Supporting data for the integrated Agent-Based Modelling and Robust Optimization on food supply network design in COVID-19 pandemic

This article presents the data as a support for “Designing a Food Supply Chain Strategy during COVID-19 Pandemic using an Integrated Agent-Based Modelling and Robust Optimization” [1]. An integration framework of Agent-Based Modelling (ABM) and Robust Optimization (RO) is proposed to address the food supply network development involving normal and pandemic condition issue regarding the actual food production data availability. In this article, the data associated with the integrated ABM simulation and RO are discussed. Particularly, this article provides the output rice production capacity data from the ABM simulation. This article also discusses how the output data from ABM simulation are processed to construct the polyhedral uncertainty set, which will later used by RO. By showing the output data from the ABM simulation and explaining how it is processed to be used in RO, other researchers and investigators could integrate their own ABM simulation model with RO to address their respective problems considering any uncertainty. Furthermore, the additional data needed for the optimization model are also included, which are mainly retrieved from the reports of government agencies.

model are also included, which are mainly retrieved from the reports of government agencies.  Table   Subject Management Science and Operations Research Specific subject area Agent-Based Modelling (ABM) and Robust Optimization (RO) for food supply network design involving normal and pandemic condition. Type of data Tables and figures. How the data were acquired The data are obtained from the ABM simulation, which gives the prediction on rice production volume given the normal and pandemic condition. Meanwhile, other input data for the optimization model are retrieved from government agencies. Data format Raw and analysed. Description of data collection There are two conditions applied within the ABM simulation: (1) normal condition and (2) pandemic condition. In other words, the impact of pandemic condition on the rice production volume is observed based on the output data from the simulation. Data source location

Value of the Data
• These data and descriptions of how it is processed are useful to give an example of ways to integrate ABM simulation with RO to address food supply chain problems considering uncertainties. • These data and descriptions will be useful for other researchers and investigators who would like to optimize a certain problem in their food supply chain system considering uncertainties, particularly when the required data are hard to be collected or even unavailable at the moment. • The data processing step provides a template for organizing any uncertain data in the problem to be used in RO.

Data Description
This article supports our original research article entitled "Designing a Food Supply Chain Strategy during COVID-19 Pandemic using an Integrated Agent-Based Modelling and Robust Optimization" [1] . While our original research article provides a high-level framework for integrating ABM and RO to address uncertain food supply chain problem with unlimited data availability and its' result, this article explains how to combine such methods with related data used. Particularly, this article explains how to integrate ABM and RO by processing the outputs from ABM to be used as the input in RO. Subsequent paragraph gives a brief explanation of ABM, RO, and why do one need to consider integrating both methods in uncertain food supply chain problem with limited data availability.
RO is a method in optimization which able to handle uncertainties in optimization problem by assuming the uncertainties are exist in a convex hull uncertainty set. Hence, it requires uncertain dataset to be used to construct its' uncertainty set. When data availability is limited, ABM is one of the simulation methods that could be used to feed RO with the required data. ABM is chosen in our original research article as it has the unique ability to represent a system based on the actors and their behaviours, please see our original research article for high-level explanation of ABM & RO integration [1] .
This section provides the output data of rice production volume from 100 repetitions of ABM simulation. The average rice production volume from 100 simulations are given in Tables 1 and  2 . As reflected in Tables 1 and 2 , there are two large rice production centers: Bekasi Regency and Bogor Regency. Meanwhile, the other regions are the metropolitan areas with smaller rice production capacity. The classic optimization techniques may use the average rice production volume from the 100 simulations. Nevertheless, the usage of average value is not accurate, par-  ticularly when the variations of the data are quite high. Therefore, RO is applied to handle the uncertainties of the data obtained from the ABM simulation. There are several studies incorporating types of uncertainties in the food supply chain problem as discussed by Kharisma and Perdana [3] . In this case, the uncertainties considered are the uncertain rice production volume generated from ABM simulation. The construction of polyhedral uncertainty set that gathers all the uncertainties of rice production volume is discussed in the next section, given the output data from the ABM simulation provided in this section. Meanwhile, other input parameters for the optimization model are given in Table 3 . Monthly rice demand and rice selling price data are provided in Table 4 , which obtained from West Java in Figures published by Statistics of Jawa Barat [7][8][9][10][11][12][13][14][15][16] . Fumigation cost (Rp6.34/kg) and spraying cost (Rp7.55/kg) are considered as rice handling costs [4] . Fumigation and spraying are carried out every three months and one month, respectively. Hence, the approximation of rice handling  cost in each month is Rp9,663.33/kg. For the food hub development cost, the budget estimation is Rp250,0 0 0,0 0 0/unit/month [6] .

Experimental Design, Materials and Methods
This section discusses the data processing of the output data from ABM simulation to obtain the polyhedral uncertainty set. The data processing for the output data of Bekasi Regency is taken as an example. For the first step, the nominal data need to be defined, e.g., the average value of daily rice production volume in Bekasi Regency. One can calculate that the average value of daily rice production volume in Bekasi Regency is 273.628 tons/day. Once the nominal data is set, the next step is to set the uncertainty which disturbs the nominal data. In this case, the deviation of daily rice production volume becomes the uncertainty, which disrupts the nominal data as illustrated in Fig. 1 . The deviation of rice production volume is given in Table 5 .
Once the nominal data and the uncertainties are defined, then one can start constructing the polyhedral uncertainty set which covers all of the uncertainties as a convex hull. In other words, one should construct the smallest possible polyhedral set which contains all of the uncertainties. There are several convex hull algorithms developed [ 2 , 5 , 17 ]. Nevertheless, the general algorithm considering n-dimensional data by taking the projections of the data points on each of 2 dimensions combination is given below: 1. Considering the n-dimensional data, take any 2 dimensions combination as the projection. 2. Based on the 2 dimensions taken, pick any single dimension as the reference. 3. Given the 2-dimensional data projections, pick a single starting point from the data which has the smallest value on the reference dimension. If there are multiple data with the smallest value on the reference dimension, then pick the data which also has the smallest value on another dimension. 4. Pick a single termination point from the data which has the biggest value on the reference dimension. If there are multiple data which have the biggest value on the reference dimension, then pick the data which also has the biggest value on another dimension. 5. Create the lower inequality constraint of the data.