Linear Programming Transport Problems Notes PDF

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Linear Programming Transport Problems Notes...

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Week 7 Linear Programming Transport Problems -

Another important type of problem is transport problems. This type of problem was originally formulated during WW2 The Allies had many factories constructing equipment, in many di ferent places They needed to transport that equipment to many diferent destinations, in diferent amounts Their goal was to minimise the time required to move the equipment, subject to limits on what equipment was available, and subject to the requirements at each destination We will consider a modern version of the same problem: here, a company has factories in diferent cities, and wants to transport their products to market

Transportation Problems in Solver -

Transportation problems always have more than 2 decision variables, so we will never try to solve them graphically. It only remains to write the problem in tableau form, and solve it using Excel Solver

Sensitivity Analysis on Transport Problems -

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Sensitivity analysis on a transportation problem is mostly similar to sensitivity analysis examples we have already seen One diference is in the interpretation of a shadow price. Previously, we interpreted the shadow price as the increase in profits we would be able to achieve if the limit on some resource (the right-hand side of some constraint) was increased by one unit But in a transportation problem, we are not trying to maximise profits: we are trying to minimise costs. The shadow price is still interpreted as the change in costs which would happen for one unit increase in the right-hand side of the constraint A negative shadow price indicates that an increase of one unit in the right-hand side of the constraint leads to a decrease in costs, which is good news.

Portfolio Allocation Problems -

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Another important type of problem is investment problems. The goal is to invest a certain amount in a portfolio of assets, with the goal of maximising expected return, while obeying constraints on risk We may formulate constraints such as: o The portfolio must not exceed 1M o No asset may be allocated less than 0 o The single riskiest asset must be allocated no more than 100K, to keep risk low

Marketing Problems -

A company might want to advertise on radio, in print, on tv, etc., and maximise the number of people it reaches with its ads, subject to a maximum spend...