1. Introduction
Nowadays, manufacturing has evolved and become more automated, intelligent, and complex. Due to the high precision and accuracy of manufacturing, robots play an important role in the automation line of manufacturing. However, manufacturing is facing an enormous environmental challenge as well as strong economic pressure because of increasing energy requirements and the associated environmental impacts of robots. Reducing the energy consumption of an automation line has been identified as an important strategy to develop economical and environmentally-friendly modes of intelligent manufacturing. Therefore, the issues of energy consumption in automatic production processes are becoming increasingly important.
Different studies relating to energy consumption modeling [
1,
2,
3], energy consumption evaluation [
4,
5,
6,
7], and energy consumption optimization [
8,
9,
10] can be found in the literature. However, research on energy consumption of a disassembly line is seldom performed. Therefore, it is necessary to collaborate on energy consumption, cost, and working load in order to optimize the trade-off among economic, working load, and energy performance of a disassembly line. The aim of this paper is to find a new way to deal with energy saving in a disassembly line in a quantitative manner that can make disassembly as profitable and energy efficient as possible. In comparison with the existing studies, this paper has three contributions. (1) In order to deal with high energy consumption in a disassembly line, the energy consumption of each stage in the disassembling process was analyzed and modeled. (2) To solve the disassembly line balancing problem with an energy saving consideration, this paper established a mathematical model of workstation selection and disassembly sequence with minimum energy consumption, minimum number of workstations, and maximum similarity degree of working load. (3) By comparing the solutions to the disassembly line balancing problem (DLBP), which does not have an energy saving consideration, this paper shows that, by considering energy consumption, and cutting unnecessary operations of direction and tool change in a disassembly line, a greater amount of energy can be saved.
The rest of this paper is organized as follows. In
Section 2, the related literature is provided and the contributions to the study are clearly identified.
Section 3 describes the problem of a disassembly line with an energy saving consideration.
Section 4 contains analyses and formulates the energy consumption of a disassembly line.
Section 5 establishes a mathematical model of the DLBP, incorporating energy consumption reduction and efficiency improvement.
Section 6 applies the proposed model to find the best schedule of workstation selection and disassembly sequence which achieves a lower energy consumption and cost with a high level of similarity degree of working load. A discussion of the energy consumption reduction of a disassembly line is given.
Section 7 concludes this paper by elaborating about future research issues.
5. Modeling of the DLBP with Energy Saving Consideration
Based on the concept and assumptions made by Gungor and Gupta about the deterministic version of the DLBP [
11], the assumptions of the DLBP with an energy saving consideration are:
A disassembly line is used to disassemble a single product type.
The supply of the EOL product is infinite.
The workstations are capable to process only one disassembly operation at a time.
Each component should be assigned to one workstation.
The time of all the components assigned to a workstation must not exceed the cycle time CT.
The precedence relationships among the components must be satisfied.
Given an EOL product consisting of
M components, the set of components in the EOL product is denoted as
Cset = {
C1,
C2, …,
Cj, …,
CM}. A matrix defines the precedence removal relationships of components, which determines the feasibility of disassembly sequences. The precedence matrix is defined as a
square matrix:
where
pljl = 1, if disassembly of
Cj can precede disassembly of
Cl; otherwise
pljl = 0.
The disassembly sequence of
Cset can be characterized by a design vector
X and is defined as:
where
xjk = 1, if
Cj is removed as the
k-th disassembly operation in the disassembly sequence; otherwise
xjk = 0.
In the disassembly line, there are
N workstations
Wset = {
W1,
W2, … ,
Wi, … ,
WN}. Each workstation is assigned a set of disassembly operations, a relation matrix is introduced to describe the relation between the workstation and disassembly operation as follows:
where
yik = 1, if the
k-th disassembly operation is assigned to
Wi; otherwise
yik = 0.
The relation matrix satisfies such constraints:
and
, implying that a component should exclusively belong to one subassembly only.
Figure 3 shows an example of a disassembly sequence and an assignment of operations to workstations of solution I in
Figure 1. As shown in
Figure 3, the disassembly sequence is
. Thus,
x11 = 1,
x22 = 1,
x33 = 1,
x48 = 1,
x55 = 1,
x64 = 1,
x77 = 1, and
x86 = 1. According to the disassembly operation assignment matrix
Y,
C1,
C2, and
C6 are assigned to workstation
W1,
C3, and
C5 are assigned to workstation
W2,
C8 is assigned to workstation
W3, and
C4 and
C7 are assigned to workstation
W4. Due to organizational requirements while performing disassembly, disassembly operations cannot be carried out in an arbitrary sequence but are subject to certain precedence relationships. The operation time of the sequence in which precedence independent operations are performed is influenced based on the order in which they are performed. One component may hinder the other component which may require additional movements to overcome the hindrance and/or the other components prevent it from using the most efficient or convenient disassembly process. For example, for the precedence sequence dependent disassembly operations
ds3 (
C3) and
ds4 (
C6), the time of the disassembly operation of
ds4 is affected by the disassembly operation of
ds3 if disassembly operation
ds3 is yet to be performed in the disassembly sequence. Thus, idling units have been added to compute the total processing time of the disassembly operation of
ds4 until the disassembly operation of
ds3 is finished.
According to the analysis and model of energy consumption in the disassembling process, the energy consumed by a workstation can be calculated as follows:
where
dcjl is the direction change coefficient (
dcjl = 1, if the direction of disassembly operations of
Cj and
Cl are different; otherwise
dcjl = 0) and
tcjl is the tool change coefficient (
tcjl = 1, if the disassembly operations of
Cj and
Cl use different tools; otherwise
tcjl = 0).
Thus, there exist three kinds of decisions in the DLBP with energy saving consideration that should be made:
Determining the number of workstations in order to minimize the total cost.
Determining the assignment of each disassembly operation and ensuring that the working load of each workstation is similar.
Finding the sequence of disassembly operations assigned to each workstation with the minimal total energy consumption.
The mathematical model of the DLBP with energy saving consideration further extends our previous research [
34] and is formulated as follows:
s.t.
where
tdai the additional time of
Wi corresponding to precedence constraints,
tdci is the direction changing time of
Wi, and
ttci is the tool changing time of
Wi.
The first objective given in Equation (12) is to minimize cost of the disassembly line, which depends on the number of workstations.
The second objective given in Equation (13) is to ensure that the working load of each workstation is similar. It was computed by the information entropy theory as well as the smaller variation of the idle time at each workstation, the smaller discrete probability distribution of data information, and the greater information entropy. In particular, information entropy should be at a maximum of 1 when the idle time of each workstation is the same. Therefore, a lower resulting value is more desirable as it indicates the maximum similarity of idle time across all workstations of the disassembly line.
As the third objective in Equation (14), the total energy consumption of a disassembly line is quantified by the sum of energy consumption of each workstation.
The constraint given in Equations (15) and (16) ensure that each disassembly operation is assigned to one workstation only.
The constraints given in Equations (17) and (18) address the feasibility of a disassembly sequence.
The constraint given in Equation (19) addresses the precedence feasibility of a disassembly sequence. This constraint ensures that the component is removed only when its precedence components are already removed.
The constraint given in Equation (20) makes sure that the number of workstations does not exceed the number of components and that there are enough workstations to complete all disassembly operations in the cycle time CT.
The constraint given in Equation (21) addresses the availability of work time and disassembly operations assigned to the workstation that must be completed in the cycle time CT. Automatic tool change is selected in this paper.