Logistics Scheduler

This repository provides an answer set program that generates an optimal schedule minimizing driving time between a set of warehouses and factories. Warehouses provide resources and require products on a weekly basis whilst factories require resources and provide products on a daily basis.

The program looks for a schedule that provides every place with what's required.

Instance generation

There also is an answer set program that can be used to either generate random instances of the problem or to validate manually crafted instances. The ./instance-generation/instance-generator.lp program outputs the facts:

• day/1 denotes the days of the week
• factory/1 denotes factories
• warehouse/1 denotes warehouses
• resource/1 denotes resources
• product/1 denotes products
• place/1 a place is a factory or warehouse
• good/1 a good is a resource or a product
• cost/3 driving cost between to places in time units; forms a metric
• consumes/3 daily consumption rate of resources per factory
• produces/3 daily production rate of product per factory
• supply/3 weekly supply rate of resources per warehouse
• demand/3 week demand rate of product per warehouse
• vol/2 denotes the volume of some good

Exact implementation details are given in the generator program. The program can be configured by the following constants:

• #const days=5.; the number of days a week has
• #const tu_per_day=8.; the number of time units a day has
• #const factory_num=2.; the number of factories
• #const warehouse_num=3.; the number of warehouses
• #const resource_num=5.; the number of resources
• #const product_num=2.; the number of products
• #const min_cost=1.; minimum drive time in time units
• #const max_cost_frac=2.; maximum fraction of a day that driving in one direction may take, i.e. 2 means that no route is longer than half a day. Must be greater than or equal to 2 otherwise the actual solver might result in UNSATISFIABLE.
• #const min_consumes=1.; minimum consumption rate of a resource at a factory (rate can always be zero)
• #const max_consumes=5.; maximum consumption rate of a resource at a factory
• #const min_produces=1.; minimum production rate of a product at a factory (rate can always be zero)
• #const max_produces=5.; maximum production rate of a product at a factory
• #const min_vol=1.; minimum volume of a good
• #const max_vol=3.; maximum volume of a good

Supply an demand rates of warehouses can' be configured as they always match what is consumes/produced by the factories times the number of days of the week.

The ./gen.ps1 PowerShell script can be used to generate an instance. It hands the models of the instance generator program to a python script that randomly selects one of the models returned by the generator at prints all its facts including the constants days and tu_per_day into an instance program file.

Example:

.\gen.ps1 -Days 5 `     # How many days does the week have?
    -TuPerDay 8 `       # How many tus does a day have?
    -SampleSize 100 `   # Number of models to generate
    -Options @() `      # Options to clingo
    -Files .\instance-generation\instance-generator.lp `
                        # Input files; at least the instance generator and optionally other constraints
    -OutFile .\instance.lp
                        # Files to write the instance to

Solving

Solving the problem is straight-forward: simply use the solver.lp file and some problem instance and wait for the optimizer to do its job:

clingo instance.lp solve.lp