Automated design space exploration for poultry processing systems using discrete-event simulation

1.2.1 Application of simulation in the design of food processing systems

Simulation is used to design an industrial plant for the production of hazelnut-based products in Bruzzone and Longo [6]. A simulation model is used to analyze the behavior of the designed system in various operating conditions. Penazzi et al. [7] shows how simulation can be used in the design and control of food job-shop processing systems. This is demonstrated through a case study in the catering industry, in which simulation is used to analyze a collection of key performance indicators.

In Owens and Levary [5] simulation is used to analyze design alternatives for an extruded food production line. The authors demonstrate how simulation may be a useful decision-support tool for deciding between several design options in the food industry. Parthanadee and Buddhakulsomsiri [8] shows how value stream mapping and simulation can be used to analyze design choices for small and medium enterprises in roasted ground coffee production.

Discrete-event simulation is used in Plà-Aragonés et al. [9] to examine alternative processing strategies and to improve production planning for a pig meat packaging facility. Comparing discrete-event simulation to deterministic or stationary methods, Plà-Aragonés et al. find that discrete-event simulation better captures plant behavior. Discrete-event simulation is used in Rijpkema et al. [10] to redesign meat production processes to make more effective use of product quality information. Simulation was used to evaluate how sorting based on product quality information affects the performance and processing efficiency of the system. As shown by Plà-Aragonés et al. and Rijpkema et al., discrete-event simulation can be an effective tool in the design of meat processing systems.

In Fujii et al. [11] simulation is used to optimize the design of the facility layout of a central kitchen in the food service industry. The proposed method for layout planning is validated through a real-scale case study. In Masoud et al. [12] a simulation-based framework is developed to optimize the facility layout and resource allocation in vegetable grafting facilities in order to maximize production capacity and efficiency. Discrete-event simulation is used in the design process of a greenhouse for industrial head lettuce production in Gao et al. [13]. A framework is proposed for integrating systematic layout planning and simulation to design greenhouses that maximize efficiency and yield.

When designing a food processing system, the first goal is always to meet the specified requirements; is the system able to produce or process the products as intended? A secondary goal is often to optimize the design in regard to certain performance measurements such as throughput and cost. Simulation allows the capabilities of potential designs to be evaluated early in the design process, across a range of production scenarios. Bruzzone and Longo [6], Penazzi et al. [7], and Plà-Aragonés et al. [9] show how simulation can be used to evaluate the performance of a food processing system across a range of production scenarios. Owens and Levary [5], Fujii et al. [11], and Gao et al. [13] demonstrate how simulation can be used to compare alternative designs in the design process of food processing systems. Rijpkema et al. [10], Parthanadee and Buddhakulsomsiri [8], and Masoud et al. [12] combine both, and show the importance of evaluating multiple production scenarios when using discrete-event simulation to compare alternative designs. Finally, Fujii et al. [11] and Masoud et al. [12] show a form of automated design space exploration to solve the facility layout planning problem. However, in both methods, the design is regarded as the spatial layout of the system, with the goal being to minimize the distance that products or workers need to travel. To the best of our knowledge, there is no previous work on automated design space exploration for the functional architecture of food processing systems.

1.2.2 Using discrete-event simulation for design space exploration

A digital factory is created using a discrete-event simulation tool in Centobelli et al. [14]. This digital factory is utilized to optimize the facility layout with respect to the flow of material. Simulation is used to compare the current and proposed layout for a range of production scenarios. An algorithm for generating a discrete-event simulation model of an assembly system layout is proposed in Kranz et al. [15]. This algorithm allows for simulation models to be generated without the need for considerable expertise in simulation. The model is generated based on predefined process logic and layout data provided in an Excel spreadsheet.

A method for automatic simulation model generation of a robotic cell layout is provided in Laemmle and Gust [16]. The method uses layout data specified in AutomationML as input. The facility layout of a specialized furniture manufacturing plant is optimized using discrete-event simulation in Rodič and Kanduč [17]. The facility layout is optimized to minimize the total travel distance for products. Simulation models of the different facility layout designs are automatically generated.

The downside of using discrete-event simulation in the design process of a production system is that developing the models can be complex and time-consuming. Kranz et al. [15], Laemmle and Gust [16], and Rodič and Kanduč [17] overcome this downside by using automated model construction. Rodič and Kanduč [17] automates both model construction and design space exploration to solve the facility layout planning problem. However, none of these works uses automated model construction to automatically explore the design space of the functional architecture of a production system.

In all of the papers previously mentioned in the state of the art, simulation is either used to directly compare design alternatives, or is used for single-objective optimization. None of these methods allow for multi-objective optimization, even though there is often more than one performance measure that needs to be considered in the design process of a production system.

2.3.1 Plant layer

The plant or physical layer of the system consists of a set of production ‘lanes’. Each lane represents a conveyor system through which the fillets are transported, with production steps occurring in-line. The plant layer can be decomposed into modules that define the production steps carried out on the fillets. The origin and destination modules represent the inflow from and outflow to other subsystems. For this case study, it is assumed that the order of processes is always the same (in the order in which they are described below). The ‘modules’ of the plant layer operate as follows:

2.3.2 Production control layer

The production controller is responsible for ensuring that the target throughput of each of the recipes is met. It does so by calculating a production strategy. A production strategy describes which fillet weights are allocated to which recipes and which fillets must be trimmed. When calculating the production strategy, the production controller takes into account which lanes are connected to which destinations, and which lanes have the capability for trimming. The interactions between the production control layer and the plant layer are shown in Figure 3. The production controller functions as follows:

1. The production controller collects data on the weights of fillets in each lane, as measured at the weigher in each lane.

2. The production controller employs a sliding window technique, consisting of the most recent N fillet weight measurements from each lane, to generate a ‘measured fillet weights’ histogram. This histogram describes the measured arrival rate of the different fillet weights in each lane. An example of such a histogram is shown in the top figure of Figure 4.

3. The production controller calculates the production strategy every t seconds using Algorithm 1. This algorithm functions as follows:

   1. The recipe with the highest priority is selected.

   2. The controller determines which lanes have a route to the destination of the recipe. The ‘measured fillet weights’ histograms of these lanes are used to calculate the expected throughput of each fillet weight interval.

   3. Starting from the lower weight limit of the recipe, the weight range allocated to this recipe is increased, until either the upper weight limit is reached, or until the expected throughput equals the target throughput of the recipe.

   4. If the target throughput is not yet reached, then the controller determines which of the selected lanes have trimming modules.

   5. Starting from the upper weight limit of the recipe, the weight range allocated for trimming is increased, until either the upper weight limit for trimming is reached, or until the expected throughput equals the target throughput of the recipe.

   6. The calculated weight ranges are assigned to the recipe. These weight intervals can no longer be used in other recipes. The process is then repeated for the next recipe until all recipes are processed.

   7. The middle figure of Figure 4 shows an example of a production strategy and the expected throughput allocated to each recipe. Fillets between 100 and 300 g are allocated to batching, with fillets between 250 and 300 g being trimmed. Fillets above 300 g are used for schnitzels.

4. Upon the arrival of a product at an assignment module, the production controller assigns a product to a recipe, and determines the required product routing and trim instructions. This is based on the production strategy for that lane and the measured weight of that fillet.

5. Whenever a product arrives at a distribution or trimming module, the corresponding product routing or trim instruction is communicated to that module for execution. An example of the resulting production output is shown in the bottom figure of Figure 4.

Figure 4:

An example of the production strategy for a system with one lane, with recipes for batching and schnitzels. The top histogram shows the arrival rate for different fillet weights, as measured at the weigher. The middle histogram shows the production strategy as calculated using Algorithm 1. The bottom histogram shows the resulting production output. Fillets between 250 and 300 g are trimmed down to around 200 g so that they can be used for the batching recipe. The trim by-product is used in the production of minced meat.

3.1.1 Case study

The design space for the case study is presented in Table 3. In the table, an example of a possible system design is highlighted. In the fillet processing system, the parameters of the design space are: which lanes have a trimming module, and how are the lanes connected to the destinations (using the three distributors which can be placed freely). Most connections in the system are fixed. For example, ‘origin1.out’ must be connected to ‘weigh1.in’; it is the only possible connection for both input and output ports, and both ports must have exactly one connection. In this specific case study, it is required that either all or none of the ports of a module are connected. Configurations of the system design that do not satisfy this condition are discarded. The case study design space is represented by a Design Space Matrix of 42 × 30, from which 11,520 possible configurations of the system design can be derived (32 permutations for which lanes have trimming modules, multiplied by the 360 permutations for how lanes can be connected to destinations).

Table 3:

This table shows the design space matrix (DSM) for the case study, and it highlights one possible design.

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1. The rows represent all output ports of the DSM, the columns represent input ports. The check marks indicate which connection between input and output ports are allowed. The two columns to the right of the matrix and the two rows below the matrix indicate the minimum and maximum number of connections that each port is allowed to have. The green encircled check marks indicate the connections in the current system design shown in Figure 3.

3.2.1 Case study

For the case study, a model library was built in Anylogic. The model library consists of all model components for the plant modules such as weighing and distribution described in Section 2.3, and one model component for the production controller. These model components are built using Anylogic’s process-modeling library. Each model component has a number of input and/or output ports. Between the input and output ports of a component, are a number of process-modeling blocks, which describe the production processes that are executed on the product, and their duration.

To model a complete system, specific instances of the model components can be placed on a canvas. These instances can be connected by their ports. Anylogic allows the model components to be connected to each other through the call of a function, allowing the same canvas to be used for all of the different designs. Figure 6 shows a simulation model constructed based on the design of the current system. This design is also highlighted in Table 3 and shown in Figure 3.

Figure 6:

The simulation model of a system design as built after the ‘model construction’ step. This figure shows the simulation model of the current system design shown in Figure 3, which is also highlighted in the DSM in Table 3.

To correctly set up the model component of the production controller, the possible routings through the system have to be calculated for this specific system design. These routings can be deduced from the connections which were selected in the DSM, and from knowledge of how fillets flow through the modules. For example, for the model in Figure 6, it can be deduced that fillets in lane 3 can be routed to either the batchingDestination2 or the filletStripsDestination, and that these fillets can be trimmed if necessary.

Besides the mincedMeatDestination, each destination corresponds to a recipe as defined in Table 2. Each destination model component records which percentage of the target throughput is fulfilled for the recipe corresponding to that destination. These are the performance measures later used in the ‘evaluation’ step.

3.3.1 Case study: selecting the simulation scenarios

As mentioned in Section 2.1, it is of vital importance that the system performs well for the many different incoming flocks. This requires that the effect of the mean fillet weight of a flock on the performance of the system is analyzed. Sensitivity analysis can be used to analyze the influence of a parameter on the system’s performance [21]. A sensitivity analysis was carried out on the current system layout, to analyze how much influence the weight distribution of the incoming flow of fillets has on how much of the target throughput can be reached. The findings of this analysis were that the fillet weight distribution does indeed have a substantial effect on how much of the target throughput can be reached (a difference of up to 20 % was identified). To account for the variation in fillet weight distribution, five summer scenarios and five winter scenarios have been selected to be simulated in the case study, with mean fillet weights ranging from 200 to 300 g. Table 4 shows the selected scenarios. Increasing the number of scenarios further would result in a more accurate estimation of the variation in performance, with the downside that it would take a longer computation time to simulate all scenarios for every design.

3.3.2 Case study: choosing the simulation parameters

Next, the simulation duration, the length of the warmup period, and the number of independent simulation runs were chosen. These parameters are tuned to find the right balance between accuracy of results and computation time. These three parameters were analyzed based on the simulation model of the current system (shown in Figure 3) and the most common production scenarios for both summer and winter (scenarios 3 and 8 from Table 4). The performance measure in these two scenarios is the average percentage of the target throughput achieved for the four main recipes shown in Table 2 (not including the fillet strips recipe). The goal was to find the right settings that give an accurate estimation of this performance measure for a low computation time.

First, the warmup period was chosen to be 200 s. The warmup period is needed because enough fillets need to be weighed before the production controller can make a production strategy. Increasing the warmup period beyond 200 s has shown to have no demonstrable effect on the accuracy of the simulation.

Next, an analysis was done on how the simulation duration affects the accuracy and precision in predicting the performance measures, and how it affects the computation time of the simulation. The simulation duration was varied between 400 and 25,600 s, and each setting was simulated 30 times. Figure 7 shows how the simulation duration affects the accuracy and precision in predicting the performance measures for scenarios 3 and 8. Calculating the precision and accuracy requires a reference point. Preferably, this would be obtained through experiments with the real-world system. However, this was not possible in this case study, so instead, the mean of 30 simulations with a duration of 25,600 s was taken as the reference.

Figure 7:

Figures (a) and (b) show a ‘boxplot’. These figures show how the simulation duration affects the accuracy and precision in predicting the performance measure in scenarios 1 and 2. The vertical axes show the percentage error in estimating the performance measure (percentage of target throughput realized). The mean performance measure of all simulations with a duration of 25,600 s is taken as the reference. A simulation duration produces accurate results if its mean is close to the reference. A simulation duration produces precise results if its estimations are close to each other (a small ‘box’ and ‘whiskers’).

In both scenarios, simulating 30 times with a simulation duration of 3200 s resulted in a mean within 0.01 % of the reference. This shows that the results are accurate; given enough simulations of 3200 s the mean will converge to that of the reference. All of the 30 simulations with a simulation duration of 3200 s were within 1 % of the mean. This shows that the results are also precise; the results of individual simulation runs are close to each other. Combined, these indicators show that one simulation run of 3200 s should give accurate results which are likely to be within 1 % error. However, there is no guarantee as these results are based on the current system, and for only two scenarios. For any other design or scenario, the same simulation parameters could be inadequate. A solution to this problem is to repeat this experiment with the recommended designs to validate the accuracy of the simulation results.

Finally, the expected total computation time for simulating one independent simulation run of 3200 s for all scenarios (10) and each design (11,520), was calculated to be less than one day. This was deemed to be a good balance between accuracy and computation time for the purpose of this case study.

3.3.3 Case study: total computation time

For each design, the constructed model was simulated once for each of the chosen scenarios. All simulations were done for 3200 s of production, during which a total of around 18,000 fillets are processed. In total, simulation of all 11,520 designs, 10 scenarios each, resulted in around 12 years of production being simulated. This took roughly half a day of computation, using a PC with an Intel(R) Core(TM) i5-8365U CPU with 16GB of RAM.

3.4.1 Case study: single-objective optimization

The single-objective optimization approach is to select the design that scored best on a chosen objective function. For example, suppose that the goal is to find the design with the highest 10-year return on investment (ROI), with the ROI being calculated as follows:

With the following variables:

1. The average percentage of target throughput reached in summer scenarios over all recipes: s.

2. The average percentage of target throughput reached in winter scenarios over all recipes: w.

3. The number of trimming modules: t.

1. Each percentage of throughput in summer and in winter results in the yearly profit: P = $10000.

2. The number of years over which ROI is calculated: Y = 10 years.

3. The base cost of the system: B = $10 million.

4. The cost of each trimming module: M = $50000.

Figure 8:

The design space exploration method recommends the design shown as it has the highest 10-year ROI. In the design, the selected connections and modules are depicted in green.

3.4.2 Case study: multi-objective optimization

The second approach is to use multi-objective optimization, in which the goal is to identify all Pareto optimal designs. For this approach, the three variables (A), (B), and (C), which were also used in the calculation of the single-objective cost function, are chosen as objectives.

Figure 9 shows the performance of each of the 11,520 designs. In the figure, each dot represents one design. The performance in summer scenarios (A) and winter scenarios (B) is displayed on the horizontal and vertical axes, respectively. The color of the dot indicates the number of trimming modules (C). When judging the designs on these three performance indicators, only the Pareto optimal designs are relevant (given that your simulation is accurate enough). For each number of trimming modules (C), the Pareto optimal designs that score best in summer (A) and winter (B) are highlighted with a bigger dot. These designs are in the top right corner of the figure. The right figure zooms in on these 27 Pareto optimal designs. Also highlighted in the figure with a star is the (Pareto optimal) design depicted in Figure 8, which had the highest 10-year ROI according to the single-objective cost function.

Figure 9:

The performance for all of the 11,520 different designs. Each dot represents one design; designs that are Pareto optimal with respect to (A) and (B) are indicated with a bigger dot. The right figure zooms in on these Pareto optimal designs. The Pareto optimal design which has the highest 10-year ROI is highlighted with a star, and is shown in Figure 8.

A system designer can use Figure 9 to select which design is most suited to the needs of the project. The designs with the highest performance are in the top right of the figure; these are the designs with three or four trimming modules. The poor performance for systems with five trimming modules might be unexpected as more trimming modules should give more flexibility, and thus better results (as it is always possible not to use the trimming module). However, Algorithm 1 for calculating the production strategy is rather naive, as it prioritizes the throughput of recipes with a higher priority over getting an optimal overall throughput. One takeaway of this analysis might be that a better algorithm needs to be developed.

3.4.3 Case study: further analysis of the design space

This section shows how the collected performance data can be used to further analyze the design space with regard to specific design questions. An example of such a design question is whether lane 4 should or should not have a trimming module. Figure 10 shows which designs perform better in performance measures for summer (A) and winter (B): designs with, or without a trimming module in lane 4. As can be established from the figure, designs with a trimming module in lane 4 outscore designs without one. Note that the number of trimming modules is not considered, resulting in a different set of Pareto optimal designs.

Figure 10:

The performance in summer and winter of systems with or without a trimming module in lane 4.

Similarly, it is possible to answer design questions with respect to specific performance measures. Previously, the performance was average over all of the four recipes. Suppose that the system designer wants to analyze which designs are best for fulfilling the target throughput of only recipe 1.

Figure 11 shows the performance of each design with respect to recipe 1. As can be seen in the figure, a design with at least 3 trimming modules is required to obtain a 100 % throughput for recipe 1 in all winter and summer scenarios. The ‘clustering’ in Figure 11 is due to design choices being discrete. There is a limited number of ways to connect the incoming lanes to the destination of recipe 1. The difference in performance between designs in a cluster is due to random variation in the weights of fillets.

Figure 11:

The performance of each design with respect to recipe 1. Pareto optimal designs with 3, 4, and 5 trimming modules in the top right corner overlap, which is why the marker shows three colors.