Source code for An Order-Splitting Model for Supplier Selection and Order Allocation in a Multi-echelon Supply Chain

Cite

To cite this data, please cite the research article {!link to be added} and the data itself, using the following DOI.

Below is the BibTex for citing this version of the data.

@article{SSOA2021,
  author =        {Yulin Sun, Cong Guo, and Xueping Li},
  journal = {`TBD`}
  year =          {2021},
  doi =           {`TBD`},
  url =           {https://github.com/ILABUTK/Supplier_Selection_and_Order_Allocation_Optimization},
} 

Abstract

We consider an integrated supplier selection and inventory control problem for a multi-echelon inventory system with an order-splitting policy. A buyer firm consisting of one warehouse and $N$ identical retailers procures a type of product from a group of potential suppliers; the acquisition of the warehouse takes place when the inventory level depletes to a reorder point $R$, and the order $Q$ is simultaneously split among $m$ selected suppliers. We develop an exact analytical model for the order-splitting problem in a multi-echelon system, and formulate the supplier selection problem in a Mixed Integer Nonlinear Programming (MINLP) model. This model determines the optimal inventory policy that coordinates stock levels between each echelon of the systems while properly allocating orders among selected suppliers to maximize the expected profit. For verification and validation of the proposed mathematical model, we conduct several numerical analyses and implement simulation models which helps us demonstrate the model's solvability and effectiveness.

Source Code

We implement the MINLP model using Matlab with the Knitro package. Main files & folders:

• MainRun.m: the main entry of the program, the base case
• IBCostSeven.m: costs calculations
• ConNonIA.m: nonlinear constraints
• ObjfunSplit.m: the objective function
• knitro.opt: Knitro settings
• Folder Long distant supplier: investigate the scenario where we have some long distant suppliers
• Folders Run{x}: scenarios with different arrival rates {lambda}

How to enable active-set algorithm

Sample code:

%----------------Ktrlink----------------------
Knitrooptions = optimset('Algorithm', 'active-set', 'Display','iter','MaxIter',1000,'TolX',1e-6,'TolFun',1e-6,'TolCon',1e-6);
[x,fval,exitflag,output,lambda]=knitromatlab_mip(@(x)ObjfunSplit(x,k,h,b,N,Lambda,Lr,Lw,Or,Ow,Pw,w),X0,A,bq,Aeq,beq,lb,ub,@(x)ConNonlA(x,BigM,N,Lambda,Lw),xType,'knitro.opt');

For more details on the active-set algorithm, please refer to the following paper.

@ARTICLE{Byrd2004,
    author={Byrd, {Richard H.} and Gould, {Nicholas I.M.} and Jorge Nocedal and Waltz, {Richard A.}},
    journal={Mathematical Programming},
    title={An algorithm for nonlinear optimization using linear programming and equality constrained subproblems},
    volume={100},
    year={2004},
    number={1},
    pages={27-48}
}

sqp and interior-point options

One may explore the use of different options.

Sample code:

%------------------------NLP Fmincon Solvers------------------------
%fmincon use the SQP algorithm, also with the parallel computing
option1 = optimoptions('fmincon','UseParallel',true,'Display','iter','Algorithm','sqp','TolFun', 1e-10, 'TolX', 1e-10, 'TolCon', 1e-10, 'MaxFunEvals', 2000);
%option2 = optimoptions('fmincon','UseParallel',true,'Display','iter','Algorithm','interior-point','TolFun', 1e-10, 'TolX', 1e-10, 'TolCon', 1e-10, 'MaxFunEvals', 4000);

[x,fval,exitflag,output,lambda] = fmincon(@(x)ObjfunSplit(x,k,h,b,N,Lambda,Lr,Lw,Or,Ow,Pw),XStart,A,[],Aeq,beq,lb,ub,@(x)ConNonl(x,SmallM,BigM),option1);

For more details on the fmincon solver, please visit the official web site.