CN106020142A - Flexible job shop scheduling method considering energy consumption cost and weighted tardiness cost - Google Patents

Abstract

The invention discloses a flexible job shop scheduling method considering energy consumption cost and weighted tardiness cost. The scheduling method comprises the following steps: S1) carrying out classification on shop energy consumption into processing energy consumption, non-processing energy consumption and shop environment unit time energy consumption; S2) establishing mathematical models for the processing energy consumption, the non-processing energy consumption and the shop environment unit time energy consumption respectively; S3) establishing a mathematical model of the total shop energy consumption; and S4) calculating the cost of the total shop energy consumption. The invention provides the scheduling method capable of reducing shop energy consumption cost for the existing shop energy consumption; and through the scheduling method, the total shop energy consumption cost can be reduced by about 60%.

Description

Consider that energy consumption cost drags the flexible job shop scheduling method of current cost with weighting

Technical field

The present invention relates to energy consumption optimization method, be specifically related to a kind of consider that the flexible work of current cost is dragged in energy consumption cost and weighting Industry Job-Shop method.

Background technology

The energy is to manufacture one of indispensable basic resource for the whole world.Along with the global evolution of industry, global energy disappears Expense amount was doubled in 50 years.At present, industrial energy consumption accounts for the half of world energy sources consumption figure, energy cost upper One of most important factor of Sheng Shi manufacturing enterprise.

In face of the fierce market competition, increasing enterprise, especially reduces energy consumption extremely for medium-sized and small enterprises Close important, but in the production process of workshop, owing to the factor of impact is the most, thus cause there is presently no one The dispatching method of workshop energy consumption cost can be reduced.

Summary of the invention

For the deficiencies in the prior art, the purpose of the present invention aims to provide the dispatching party that can reduce workshop energy consumption cost Method.

For achieving the above object, the present invention adopts the following technical scheme that

Considering that energy consumption cost drags the flexible job shop scheduling method of current cost with weighting, described dispatching method includes as follows Step:

S1, classifying workshop energy consumption, workshop energy consumption is divided into: process energy consumption, non-process energy consumption and workshop condition list Bit time energy consumption；

S2, to process energy consumption founding mathematical models, particularly as follows:

$\mathrm{PE}\left(\mathrm{sch}\right)={\mathrm{\Σ}}_{k=1}^m{\mathrm{\Σ}}_{i=1}^n{\mathrm{\Σ}}_{j=1}^{o^i}(E_{\mathrm{ijk}}\×x_{\mathrm{ijk}})$

To non-process energy consumption founding mathematical models, particularly as follows:

$\mathrm{NPE}\left(\mathrm{sch}\right)={\mathrm{\Σ}}_{k=1}^m{\mathrm{TEM}}_k\left(\mathrm{sch}\right)$

To workshop condition unit interval energy consumption founding mathematical models, particularly as follows:

EE (sch)=C_max×MPE

Wherein:

N: piece count；

M: machine quantity；

J: workpiece set,

d_i: workpiece J_iThe date of delivery of (1≤i≤n)；

w_i: workpiece J_iWeight coefficient；

M: collection of machines,

O_i: workpiece J_iOperation quantity；

OP_ij: workpiece J_iJth (1≤j≤the O of (1≤i≤n)_i) procedure；

MP_ij: OP_ijThe set of optional processing machine；

g_ij: OP_ijThe quantity of optional processing machine；

At machine M_kThe l procedure of upper processing；

h_k: at machine M_kThe operation quantity of upper processing；

OperationDeadline；

OperationTime started；

p_ijk: OP_ijAt machine M_kOn the processed time；

t_ijk: OP_ijAt machine M_kOn cutting time；

s_ij: OP_ijThe processed time started；

c_ij: OP_ijThe processed deadline；

C_i: workpiece J_iCompletion date, i.e.

C_max: the Maximal Makespan of all workpiece, i.e.

MPE: the workshop condition unit interval energy consumption amount of money；

MPT: unit drags the phase to punish the amount of money；

MPP: the unit power amount of money；

PE: process energy consumption；

NPE: non-process energy consumption；

EE: workshop condition unit interval energy consumption；

S3, the mathematical model of structure workshop total energy consumption, particularly as follows:

Minimize Cost (sch)=TM (sch) × MPT+ (PE (sch)+NPE (sch)) × MPP+EE (sch)；

Wherein: Minimize Cost is the total amount of workshop energy consumption；

TM for dragging the phase to punish,

T_iFor dragging time phase: T_i=Max{0, C_i-d_i}；

S4, the mathematical model of workshop total energy consumption built according to S3 calculate the amount of money of workshop total energy consumption.

The beneficial effects of the present invention is:

The present invention is that existing workshop energy consumption provides a kind of dispatching method that can reduce workshop energy consumption cost, by fortune With the dispatching method of the present invention, it is possible to decrease the total energy consumption amount of money is close to 60%.

Accompanying drawing explanation

Fig. 1 is that the present invention considers that energy consumption cost drags the flow chart element of the flexible job shop scheduling method of current cost with weighting Figure.

Detailed description of the invention

Below, in conjunction with accompanying drawing and detailed description of the invention, the present invention is described further:

As it is shown in figure 1, the present invention considers that energy consumption cost and weighting drag the flexible job shop scheduling method of current cost concrete Comprise the following steps that

S1, classifying workshop energy consumption, workshop energy consumption is divided into: process energy consumption, non-process energy consumption and workshop condition list Bit time energy consumption；

S2, build (PE) vertical mathematical model to processing energy consumption

Every machine M_kHave a power consumption of three constants: standby time state, switch to start shooting running status, actual behaviour Make state (representing with cutting operation).

Machine M_kInput power P_kT () is a step function, machine M_kIdle power beIf OP_ijAt machine M_kBe processed, then during the operation increased, power isExtra cutting power is

Operation OP_ijThe process time is time interval p of coolant switch_ijk, cutting time t therein_ijkIt is typically Gao Gong The relatively short period of time interval that rate arrives, t_ijkIt is included in p_ijkIn, so there being p_ijk＞ t_ijk。

Assume that in operation, power keeps constant, then machine M_kIn treatment process OP_ijBasic energy expenditure The energy expenditure of the increase of the state that put into operation by machine isThe extra cutting operation increased again Energy expenditure be

Therefore, machine M_kUpper treatment process OP_ijJPE be(JPE: at workpiece The energy consumption that reason is relevant " include the prime power consumption of machine, such as idle power, run processing and consume, cutting consumes.)

Then:

To non-process energy consumption (NPE) founding mathematical models

If TEM_k(sch) it is that a feasible schedule plan sch consumes at machine M_kOn NPE.WithRepresent s respectively In at machine M_kOn operationTime started and the end time, then

${\mathrm{TEM}}_k\left(\mathrm{sch}\right)=P_k^{\mathrm{idle}}\×\left[{\max }_{1\≤l\≤h_k}\right\{c_k^l\}-{\min }_{1\≤l\≤h_k}\{s_k^l\}-{\mathrm{\Σ}}_{l=1}^{h_k}(c_k^l-s_k^l)],$

Then

To workshop condition unit interval energy consumption founding mathematical models

Workshop condition unit interval energy consumption refers to the energy consumed except machine resources during processing workpiece, and other must consume The energy maintain workshop normal operation.Power consumption such as the illuminator in workshop, ventilating system, air-conditioning, heating etc..

EE (sch)=C_max×MPE

The definition of the most above-mentioned each parameter is specific as follows:

N: piece count；

M: machine quantity；

J: workpiece set,

d_i: workpiece J_iThe date of delivery of (1≤i≤n)；

w_i: workpiece J_iWeight coefficient；

M: collection of machines,

O_i: workpiece J_iOperation quantity；

OP_ij: workpiece J_iJth (1≤j≤the O of (1≤i≤n)_i) procedure；

MP_ij: OP_ijThe set of optional processing machine；

g_ij: OP_ijThe quantity of optional processing machine；

At machine M_kThe l procedure of upper processing；

h_k: at machine M_kThe operation quantity of upper processing；

OperationDeadline；

OperationTime started；

p_ijk: OP_ijAt machine M_kOn the processed time；

t_ijk: OP_ijAt machine M_kOn cutting time；

s_ij: OP_ijThe processed time started；

c_ij: OP_ijThe processed deadline；

C_i: workpiece J_iCompletion date, i.e.

C_max: the Maximal Makespan of all workpiece, i.e.

MPE: the workshop condition unit interval energy consumption amount of money；

MPT: unit drags the phase punishment amount of money (unit/unit)；

MPP: the unit power amount of money (unit/kilowatt hour)；

PE: process energy consumption；

NPE: non-process energy consumption；

EE: workshop condition unit interval energy consumption；

(2) concrete logical variable is:

x_ijkIf: OP_ijAt machine M_kUpper processed, then x_ijk=1, otherwise x_ijk=0；

y_iji′j′kIf: OP_ijPrior to OP_i′j′At machine M_kComplete (x_ijk=1, x_i′j′k=1, i ≠ i ', j ≠ j '), then y_iji′j′k =1, otherwise y_iji′j′k=0；

(3) constraints is:

s_ij>=0, c_ij>=0, wherein 0≤i≤n, 1≤j≤O_i； (1)

s_ij+x_ijk×p_ijk≤c_ij, wherein 1≤i≤n, 1≤j≤O_i, 1≤k≤m； (2)

c_ij≤s_i(j+1), wherein 1≤i≤n, 1≤j≤O_i-1； (3)

Wherein 1≤i≤n； (4)

s_ij+p_ijk≤s_i′j′+L(1-y_iji′j′k), wherein 0≤i≤n, 1≤j≤O_i, 1≤i '≤n, 1≤j '≤O_i′, 1≤k ≤m；

(5)

c_ij≤s_i(j+1)+L(1-y_{i′j′i(j+1)k}), wherein 1≤i≤n, 1≤j≤O_i-1,0≤i '≤n, 1≤j '≤O_i', 1 ≤k≤m；

(6)

Wherein 1≤i≤n, 1≤j≤O_i； (7)

Wherein 1≤i '≤n, 1≤j '≤O_i′, 1≤k≤m； (8)

Wherein 1≤i≤n, 1≤j≤O_i, 1≤k≤m； (9)

Formula (1) represents that parameters variable must be 0 or positive number；Formula (2) and formula (3) represent the operation of each workpiece Sequencing retrains；Formula (4) represents the constraint of the completion date of workpiece, i.e. the completion date of each workpiece can not exceed always Completion date；Formula (5) and formula (6) represent that same machine of synchronization can only process one procedure；Formula (7) represents machine about Bundle, i.e. synchronization can only and be only capable of by a machining with one procedure；There is each machine in formula (8) and formula (9) expression Circulation operation can be there is on device.

S3, the mathematical model of structure workshop total energy consumption, for unified dimension, be all scaled the amount of money by object function, the most total Object function be particularly as follows:

Minimize Cost (sch)=TM (sch) × MPT+ (PE (sch)+NPE (sch)) × MPP+EE (sch)；

Wherein: Minimize Cost is the total amount of workshop energy consumption；

TM for dragging the phase to punish,

T_iFor dragging time phase: T_i=Max{0, C_i-d_i}；

S4, the mathematical model of workshop total energy consumption built according to S3 calculate the total amount of workshop energy consumption.

Wherein, in order to verify the practicality of this method and the practical situation of energy consumption can be reduced, 10 machines are used Device produces 100 workpiece and uses in conventional workshop conventional energy consumption dispatching method to carry out producing and in conventional method respectively Workshop uses the energy consumption dispatching method of the present invention to produce, and is proven, and 100 workpiece of 10 productions of machinery are at conventional car Between use the energy consumption dispatching method of routine when producing, its required total energy consumption amount of money spent is 134236.3 yuan；And 10 100 workpiece of platform production of machinery are when the energy consumption dispatching method that conventional workshop uses the present invention produces, and it is required spends The total energy consumption amount of money be 63158.5 yuan, it follows that use the present invention energy consumption dispatching method, it is possible to decrease the total energy consumption amount of money connects Nearly 60%.

It will be apparent to those skilled in the art that can technical scheme as described above and design, make other various Corresponding change and deformation, and all these change and deformation all should belong to the protection domain of the claims in the present invention Within.

Claims (1)

1. consider that energy consumption cost drags the flexible job shop scheduling method of current cost with weighting, it is characterised in that described dispatching party Method comprises the following steps that

S1, classifying workshop energy consumption, workshop energy consumption is divided into: when processing energy consumption, non-process energy consumption and workshop condition unit Between energy consumption；

S2, to process energy consumption founding mathematical models, particularly as follows:

$PE\left(sch\right)={\mathrm{\Σ}}_{k=1}^m{\mathrm{\Σ}}_{i=1}^n{\mathrm{\Σ}}_{j=1}^{o^i}(E_{ijk}\×x_{ijk)}$

To non-process energy consumption founding mathematical models, particularly as follows:

$NPE\left(sch\right)={\mathrm{\Σ}}_{k=1}^m{\mathrm{TEM}}_k\left(sch\right)$

To workshop condition unit interval energy consumption founding mathematical models, particularly as follows:

EE (sch)=C_max×MPE

Wherein:

N: piece count；

M: machine quantity；

J: workpiece set,

d_i: workpiece J_iThe date of delivery of (1≤i≤n)；

w_i: workpiece J_iWeight coefficient；

M: collection of machines,

O_i: workpiece J_iOperation quantity；

OP_ij: workpiece J_iJth (1≤j≤the O of (1≤i≤n)_i) procedure；

MP_ij: OP_ijThe set of optional processing machine；

g_ij: OP_ijThe quantity of optional processing machine；

At machine M_kThe l procedure of upper processing；

h_k: at machine M_kThe operation quantity of upper processing；

OperationDeadline；

OperationTime started；

p_ijk: OP_ijAt machine M_kOn the processed time；

t_ijk: OP_ijAt machine M_kOn cutting time；

s_ij: OP_ijThe processed time started；

c_ij: OP_ijThe processed deadline；

C_i: workpiece J_iCompletion date, i.e.

C_max: the Maximal Makespan of all workpiece, i.e.

MPE: the workshop condition unit interval energy consumption amount of money；

MPT: unit drags the phase to punish the amount of money；

MPP: the unit power amount of money；

PE: process energy consumption；

NPE: non-process energy consumption；

EE: workshop condition unit interval energy consumption；

S3, the mathematical model of structure workshop total energy consumption, particularly as follows:

Minimize Cost (sch)=TM (sch) × MPT+ (PE (sch)+NPE (sch)) × MPP+EE (sch)；

Wherein: Minimize Cost is the total amount of workshop energy consumption；

TM for dragging the phase to punish,

T_iFor dragging time phase: T_i=Max{0, C_i-d_i}；

S4, the mathematical model of workshop total energy consumption built according to S3 calculate the amount of money of workshop total energy consumption.