This project solves planning problem on a supply chain graph. The chain should be defined in a text file with specific format. This document briefly describe how to install the planner, define a supply chain and solve it.

The planner models a supply chain as a maximum flow problem, which is then formulated as a mixed integer linear program and fed into the LP solver. If you need a deeper look into the algorithm used for planning see this document.

To run the planner, pythen 3.6 and above is required. Since the planner formulates the problem as an MILP (mixed integer linear program), it also requires an MILP solver. It uses PuLP as the linear programming modeler, which can call several external solvers. CBC solver, which is bundled with PuLP should be enough for test purposes. PuLP can be installed via pip, i.e.

pip install pulp

or using make (at project root directory):

make init

The usage of the planner is as follows:

python planner.py <model> [<lp>]

• model is the chain described by the input format (see examples).

• lp is the name of output file containing the mixed linear integer program corresponding to the model. This argument is optional.

A supply chain specification comprises of component and product. Products are at the final stage denoting the result of a chain. An example of product declaration can be as follows.

product p1, p2=30;

As we want to maximize the production, the above line puts their sum in the objective function. That is to say, the objective of this supply chain will contain p1+p2. In addition, it imposes constraint p2<=30 on the plan to ensure the number of product p2 is not above 30. Suppose the above line defines the whole chain, the induced MILP looks like:

max p1 + p2
subject to
   p2 <= 30
   p1 and p2 are integer

It is indeed not a realistic chain, since a chain usually trace the products back to suppliers and depots via components. Components can be seen as the intermediate products between suppliers and depots and the final products. They are defined in a similar way as products. For instance,

component c1, c2=10;

defines component c1 and c2, with c2 being fed by an depot of size 10. The semantics of this definition is constraint c2<=10, which makes sure the number of component c2 never goes above the capacity of the depot. It is possible to connect the a component directly to a supplier, e.g. by

c1<-supplier;

This means the supplier can deliver any number of c1 required for the plan. Components and products can be connected to each other to produce other components and products. Operator + combines two or more components and produces a result. As an example,

p1<-c1+c2

combines n items of component c1 with n items of component c2 and yields n items of product p1. The semantics of this operator is similar to AND gate, considering it obligates the same quantity of c1 and c2 be available at the time. In the induced MILP, it introduces the following constrains:

p1=c1
p1=c2

Components can likewise be combined by an OR gate.

p1<-c1|c2

In this case, p1 is produced either of c1 or c2, exclusively. It introduces the following constrains:

x1 + x2 = 1
x1 * c1 + x2 * c2 = p1
x1 and x2 are binary

Binary variables x1 and x2 determine which component c1 or respectively c2 is selected to produce p1. The constraints involve multiplication of two variables and thereby not linear. Their linearization is explain in detail here.