Pulp Python: How to formulate a time-based variable for shipping demurrage

[Chris Price]

I am working on a shipping optimisation problem that aims to minimise demurrage charges as a result of low/insufficient inventory.

I have daily vessel requirement (sales) data in the format sales[vessel_start_date][vessel][product_required_tonnes]. I also have the daily stock inventory level in the form port_inventory[date][product_availability_tonnes]

• Demurrage is defined as: (total_days_in_port - laycan_days) * per_diem_charge. It is incurred when there is insufficient material at the port to load the vessel and the vessel's laycan period (vessel_start_date plus 10 days) has expired.

• Each vessel takes two days to load. 
• Each vessel can carry multiple products

As demurrage is only incurred if one or all elements of the vessel requirements are not satisfied I need to understand whether I need a binary variable and a decision var combination to understand which vessels incur demurrage. The model will inevitable have to allow some vessels to incur demurrage if they are cheaper than others.

I would be very grateful if anyone could help me formulate this expression in pulp or mathematically or even give me a steer. Many thanks.

[Stuart Mitchell]

At a first glance I would have a binary variable defining vessel loading (start date)

The cost of this variable with include possible Demurrage,

And there will be a constraint that only one start date is 1 for a particular vessel.

Other constraints on product availability and loading capacity should be able to be formulated with these variables

Stu

Stuart Mitchell

PhD Engineering Science

Extraordinary Freelance Programmer and Optimisation Guru

www.stuartmitchell.com

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[Chris Price]

Many thanks for your help Stuart.

Could you please describe how this binary variable would control the cost of demurrage if a vessel is waiting after its 10-day loading period?

Chris

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[Chris Price]

Circling back on this, could you please kindly show a brief example of how you would formulate this in Pulp?

Many thanks

[Stuart Mitchell]

given this statement

Each vessel takes two days to load. 

Cost of X_{vessel, start-date} = (start-date+2 - laycan_days) * per_diem_charge.

Stuart Mitchell

PhD Engineering Science

Extraordinary Freelance Programmer and Optimisation Guru

www.stuartmitchell.com

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[Chris Price]

Thank you Stuart. 

My question is, how can I calculate the difference between the two dates in pulp using variables? because pulp doesnt recognise datetime format?

Essentially I need to work out how to model the below:

vessel_ready_to_load[date][vessel]-vessel_actual_load_date[vessel]*per_diem_charge ==demurrage_charge[vessel]

Many thanks,

Chris

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[Stuart Mitchell]

Hi chris you need to be quite clear on what is a pulp variable and what is data.

Without knowing this it is hard to give advice

Stu

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