Scientific Programming

Volume 2016, Article ID 8264879, 9 pages

http://dx.doi.org/10.1155/2016/8264879

## A Recovery Model for Production Scheduling: Combination of Disruption Management and Internet of Things

^{1}School of Light Industry & Chemical Engineering, Dalian Polytechnic University, Dalian 116034, China^{2}School of Business Administration, Dongbei University of Finance and Economics, Dalian 116025, China

Received 13 June 2016; Accepted 25 August 2016

Academic Editor: Chengyan Yue

Copyright © 2016 Yang Jiang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

It is difficult to generate the new schedule effectively for minimizing the negative impact when an unanticipated disruption occurs after a subset of tasks has been finished in production scheduling. In such cases, continuing with the original schedule may not be optimal or feasible. Based on disruption management and Internet of things (IoT), this study designs a real-time status analyzer to identify the disruption and propose a recovery model to deal with the disruption. The computational result proves that our algorithm is competitive with the existing heuristics. Furthermore, due to the tradeoff between all participators (mainly including customers, managers of production enterprise, and workers) involved in production scheduling, our model is more effective than the total rescheduling and right-shift rescheduling.

#### 1. Introduction

Providing customers with satisfactory service is the central concern for production enterprises. However, given the complexity of processing environments, random or unanticipated events, including anomaly status of processing environment and machine breakdown, constantly occur in production scheduling. As a result, the original schedule is likely to be suboptimal and may not even be feasible. In this study, we use the term “disruption” to describe the reasons that trigger a rescheduling process.

Research on rescheduling is extensive [1, 2]. We differentiate our model from the existing findings in which the new schedule will be evaluated. The objective of most rescheduling research is to find an optimal schedule in the new environment with respect to the original objective function. In our model, we consider both the original objective function and the deviation from the original schedule. The reason for considering the deviation is that once the original schedule is generated, many preparations have already been made, such as allocating resources, distributing raw materials, and fixing customer delivery dates. Hence, if any change to the original schedule has a negative impact on these preparations, then the new schedule has to minimize the deviation [3].

In this paper, we combine disruption management and IoT to deal with the disruption. IoT is to realize the information sharing of global things from any place, which is able to monitor the process of production scheduling and identify the disruption quickly. Furthermore, disruption management aims to dynamically revise the original schedule and obtain a new schedule that reflects the constraints and objectives of the evolved environment [4].

The rest of the paper is organized as follows. Section 2 provides a brief review of the related work. Section 3 designs a real-time status analyzer based on IoT to identify the disruption. Section 4 constructs a recovery model combining quantitative model and prospect theory to measure the deviation, and Section 5 proposes an improved ant colony optimization (IACO) to obtain the new schedule quickly. Section 6 shows the validity of the demonstrated model and IACO. Finally, Section 7 provides conclusions and directions for future research.

#### 2. Related Work

Determining how to handle disruption is a significant issue in the decision-making process. Disruption management is an example of rescheduling in real time, which is necessary in some cases because disruption is unanticipated and cannot be embedded in making the original schedule in advance. Through disruption management, a new schedule that minimizes the negative impact can be obtained.

Disruption management was first applied to the airline industry, in which flight disruptions often entail huge cost loss [5, 6]. The successful implementation of the idea led to a growing interest in applying disruption management to other fields. In the study of production scheduling, Lee and Yu [7] studied the parallel-machine scheduling problem under the disruptive environment by minimizing the sum of weighted completion times and provided a pseudopolynomial time algorithm to solve the problem. Tang and Zhang [8] investigated the disruption caused by machine breakdown and proposed the Lagrangian relaxation approach to deal with the disruption. Wang et al. [9] discussed parallel-machine scheduling problems with a deteriorating maintenance activity and provided a polynomial time algorithm to solve the total completion time minimization problem. Liu et al. [10] studied the disrupted single-machine scheduling problem. The deviation was measured by the completion times of jobs and quantum-inspired hybrid heuristics were presented. Khedlekar et al. [11] studied the flexible managerial decision policy for disruption in production system. They solved the disruption problem analytically to determine the production period before and after disruptions. Paul et al. [12] developed the recovery model and dynamic solution approach to deal with disruptions for production-inventory system. Sarker et al. [13] focused on production scheduling under uncertain disruption and adopted an improved memetic algorithm to solve the problem.

Another stream of literature relevant to our research is the recently emerging subject of behavioral operation management [14]. The operation contexts primarily investigated were supply chain management, newsvendor problem, forecasting, and decision-making, which is concerned with the theories of individual decision-making biases, social preferences, and cultural elements [15]. Su [16] proposed a decision framework of bounded rationality applied to the classic newsvendor model. Gino and Pisano [17] explored the theoretical and practical implications of incorporating behavioral and cognitive factors into models of operations. Chen et al. [18] presented a model of bounded rationality based on the quantal response equilibrium, in which players were not perfect optimizers and faced uncertainty in the actions of their opponents. Katsikopoulos and Gigerenzer [19] briefly discussed some research on the heuristics in behavioral operation management and showed how the study of quantitative models of heuristics can complement it. Chen and Zhao [20] developed a behavioral model with different mental weights on the underage and overage costs to characterize the perception bias of a retailer on a critical fractile.

In summary, identifying the disruption was likely to be neglected in previous literature because the researchers focused on obtaining the revising schedule quickly. In addition, the existing researches assumed that humans in production scheduling were perfectly rational and emphasized the optimization of material and financial resources. They disregarded these facts that people facing a new situation often have different perceptions and the obtained solution may not be optimal or feasible. Accordingly, how to identify the disruption and measure the deviation still needs further study.

#### 3. A Real-Time Status Analyzer Based on IoT

In production scheduling, the ambient condition subtly changes all the time. However, considering and adjusting it as a whole are worthy only when the current schedule does not work properly. Thus, a real-time status analyzer based on IoT is designed and developed to identify the disruption before adopting the recovery model.

##### 3.1. System Architecture

The status data are sent to computer terminals (CTs) of the Internet via wireless sensor networks (WSNs) and satellite. The data processing center analyzes the data, and it is alerted when a disruption occurs. The system can achieve the following three functions.

*(1**) Data Acquisition*. Jobs in the shop are frequently sensitive to temperature, humidity, and pressure. Thus, the status of processing environment needs to be monitored in real time. All data of the basic properties and environmental status of jobs are also sent to the radio frequency identification (RFID) reader via the WSNs. Finally, the aforementioned information is summarized and sent to the corresponding CTs.

*(2**) Exception Analysis*. Based on the initial schedule and according to different characteristics of jobs, the corresponding thresholds for equipment status, shop temperature, humidity, and pressure are preset. Thus, the massive time-varying data can be monitored and analyzed in real time to determine whether any exception occurs.

*(3**) Real-Time Alert*. When an exception occurs as revealed by the monitored data, the disruption occurs and the system gives out alerts immediately, thereby revising the original schedule and obtaining a new schedule that minimizes the negative impact.

##### 3.2. Redundant Data Processing

RFID is prone to be absorbed and disrupted by the ambient condition, thereby resulting in any omission or deficiency in the reading process of the reader. This study aims to avoid such problems by proposing increasing the number of readers or the read-write frequency, thereby ensuring data integrity. However, this proposal can inevitably produce a significant amount of redundant data, increasing the burden to the RFID data transmission and storage. Thus, the system efficiency is greatly reduced. Therefore, an effective way to solve problems of redundant data processing must be determined to screen all data and to reduce the burden on the system.

Basic sorted-neighborhood method (SNM) is an efficient algorithm to cope with redundant data. However, it is difficult to control the size of smoothing window. This study presents a modified SNM algorithm with specific procedures as follows.

*Step 1. *The data are sorted according to the timestamp.

*Step 2. *In the data comparison process, a smoothing window featured with adaptive adjustment is used, and the window is resized as desired.

*Step 3. *The first data entry in the current window is compared with the next, and whether it is repeated is determined. If it is repeated, Step 4 follows; otherwise, Step 5 is next.

*Step 4. *When the repeated entry is found, the entry with the oldest timestamp is deleted and that with the latest timestamp is retained.

*Step 5. *Whether the first entry in the window is the last is determined. If it is the last, Step 6 follows; otherwise, Step 3 is next.

*Step 6. *Whether any unprocessed data exists is determined. If so, Step 1 follows; otherwise, the entire workflow ends.

#### 4. Recovery Model for Production Scheduling

Considering its wide application in production and manufacturing industries, the Job-Shop Scheduling Problem (JSP) is chosen as an example to construct the recovery model.

##### 4.1. Construction of the Model for Original Schedule

###### 4.1.1. Problem Definition

The problem is confined to the following conditions. Given jobs, each job has operations and must be processed on machines. The objective is to find a schedule of minimal time to complete all jobs, where(1)the machine can only process one job at a time,(2)every job is available for processing at time 0,(3)once processing is initiated, the operation must be completed on the machine without interruption.

###### 4.1.2. Notations

: the number of jobs. : the number of machines. : the set of jobs, . : the set of machines, . : the completion time of job in machine . : the processing time of job in machine . : the due date of . : a large positive number.

###### 4.1.3. Mathematical Model

The JSP model is constructed as follows:

In this model, the objective function (2) aims to minimize the makespan, which is the minimal time to complete all jobs. Formulas (3) and (4) are the technological and processing constraints. Formula (5) ensures that all jobs are completed before their due date.

##### 4.2. Construction of the Recovery Model

When the optimal schedule is executed, the disruption occurs and is identified by the real-time status analyzer. Consequently, we need to construct the recovery model and obtain a new schedule.

Machine breakdown is the typical disruption in production scheduling. In this paper, the recovery model is illustrated by the example of machine breakdown.

###### 4.2.1. Problem Hypothesis

(1)The original schedule is known.(2)The time when disruption ends is regarded as 0.(3)The processing job when disruption occurs must be reprocessed after the disruption ends. In other words, jobs are uninterruptible.

###### 4.2.2. Notations

: the number of unprocessed jobs. : a subset of unprocessed jobs, . : the set of operations processed before operation in the original schedule for machine . : the set of operations processed after operation in the recovery schedule for machine . : the intersection of and , . : the cardinality of subset . : completion time of in the original schedule. : completion time of in the recovery schedule. : the makespan in the original schedule. : the makespan in the recovery schedule. : the sequence deviation between the original schedule and the recovery schedule. : unsatisfaction degree of customer for completion time deviation. : unsatisfaction degree of managers for operational cost deviation. : unsatisfaction degree of workers for sequence deviation. , : parameters related to gains and losses for customers. , : parameters related to gains and losses for managers. , : parameters related to gains and losses for workers. , , : loss aversion coefficient for customers, managers, and workers, respectively.

The other notations are the same as the ones in previous sections.

###### 4.2.3. Impact of Disruption

The general process of one schedule is as follows: (i) managers of production enterprises generate an optimal schedule according to the requirements of customers, (ii) workers execute the schedule to process jobs, and then (iii) customers receive their products within the required time. The impact of disruption on the above three participators (i.e., managers, workers, and customers) is analyzed below.

*(1**) Managers*. After disruption occurs, the processing sequence of unprocessed jobs will change, leading to the increase of makespan. The makespan is relevant to the operational cost, which is the central concern of managers. Accordingly, minimizing the makespan of unprocessed jobs is the key objective of managers when generating the recovery schedule.

*(2**) Workers*. The processing sequence of unprocessed jobs will be changed after disruption occurs. Considering that many preparations have been made in advance based on the original schedule, workers have to reallocate raw materials and tools, which will lead to the increase of extra workload. Therefore, the recovery schedule should minimize the sequence deviation to reduce the negative impact on workers.

*(3**) Customers*. Once the environment is interrupted by disruption, a chain reaction will be generated to affect the completion time of unprocessed jobs, and a number of customers will not be served within the required time. Thus, the recovery schedule should reduce the deviation of completion time to improve the satisfaction and loyalty of customers.

###### 4.2.4. Function of Measuring Deviation

Prospect theory [21] is one of the most important decision-making theories. It can perfectly describe the decision-making based on bounded rationality under the uncertainty condition. Hence, on the basis of prospect theory, this paper measures the deviation of participators [22].

*(1**) Measuring the Deviation of Customers*. The value function of customer can be described as follows:where the reference point is (). means losses for customer ; otherwise, it means gains for customer .

The unsatisfied membership function of customer for completion time deviation can be given as follows:where .

*(2**) Measuring the Deviation of Managers*. The value function of managers can be constructed as follows:where the reference point is . means losses for managers; otherwise, it means gains for managers.

The unsatisfied membership function of managers for operational cost deviation can be given as follows:where .

*(3**) Measuring the Deviation of Workers*. The value function of workers can be constructed as follows:where the reference point is 0 because the sequence deviation does not exist in the original schedule. In recovery schedule, is equal to . means losses for workers.

The unsatisfied membership function of workers for sequence deviation can be given as follows:where .

###### 4.2.5. Recovery Model

On the basis of the above functions of measuring deviation, the objective function of the recovery model is constructed through lexicographic multiple goal programming as follows:

Formula (12) aims to minimize the sum of the unsatisfaction degrees of customers, managers, and workers. , , and represent the different priorities, which can be flexibly adjusted in the practical application.

#### 5. IACO for the Recovery Model

The proposed model is NP-hard, which has an optimal solution that is difficult to obtain. Ant colony optimization (ACO) is an evolutionary computation technique developed by Colorni et al. [23]. Compared with other heuristics, ACO has the characteristics of positive feedback, distributed computation, and constructive greedy heuristic. In particular, the ACO has been shown to be an efficient algorithm for solving NP-hard problems [24–26]. However, the algorithm still has the weaknesses of local optimization and low search speed. In this study, we illustrate IACO to solve the recovery model.

##### 5.1. Introduction of Adjusting the Pheromone Trail

(1)In ACO, pheromone trails left by ants do not always show the evolutionary direction, and the pheromone deviating from the optimal solution has the probability of increasing, which leads to premature convergence. This study proposes an approach to enhance the global search capability of ACO by adjusting the pheromone trail adaptively with the evolutionary process.(2)The updated pheromone trail may reach the maximum value or minimum value after every search process is completed. leads to premature convergence, and increases the computational time. Thus, IACO limits the pheromone trail in the interval (). After the pheromone trails are updated, is replaced by when or by ()/2 when .(3)ACO has difficulty obtaining the optimal solution because the trail persistence is fixed. The smaller the value of is, the better the global search capability will be. However, the computational time will increase gradually. On the contrary, increasing can improve the computational time, but the algorithm can easily be trapped in the local optimal solution. Therefore, IACO adopts a dynamic rather than a fixed value.

##### 5.2. Approach of the Crossover and Mutation

The crossover and mutation operations can increase the variance of the population and search the solution space completely in genetic algorithm (GA). Thus, these two operations are adopted in IACO to avoid premature convergence.

*(1**) Crossover Operation*. In the paper, a schedule is represented by the following encoding structure:where represents the sequence of operations of job . Each solu in is an unrepeated integer number in the interval .

When the search becomes trapped in the local optimal solution, crossover operation is conducted as follows:(i)Assume that encoding of schedule is and encoding of schedule is .(ii)Randomly generate an integer number in the interval . Then, exchange and , and generate two new encodings, that is, and .(iii)Update the encoding of optimal solution.

*(2**) Mutation Operation*. Mutation plays a significant part in improving the diversity of the population. Similar to GA, IACO is designed to avoid premature convergence and obtain a better solution by significantly decreasing pheromone trails in any path of the local optimization routing. These paths will be selected by small random probabilities because the distribution of the pheromone trails will be destroyed by too many mutation operations.

##### 5.3. Combination with Other Heuristics

ACO has the characteristic of strong coupling, which makes it easy to combine with other heuristics. Exchange mechanism is originally applied in the vehicle routing problem with time windows. It can obtain a new solution from the current solution by exchanging the nodes. We demonstrate a neighborhood exchange mechanism to significantly improve the convergence speed of ACO.

*(1**) Operators of the Neighborhood Exchange Mechanism*. Two neighborhood operators (among those listed below) are included in this study.(i)*Random Swaps of Subsequences*. This operator randomly selects and with and swaps and in the solution sequence. Figure 1 shows an example of this operator.(ii)*Random Insertions of Subsequences*. This operator randomly selects and with and puts in front of . An example is shown in Figure 2.