrium volume V₁ and price P: /GR = VEP. At present P = $15 per carload for freight over this segment. a. Consider the possibility of adding 1, 2, or 3 more trains per day, maintaining the same train lengths. Predict the equilibrium flows and the corresponding costs and revenues for these strategies. Which of these strategies (Tº, T¹, T², T³) would you recommend to management, and why? b. If your objective were maximum service to users, which would you recommend, and why? Compare with your answer to part a and discuss. c. For a given frequency, what are the advantages and disadvantages of varying train lengths? If you knew that for a frequency Qi the de- mand would be Vi, what train length would you recommend? = = d. Consider these alternative strategies: T4 = (Q4 = 3, L4 :75), T5 (4, 75), T6=(5, 75), T² = (4, 70), T8 (5, 70), T⁹ = (5, 60). Which of these would you recommend from the operator's perspective? for Q = 4? for Q = 5? Which of the ten strategies Tº-T⁹ would you recommend from the operator's perspective ? from the user's perspec- tive ? Discuss. e. Using your result to part c, find the train length LOPT that is best from the operator's perspective for each frequency Q = 3, 4, 5, and predict the impacts of the corresponding strategies. Plot the results on axes defined by VD and /NR and discuss. Which would be best from the operator's perspective? from the user's perspective? Why? Which would you recommend, and why? f. How might the results change for ß = 0.2? = 0.8? (Check only for L = LOPT for this range of frequencies.) g. Critique the assumptions (implicit and explicit) of this formulation of the problem: Under what conditions, and to what extent, do you think they would be reasonable? (For example, what do you think of the explicit assumption that demand is independent of the train length ?)

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a To predict equilibrium flows costs and revenues for adding 1 2 or 3 more trains per day with the same train lengths we can use the demand function and cost equations provided Well calculate the tota... View the full answer