Determine whether the optimum number of terminals

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Reference no: EM132384324

Chapter 3- Optimization Methods: One-to-One Distribution

Book - Logistics Systems Analysis By Carlos F. Daganzo, Fourth Edition

Question :

Freight is to be exported from a region of variable width, lying on one side of a transportation artery (e.g., a highway or railroad line) that is one thousand distance units (Du) long, L = 1,000 Du's. From the origins freight can only be carried perpendicularly to the artery, unless of course it moves on the artery itself. Freight must flow out of this region through a system of terminals (e.g., ports) that are to be located on this artery. The cost of travel within the region is one monetary unit (Mu) per weight unit (Wu) per Du. The cost of travel beyond the terminals is not considered as part of our study. The freight transportation needs per unit time (Tu) are expressed as a transportation demand density [Wu/(Du*Tu)] which depends on the position along the artery expressed in Du's, x . The demand density, w(x) , is expressed as follows:

w(ƒ) = 5 if 0 ≤ x ≤300

= 1 if 300 < x < 700, and

= 5 if 700 ≤ x ≤ 1000

Then:

(i) Determine the optimal location and the total access cost per Tu when we locate n = 1, 2 and 3 terminals. (Use the procedure developed in Sec. 3.4),

(ii) Show which locations you would use if only the attached 50 locations are feasible. Calculate for each case the percent change in access cost,

(iii) If each terminal costs cT = 80,000 Mu's per Tu to operate (including any relevant amortized fixed costs), determine whether the optimum number of terminals that should be operated, n*, is 1, 2, or 3. Calculate as well the total regional cost per unit time, including both transportation and terminal operations, z*. Do the calculation with and without the location constraints described in (ii),

(iv) Determine n* and z* for arbitrary cT using the continuum approximation (CA) method. Compare the results for cT = 80,000 with those for part (iii). Discuss how the CA results might differ from the true optimum as cT 0, with and without the 50 location restriction,

(v) Extra credit: Find the exact optimal solution to part (ii) using dynamic programming. Solve for n = 1, 2, 3, ..., 10. Then determine the ranges of cT for which the optimum number of terminals is 1, 2, etc. Calculate and plot the resulting z* as a function of cT and compare the result with your findings in parts (iii) and (iv).

Reference no: EM132384324

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