1.4(E) In railroad operations there is substantial debate about train length. In a particular market longer...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
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 ?)
Expert Answer:
Answer rating: 100% (QA)
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
Related Book For
College Algebra Graphs and Models
ISBN: 978-0321845405
5th edition
Authors: Marvin L. Bittinger, Judith A. Beecher, David J. Ellenbogen, Judith A. Penna
Posted Date:
Students also viewed these marketing questions
-
The norm of a linear transformation TA: Rn Rn can be defined by where the maximum is taken over all nonzero x in Rn. (The subscript indicates that the norm of the linear transformation on the left is...
-
Suppose that f: Rn R and g: Rn Rn are differentiable on Rn and that there exist r > 0 and a Rn such that Dg(x) is the identity matrix, I, for all x Br(a). Prove that there is a function h: Br(a) {a}...
-
Let 5: Rn Rn and T: Rn Rn be linear transformations with matrices A and B respectively. [Theorem 3.] (a) Show that B2 = B if and only if T2 = 7 (where T2 means T o T). (b) Show that B2 = 1 if and...
-
Drag and drop the protocols from the bank to their respective layer on the OSI and TCP/IP Model. Not every layer will have protocols associated with it. Protocols TCP/IP Model OSI Model Application...
-
Prove the distributive properties in Theorem 1.4.10. In theorem For every three sets A, B, and C, A (B C) = (A B) (A C) and A (B C) = (A B) (A C).
-
Shen and Smith [Ind. Eng. Chem. Fundam., 7, 100105 (1968)] measured equilibrium-adsorption isotherms at four temperatures for benzene vapor on silica gel having the following properties: S g = 832 m...
-
Identify \(a_{1}\) and \(d\) for the following arithmetic sequence. Use this information to determine the 86th term. \[ \{4.5,8.1,11.7,15.3,18.9,22.5,26.1, \ldots\} \]
-
House Company is considering three capital expenditure projects. Relevant data for the projects are as follows. Annual income is constant over the life of the project. Each project is expected to...
-
Manufacturer lessor James Ltd manufactures specialised Machinery for both sale and lease. On 1 July 2020, James Ltd leased one of these Machinery to Freddy Ltd, incurring $1200 in costs to prepare nd...
-
Planning is one of the most important management functions in any business. A front office managers first step in planning should involve determine the departments goals. Planning also includes...
-
There are many psychological approaches to addressing social problems (e.g., clinical, developmental, cognitive, phenomenological, neurobiological, and behavioral). The social-psychological approach...
-
Complete the #TODO portion of the Python program sigma.py, provided below, to compute w: W = 1 x2 x4 x6 + x8 2! 4! 6! 8! + - +(1)" x2n (2n)! The values of x and n are provided as user inputs to the...
-
Using EOQ Model, Ram Corporation determined the economic order quantity for a merchandise item to be 800 units. To avoid stock out costs, it maintains 200 units in safety stock. What is Ram...
-
a) Show that for air undergoing a steady flow compression process, the specific work of compression (J/kg) can be expressed in the form: = 1((1) 1) Where T1 is the entry temperature of air, rp the...
-
Compute the net present value of a capital project to buy new equipment for replacing old equipment, given the following data and a minimum return of 7% Ignore income taxes. Old equipment New...
-
ABC had a stock price of $25 at the end of 2014 and paid $1 dividend at the end of 2015 with a forecasted dividend growth of 5%. What is cost of equity for ABC in 2014? 5. You are considering to...
-
Rent Income minus: Operating Costs minus: Interest minus: Depreciation Taxable Income minus: Taxes = Net Income minus: Principal = Net Operating Cash Flow minus: Cash Outlay at Start pius:...
-
A bubble-point liquid feed is to be distilled as shown in Figure. Use the Edmister group method to estimate the mole-fraction compositions of the distillate and bottoms. Assume initial overhead and...
-
In each of Exercises, classify the function as linear, quadratic, cubic, quartic, rational, exponential, or logarithmic. a. f (x) = 5 - x2 + x4 b. f (x) = 2x c. f (x) = - 3/4 d. f (x) = 4x - 8
-
Two solutions of the equation Ax + By = 1 are (3, -1) and (-4, -2). Find A and B.
-
Find the domain of (h/g) given that h(x) = 5x / 3x - 7 and g(x) = x4 - 1 / 5x - 15.
-
Calculate \(\frac{23}{42}+\frac{9}{56}\) using Desmos.
-
Express the following rational numbers in lowest terms: 1. \(\frac{36}{48}\) 2. \(\frac{100}{250}\) 3. \(\frac{51}{136}\)
-
Determine if \(\frac{12}{30}\) and \(\frac{14}{35}\) are equivalent fractions.
Study smarter with the SolutionInn App