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Based on the lecture attached, Answer the Following Question:(Q) Many airlines operate today by using a Hub Spoke model, which allows them to reduce operating costs and be able to reach service to many smaller feeder airports.As part of this week’s lecture, Post your thoughts on how to make an airline more competitive in this market.The Transportation Model
• The transportation model addresses the concept of moving a thing from one place to
another without change. It assumes that any damage in route has negative consequences,
and so it’s used to analyze transportation systems and find the most efficient route for
resource allocation. The model requires only a few data elements:
• Origin of supply
• Destination
• Unit cost of shipping (per-unit cost)
• The transportation model is the study of optimal transportation and allocation of
resources.
• The transportation model provides means of selecting the best way to distribute a product
or goods from a number of factories or warehouses (i.e., the source) to a number of
destinations so as to minimize transportation costs while meeting customers’ requirements.
• The transportation model ultimate goal is the analysis of alternatives to find the optimum
solution.
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Car Transportation Example
• Cars are transported from Los Angeles,
Detroit, and New Orleans to Denver and
Miami as shown in the table.
• The trucking company in charge of
transporting the cars charges 8 cents per
mile per car.
• Supply & Demand
• Los Angeles = 1000 (Supply)
• Detroit = 1500 (Supply)
• New Orleans = 1200 (Supply)
• Miami = 1400 (Demand)
• Denver = 2300 (Demand)
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Car Transportation Example (cont.)
Transportation Tableau allows for compact representation of the problem
using this special format.
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Car Transportation Example (cont.)
Transportation Model in Linear Programming Form
Decision Variables: xi,j, where i = source and j = destination
Objective Function:
Minimize: z = 80×11 + 215×12 + 100×21 + 108×22 + 102×31 + 68×32
Subject to:
x11 + x12 = 1000 (Los Angeles)
x21 + x22 = 1500 (Detroit)
x31 + x32 = 1200 (New Orleans)
x11 + x12 + x13 = 2300 (Denver)
x21 + x22 + x32 = 1400 (Miami)
Non-negativity Constraint
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Car Transportation Example (cont.)
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• Production-Inventory Control
• Example includes production cost, plus carrying cost
(previous) for inventory and the penalty for having backorders (future) to synchronize production with demand.
• Tiered Service
• Example focuses on tool sharpening with options for
replacement of blades and tiered turn around times on
sharpened blades ranging from overnight to two days.
• Workforce Allocation (to be discussed later)
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Production Inventory Control Example
The unit “transportation” cost from period i to
period j is computed as:
Production cost in i, i= j
c ij=
Production cost in i + holding cost from i to j, i < j Production cost in i + penalty cost from i to j, i > j
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Production Inventory Control Example (cont.)
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Tiered Service Example – Tool Sharpening
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Tiered Service Example – Tool Sharpening (cont.)
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The Transportation Algorithm
The basic steps of the transportation algorithm are exactly those of the
simplex method discussed in Chapter 3. However, instead of using the
regular simplex tableau, we take advantage of the special structure of the
transportation model to carry out the algorithmic computations more
conveniently.
1. Determine a starting basic feasible solution.
2. Use the optimality condition of the simplex method to determine the
entering variable from among all the non-basic variables.
3. Use the feasibility condition of the simplex method to determine the
leaving variable from among all the current basic variables, and find the
new basic solution.
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Transshipment
• The transportation model always assumes direct shipments
between sources and destinations. This may not be the case in
many situations where it may be cheaper to transship through
intermediate nodes before reaching the final destination.
• A modeling trick based on the use of buffers can be used to
convert the transshipment model into a regular transportation
model. This conversion is interesting, but rarely used.
• Section 22.1 in the online resources for this textbook discusses
this in more depth.
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The Assignment Model
The classical assignment model deals with matching workers (with varying skills)
to jobs. Presumably, skill variation affects the cost of completing a job. The goal is
to determine the minimum cost assignment of workers to jobs. The general
assignment model with n works and n jobs is represented in the table below.
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