Online Supplement of "Finding Feasible Systems for Subjective Constraints Using Recycled Observations."

by Yuwei Zhou¹, Sigrun Andradottir¹, Seong-Hee Kim¹, and Chuljin Park²

¹ H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA

² Department of Industrial Engineering, Hanyang University, Seoul, South Korea

This repository contains the codes for the experiments in Section 6 of the paper "Finding Feasible Systems for Subjective Constraints Using Recycled Observations".

1. Proposed Procedures

We provide the folder procedures to that contains the codes for the proposed procedure ${\cal RF}$ and the other four competing procedures. We list the corresponding name for each file as follows.

• rf.cpp: this code is used to test the performance of Procedure ${\cal RF}$.
• recycle.cpp: this code is used to test the performance of Procedure ${\rm Recycle}^{\cal B}$.
• restart_max.cpp: this code is used to test the performance of Procedure ${\rm Restart}^{\rm max}$.
• restart_sum.cpp: this code is used to test the performance of Procedure ${\rm Restart}^{\rm sum}$.
• restart_prob.cpp: this code is used to test the performance of Procedure ${\rm Restart}^{\rm prod}$.

We use a 32-bit random number generator, MRG32k3a(), to generate independent and identically uniformly distributed random variates over interval (0,1) which are further used to generate normal random variables. The complete code for this random number generator can be found here. Note that Section 6 only provides the performance of ${\rm Restart}^{\rm max}$ which outperforms the other two restart procedures.

We discuss how to set the inputs to run the codes. Note that the codes for all five procedures use the same structure for user inputs, therefore, we only discuss how to set the inputs for rf.cpp.

1. Input values for the following variables depend on the problem (starting from line 18).

• Nnot: value of $n_0$.
• NumMacro: number of macro-replications.
• NumSys: number of systems considered.
• NumConstraint: number of constraints of the systems
• NumThreshold: maximum number of thresholds of all constraints.

2. Choose the value for the IZ-parameter $\epsilon_\ell$ and thresholds $q_{\ell m}$, where $\ell=1,\ldots,s$ and $m=1,\ldots,d_\ell$. Modify function configuration() (starting from line 366) for the following variables.

• epsilon[j]: values of $\epsilon_j$.
• q[m][j]: values of $q_{j m_j}$.

3. Choose the shape of the continuation region and compute $\eta_\ell$, where $\ell=1,\ldots,s$ as described in the paper. Modify the values of variable eta[j] (starting from line 71). Depending on the type of a chosen continuation region between triangular-shaped and straight-line ones, modify R[i][j] (lines 149 and 195).

4. Decide the correlation between constraints. Modify the following variables from function read_chol_matrix().

• Choose a desired input file cholMatrix_rhoX.txt, where X is the correlation between each pair of constraints.
• Depending on the number of constraints considered, choose a correct number of inputs for variable chol_matrix (comment out unnecessary variables).

5. Decide a variance configuration between constraints. Modify variable system_info[i] from function configuration() (line 382). We set system_info[i]=1,2,3 for CV, IV, and DV, respectively.

The users may choose their own random seeds to generate observations for the feasibility check (by modifying the values of seeds in line 36). In order to retrieve the identical experimental results as in the paper, the users need to use the same random seeds as in the codes.

2. Inventory Example

We provide the folder inventory that contains the codes for different procedures and a required input file for the $(s,S)$ inventory example in Section 6.4. Note that we include two separate cases depending on whether CRN is applied.

To run the code, the file TrueValue.txt, that contains the estimated mean performance of the two performance measures, is required. The values in this file are obtained through a Markov chain model as discussed in the paper.

To test the case when CRN is applied, we add a function generate_demand() (line 99 of rf.cpp as an example) to generate demands that are shared by all systems (which allows the systems to receive demands generated based on the same random seeds). We also need to modify function generate_one_obs() (line 343 of rf.cpp) for the variable Demand.

In order to retrieve the identical experimental results as in the paper, we run the code in parallel by setting different random seeds. More specifically, we run ten simulations in parallel and the number of macro-replications for each simulation is 10,000. The random seeds of each simulation run are set separately as in lines 39-47 of rf.cpp. After we receive the results from all ten simulation runs, we take the average for the results in Section 6.4.