Algorithm Design and Comparison for an Optimisation Problem – Engineering  Assignment Help

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Assignment Task :
ASSESSMENT TASK 
This is a group assignment with an individual element. Your group should have 4-5 members, and you  must enrol to your group on Brightspace by 30/10/2020. After this deadline you will be assigned to a  group randomly. 
 
Background 
In this assignment you will address a real-world problem of delivery planning for the LPG (Liquefied  Petroleum Gas) distributor. In the areas where mains gas for heating purposes is not available, LPG is  the closest alternative. It has the lowest carbon emissions per kWh out of all fossil fuels available in rural  areas, does not pose any ground or water pollution hazards and can be used for both heating and  cooking. LPG distribution companies source the fuel from major oil refineries and deliver it to the bulk  customers by a fleet tanker lorries like the one in Figure 1. 
Tanker
 
You have been employed by SaO Gas Ltd as data scientists. You are to produce delivery schedules for  the fleet of 25 tanker lorries operating from 4 depots in the country of Optilandia (which surprisingly use £  as their currency), minimising the overall cost of delivery for the distributor under certain constraints. 
 
As an example, a large tanker can be loaded with up to 22 tonnes of LPG at one of the depots (you can  assume that depots never run out of gas). It costs the distributor £2 per mile to use the large tanker (even  if it is empty) plus £0.50 per mile for every tonne of LPG the tanker carries. So, a large tanker with 10  tonnes of LPG travelling 20 miles costs: 20 [miles] x (2.00 [£] + 10 [tonnes] x 0.50 [£]) = 140 [£]. However
 
There are two problems you should address: 
1. Schedule LPG delivery to all customers in order to fully fill their tanks while minimising the  overall cost of delivery. There are no additional constrains apart from the tanker lorry capacity – a lorry can for example visit any of the depots multiple times in order to load additional gas. 
2. Schedule LPG delivery in order to maximise the amount of gas delivered to the customers,  while minimising the overall cost of delivery (including any potential penalties! – see below)  and while observing the following constraints in addition to tanker lorry capacity: a. Each lorry can travel up to 250 miles 
b. Each lorry can only stop up to 5 times, this includes customer deliveries and any  additional visits to the depot 
c. Each lorry must end its journey in one of the depots (this doesn’t count towards the 5  stop limit and doesn’t have to be the depot from which the lorry started its journey) d. If you don’t deliver to customers who have less than 15% of gas in their tanks, SaO Gas  Ltd will incur a penalty of £1,000 for each such customer 
 
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