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Competitive market factors, such as more stringent government regulations, larger number of competitors, and shorter product life cycle, in recent years have created more significant pressure on the management in all supply chain parties. To this end, the ability of analyzing and evaluating systems and related operations involving the deployment of complex multiobjective material handling systems is vital for distribution practitioners. In this respect, simulation modeling techniques together with optimization have emerged as a very useful tool to facilitate the effective analysis of these complex operations and systems. In this paper, we apply a multiobjective simulation-based optimization framework consisting of a hybrid immune-inspired algorithm named Suppression-controlled Multiobjective Immune Algorithm (SCMIA) and a simulation model for solving a real-life multiobjective optimization problem. The results show that the framework is able to solve large scale problems with a large number of parameters, operators, and equipment involved.

Simulation modeling is indeed a powerful industrial engineering technique for studying the functioning, performance, and operation of complex systems. As such, it becomes an extremely useful tool for stakeholders and decision-makers in various industries and domains including multiobjective optimization. By changing input data and operating parameters of a system being studied with simulation, predictions about the system’s behaviors can be obtained through computer-aided simulation for helping management make the right decisions. Unlike a mathematical model, simulation can handle a variety of complex factors that are commonly found in real world. In addition, simulation is a cost-effective means for existing process redesign and new system design because alternative solutions can be studied and evaluated for correctness and feasibility before actual implementation. More importantly, the accuracy of the performance measures of the complex systems obtained from simulation models is normally higher than that of analytical methods because analytical methods in general involve making unrealistic assumptions for the systems or problems under investigation [

In real world, many problems no matter whether they are in the domain of engineering, finance, business, or science can be formulated into different forms of optimization problems. These problems are characterized by the requirement of finding the best possible solution that fulfills certain criteria under certain constraints. Most of the real-world optimization problems normally involve multiple objectives rather than one single objective, in which some objectives conflict with others. Solving this kind of problems is never an easy task because objectives of such problems are often found to be noncommensurable and conflicting. Very often, there is no single best solution to the multiobjectives optimization problems, but rather a set of optimal solutions that exists among the objectives. However, using simulation modeling alone cannot provide us with optimal solutions to these optimization problems. Therefore, an optimization algorithm is needed to guide the search process to the optimal solutions. Over the past decades, different algorithms have been developed for solving multiobjective optimization problems. However, some algorithms, such as Simulated Annealing (SA) [

This paper proceeds as follows: Section

Material handling, which is the total management of material concerns in an operation, is a vital element of industrial processes. Material handling involves a variety of operations including the movement, storage, protection, and control of materials, products, and wastes throughout the processes of manufacturing, distribution, and disposal. Having efficient MHS is of great importance to various industries to maintain and facilitate a continuous flow of material through the workplace and guarantees that required materials are available when needed. It is especially important to logistics and manufacturing industries as it accounts for a large percentage of the operation in these industries. In the manufacturing sector, the time spent on different kinds of product handling and transportation can be as much as the time used on the value-added processes. Banks et al. [

There are different kinds of material handling equipment and systems available that range from simple hand truck and pallet rack to complex conveyor system and Automated Storage and Retrieval System (AS/RS). A typical MHS is composed of different smaller components closely working together, thus making business activities more efficient and cost-effective. Over the past decade, MHS and its function have undergone a big change because of new advances in technologies, such as the development and applications of automation techniques and robotics, by which a large number of manual handling jobs are replaced by machines. Since the entire production or distribution process is automated, MHS has to respond just-in-time to the requirements of different processing activities. These new technologies, today, increasingly become prevalent in different industries as they help ease drudgery for manual labors and some of the mechanized or automated handling jobs are physically impossible to be done by workers.

Norman [

In the literature, there are a number of studies that dedicatedly contribute to the optimization of MHS via simulation. For example, Ebbesen et al. [

In practice, optimization problems involve several objectives that often conflict with each other and must be simultaneously optimized so that a possibly uncountable set of trade-off solutions rather than a single optimal point is found with respect to the contradicting objectives. Therefore, the aim of these problems is to find out the global trade-off solutions that effectively spread over the Pareto front. No solution from the Pareto front is worse than any other solution because it is better in at least one objective. These problems are normally termed as multiobjective problems, which were first studied in an economic context and then extended to the fields of science and engineering [

As is known, the notion of optimality for multiobjective optimization problems is different from that of single objective optimization problems because the aim of multiobjective optimization problems is to find a set of optimal trade-off solutions rather than a single optimal solution. Thus, in the absence of preference information on the objectives, the concept of Pareto optimality is adopted in this study for solving multiobjective optimization problems [

A point

Consider, without loss of generality, two decision vectors

However, when any of these conditions are violated, the two solutions

Pareto optimal set of solutions is a collection of all Pareto optimal solutions, which is defined as

Pareto optimal solutions are those solutions in the decision variable space whose corresponding objective vector elements cannot be all simultaneously improved [

A surface or line containing all nondominated solutions is called Pareto front, which is represented by

According to the literature, finding an analytical expression of the Pareto front is a very difficult task. Therefore, a common approach for Pareto front generation is to find out the points within Ω and their corresponding value

Of a solution set

Modern optimization approaches are very often population-based and evolutionary in nature. In such methods, the search for the global optima essentially comprises an iterative process that replaces the candidate solutions in the population by newly generated ones with an aim of achieving continuous improvement in the performance of the best candidate solutions through the help of mechanisms that guide the search to find a set of nondominated solutions. The use of the modern optimization approaches, especially population-based evolutionary algorithms, to solving the complex multiobjective optimization problems has been motivated mainly because of the following critical reasons. First, population-based evolutionary algorithms can recognize the specificity of multiobjective optimization problems by working simultaneously on all objectives and finally generating a group of optimal trade-off solutions, thus forming a uniformly distributed Pareto front. Second, as the name implies, the population-based approaches can deal with a population of candidate solutions simultaneously, allowing the generation of several elements of the Pareto optimal set in a single run of an optimizer instead of performing many separate runs when using classical mathematical programming methods [

During the past few decades, a large number of publications have been done in population-based evolutionary algorithms and proved to be effective for solving multiobjective optimization problems since the first multiobjective evolutionary algorithm has been developed by Schaffer [

The optimization framework adopted in this study is developed by taking advantage of the idea of separation between the optimization method and the simulation model. For this reason, the optimization framework can remain the same or require only minor modifications such as changing range of parameters, data type of decision variables, and number of decision variables, to optimize the simulation model that incorporates new requirements. This framework in fact is a modified version of Leung and Lau’s work [

The framework for multiobjective simulation-based optimization (source: modified from Leung and Lau’s work [

The framework consists of two critical components, namely,

In essence, the AIS-based multiobjective optimization algorithm is a search algorithm. The simulation results (output performance metrics) direct the algorithm to search for a new set of input parameters that takes the system towards its optimal setting with respect to certain criteria. Hence a feedback mechanism is incorporated to direct the search for optimal solution in a controlled manner. In other words, the generation of a new set of input parameters for the simulation model is based on the simulation results of past evaluations. As such, the input parameters and the output performance metrics shown in the figure in fact serve as the feedback to the simulation model and the optimization algorithm, respectively. This iterative process repeats until prespecified termination criteria are met. The criteria could include the following: for example, no improving solutions can be found or the predefined number of iterations is reached.

In this framework, the optimization algorithm was implemented with Excel VBA, whereas the simulation model was developed by using the FlexSim simulation tool [

The fundamental of the hybrid AIS-based optimization algorithm [

Mapping between the biological immune system and SCMIA.

Biological Immune System | SCMIA |
---|---|

Antigen (Ag) | Objective function (simulation model in simulation study) to be optimized |

Antibody (Ab) | Candidate solution (a set of decision variables) to be optimized |

Ag-Ab affinity | Fitness value of each candidate solution evaluated based on Pareto dominance |

Ab-Ab affinity | Crowding-distance proposed by Deb et al. [ |

Immune suppression | Mechanism to control the number of nearby candidate solutions based on similarity among candidate solutions in both the objective space and decision variable space |

Memory cell | Current best nondominated solution |

The algorithm comprises five immune operators: cloning operator, hypermutation operator, suppression operator, selection and receptor editing operator, and memory updating operator, and one genetic operator: crossover operator. Each of them takes responsibility for different tasks for the purpose of finding uniformly distributed Pareto front. The block diagram showing the computational steps for SCMIA is presented in Figure

Computational steps for SCMIA.

In this phase, if the distances for all objectives between two antibodies are smaller than the thresholds, the two antibodies are said to be similar and hence the cell with poorer Pareto fitness

In second phase, the suppression will only be applied to the similarity between nondominated cells and dominated cells and the similarity between two antibodies is defined as follows:

In this phase, if the distance between two cells is smaller than the threshold in decision variable space, the two cells are said to be similar and hence the dominated cell will be suppressed and eliminated from the population. Eventually, surviving populations

To enhance the population diversity and facilitate the search of uniformly distributed nondominated solutions, the threshold values for the decision variable space and the objective space are adaptive values that are dynamically calculated based on the maximum and minimum values found at each iteration. The adaptive threshold values are computed according to the following equations:

If the size of

If the size of

If the size of

After performing the final memory updating procedure at the last iteration, the memory set

The algorithm is conducted by applying these heuristic and stochastic operators on the antibody population for balancing both the local and global search capabilities. For the detailed discussion of the hybrid multiobjective algorithm, one can refer to [

In this study, a set of experiments based on a real-life multiobjective optimization problem was performed to evaluate the performance and capability of the optimization framework and algorithm. In order to provide a better view on the performance of each method, both the graphical presentations of the simulation results and the statistical results of performance metrics on the problem under investigation were analyzed. All these experiments were conducted using a computer with Xeon E5-2620 2 GHz CPU with 2 GB RAM.

In this simulation-based optimization study, two performance metrics, namely, error ratio (ER) [

In this section, a real-life multiobjective optimization problem, that is, the distribution operation of the material handling system (MHS) implemented at the distribution center (DC) of S.F. Express (Hong Kong) Limited, was studied through the simulation-based optimization approach. S.F. Express launched its service in Hong Kong in 1993. At present, its service network is covering almost all areas of Hong Kong, which is mainly served by the DC located in Tin Shui Wai (TSW) in northern New Territories (Figure

The distribution flow of S.F. Express’s imported goods in Hong Kong.

The DC has two major conveyor systems: one for handling the exported goods and another for imported goods. In this study, we focus on the physical goods flow at the DC, where the items are imported from China and then distributed to all parts of Hong Kong. At the DC, most of the items received at inbound docks (Figure

Inbound docks connecting to the conveyor system.

Outbound docks connecting to the conveyor system.

The MHS is a circular shaped automated conveyor system, which comprises a number of interconnected 5-, 10-, and 20-meter long straight modular conveyor units and 2.5-meter radius curved conveyor units. The layout of the MHS is depicted in Figure

The docks and trucks at the DC.

The simulation model of the MHS implemented with FlexSim.

At each conveyor entrance, 7 workers are deployed to deconsolidate the incoming bulky consolidated parcels uploaded from the big inbound truck (16 tonnes) for facilitating the subsequent sortation process. To enable the distribution process to go well and items to be accurately sorted according to customer requirements, 4 workers are assigned to each conveyor exit serving 2 destinations (except the 2 exits close to the entrances serving 1 destination that requires 2 workers) and equipped a barcode reader for confirming the destination of each small parcel and helping to load the parcel to the small outbound truck (5.5 tonnes).

Each step of the operation is performed sequentially in the simulation process and the operation is given as follows:

When the operation starts, each of the incoming bulky consolidated parcels is unloaded by the workers from the 4 inbound trucks to the staging area of the 4 inbound docks.

And then each bulky consolidated parcel is deconsolidated into multiple small parcels and transported to the conveyor entrances by the workers.

After the parcels arrive at the conveyor, they are transported to the different exits of the conveyor system according to their destinations.

When the parcels reach the corresponding exits, they are moved to the outbound docks by the workers and ready for delivery.

To focus our study on the behavior of the MHS, certain real-world factors were simplified. Thus, the following assumptions were made:

Every day, the DC handles around 3 to 4 batches of parcels. Since the operation is similar in each batch, only one batch in the simulation model is simulated and studied. There are 400 bulky consolidated parcels in each batch coming from 4 supply sources (each contributes 100 bulky parcels) in which the processing time (cycle time) in one batch and the workers’ utilization are studied.

The time for unloading bulky parcels follows a uniform distribution.

The time for deconsolidation of the bulky parcels follows a normal distribution in which each bulky parcel is separated into 10 small parcels. Therefore, there are 4000 small parcels in total being handled by the MHS.

The system only processes two types of parcels (namely, bulky consolidated parcels and small parcels) because they are packed similarly in terms of volume and weight.

The demand for each destination is similar which follows a uniform distribution, that is, the parcels are uniformly distributed among the 30 destinations.

The simulation model with specific system configuration and behavior is implemented with FlexSim (Figure

Entities are the 400 bulky consolidated parcels and the 4000 small parcels deconsolidated from the bulky parcels, which are processed through the system causing changes in the system state over time.

Activities are the deconsolidation of bulky consolidated parcels unloaded from each incoming truck (represented by a source in the simulation model), the picking of small parcels from the circular conveyor to each outgoing truck (represented by a sink in the simulation model) according to their destinations.

Item attribute is the product type associated with its destination (one product type corresponds to one specific destination).

Initial model settings.

Item | Value |
---|---|

Conveyor speed | 2.5 m/sec (limit: 1–2.5 m/sec) |

| |

Conveyor spacing | 1 parcel |

| |

Number of workers deployed for each conveyor entrance | 7 workers (limit: 1–9 workers) |

| |

Number of workers deployed for each conveyor exit (serving 1 destination) | 2 workers (limit: 1–4 workers) |

| |

Number of workers deployed for each conveyor exit (serving 2 destinations) | 4 workers (limit: 1–6 workers) |

| |

Handling Capacity of Worker | 1 parcel |

| |

Arrival pattern for each source | Uniform distribution with a min. of 5 sec and a max. of 10 sec |

| |

Processing time of deconsolidation process | Normal distribution with a mean of 30 sec and a standard deviation of 2 sec |

| |

Demand for each destination | Uniform distribution with a min. of 220 units and a max. of 280 units |

The above model parameters are set based on the real system settings and observation.

Several parameters, including number of generations, initial population size, active population size, maximum clone size, and mutation factor are studied through sensitivity analysis so as to examine the individual parameters’ impact on the overall performance of the system and to determine the value for each parameter. Given with the results of the sensitivity analysis, the parameters of SCMIA were set as follows.

To allow a fair comparison among the algorithms compared, the parameters of the benchmarking algorithms were set with similar values and the values suggested by the authors.

We conducted two experiments to evaluate the performance of the SCMIA and the simulation-based optimization framework, that is,

Performance comparison between the results obtained from the simulation alone and that from the simulation-based optimization approach by using different optimization algorithms (the best results are bolded).

Cycle Time (the improvement in % compared with the one without optimization) | Workers’ Utilization (the improvement in % compared with the one without optimization) | |
---|---|---|

Simulation without optimization | 6788.64 sec | 45.04% |

Simulation-based optimization with SCMIA | 5763.86 sec (15.10%) | 65.46% (45.34%) |

Simulation-based optimization with MISA | 5754.88 sec (15.23%) | 63.45% (40.87%) |

Simulation-based optimization with NNIA | | 62.00% (37.66%) |

Simulation-based optimization with NSGA-II | 5680.23 sec (16.33%) | 62.90% (39.65%) |

Simulation-based optimization with SPEA2 | 5948.53 sec (12.38%) | |

The table shows that the cycle time of the whole distribution system at the DC is reduced by about 12–16% and the workers’ utilization is increased by 38–49% when optimization algorithms are deployed in the simulation process. This proves that the use of the optimizers can enhance the performance in the system’s cycle time and the workers’ utilization. However, the higher the utilization achieved, the longer the cycle time spent, and vice versa. When comparing SCMIA with other benchmark algorithms, SCMIA is able to produce comparable results in both the cycle time and workers’ utilization.

Graphical comparisons of the known Pareto fronts generated by the five algorithms.

The performance regarding the optimality and diversity of SCMIA in this multiobjective optimization problem was then examined by applying the metrics, namely, spacing and error ratio as shown in Table

Spacing and error ratio values generated by the five algorithms (the best results are bolded).

SCMIA | MISA | NNIA | NSGA-II | SPEA2 | |
---|---|---|---|---|---|

Mean | |||||

Error Ratio (ER) | | 0.85 (0.16) | 0.78 (0.18) | 0.76 (0.14) | 0.74 (0.06) |

Spacing ( | | 58.02 (55.82) | 49.23 (26.10) | 51.85 (17.58) | 39.32 (37.16) |

In this experiment, we compared the results of the mean and standard deviation of the two metrics over 30 trials obtained by SCMIA with that of the other benchmark algorithms. From the results shown in Table

Computational times of the five algorithms.

SCMIA | MISA | NNIA | NSGA-II | SPEA2 | |
---|---|---|---|---|---|

Time (hours) | 33.75 | 104.19 | 24.46 | 24.54 | 23.75 |

This study applies a multiobjective simulation-based optimization framework incorporating a hybrid immune optimization algorithm SCMIA for the evaluation of the optimality of the distribution system with respect to two criteria: system cycle time and workers’ utilization through simulation modeling. Based on the results of the simulation-based optimization study, the following conclusions and implications can be drawn regarding the performance of the framework and algorithm.

SCMIA generally performs better than other benchmark algorithms especially in the diversity aspect. This is largely attributed to the operators employed in the algorithm. For example, the selection operator incorporates the crowding-distance as a measure to select nondominated antibodies for undergoing the subsequent evolutionary processes so that the antibodies in less crowded regions will have a higher priority to be selected. The cloning operator and hypermutation operator are based on the same measure to generate a number of copies for exploring the solution space and bringing variation to the clone population, respectively, where less crowded individuals are given more chances for cloning and hypermutation in order to hopefully produce better offspring and increase population diversity. The crossover operator helps further enhance the diversity of the clone population and the convergence of the algorithm because some good genes from the active parent can be passed to the offspring. The suppression operator helps reduce antibody redundancy by eliminating similar individuals, hence significantly minimizing the number of unnecessary searches and increasing the population diversity. The memory updating operator takes account of the antibody similarity in terms of both the objective space and the decision variable space to formulate the memory population. As a result, SCMIA is able to generate a well-distributed set of solutions while it is a good approximation to the reference Pareto front. Other than the optimality and diversity, the stability of each algorithm can also be observed based on the standard deviations of the metrics shown in Table

The results overall demonstrate the ability of the multiobjective simulation-based optimization framework to serve as a decision support tool for helping management to effectively and efficiently find near optimal system operating parameters such as the speed of machines, the number of workers, or any other decision variables of interest in order to fulfill different objectives including system’s cycle time and workers’ unitization. As a result, significant savings in money, energy, and so forth, are achieved through the effective and efficient deployment of material handling systems and well-coordinated activities based on the optimized results. The research also sheds light into important issues of logistics system operation and management based on the case study, such as manpower allocation and design capacity of facilities.

Based on the findings of the current undertaking, it is worthwhile to extend the framework to tackle other complex problems involving many objectives to be solved in an efficient and effective manner in the future. Future research could also extend this approach to solve other real-world complex business problems other than the problems associated with material handling systems so as to establish the practical value of the framework in the simulation-based optimization context.

The authors declare that there are no conflicts of interest regarding the publication of this paper.