INFORMATION AND SYSTEMS SCIENCES Computing and Information
Volume 2, Number 1, Pages 59–66
OPTIMIZATION OF SPARE PART STORES BASED ON AN IMPROVED GENETIC ALGORITHM IN A SUPPLY CHAIN
JIANHUI WANG, YONGLIANG YAN, LIN XU, SHUFANG SUN, AND BO YAN Abstract. A Genetic Algorithm of Deuce Symmetrical Crisscross based on the real value (GADSC) is proposed for the spare part store management of enterprizes under the background of supply chains, aimed at the minimum of management cost and interrelated expenses. The Improved Genetic Algorithm (IGA) and the function are also proposed. Under the background of spare part store management, the optimization model is studied the optimal value is obtained. The stimulation result shows that the model can optimize the number of stores and reduce the cost of store management, so that a new method is gotten to optimize the spare part store management.
Key Words. Improved Genetic Algorithm, spare part store management, supply chain, store optimize.
Nowadays the incorporate trend of the information-based global economy is more and more clear. In the past decade the world has changed from a marketplace with several large independent markets into a highly integrated global market that demands a large variety of products, complying with high quality, reliability, and environmental standards[1]. Furthermore, today’s more demanding customers, the fast development of new products, and the increasing competitiveness of the market players have turned the market into a fast-changing environment. Under these circumstances, demands change rapidly over time, and hence their forecast, as well as the planning process to satisfy them, becomes difficult. Therefore, one of the challenges for today’s enterprises is to capture the economical potentials that the new environment offers while minimizing the negative impact of these rapid fluctuations. This goal can be achieved only if the enterprises become more flexible, reliable, and responsive. In light of this, it is necessary to study and characterize the dynamic behavior of enterprise systems and to adopt systematic procedures for decision-making processes.
1. Spare part management in supply chain
Supply chain is defined as the link of all the enterprises who are involved in the actions to provide product to the final consumers. These enterprises make up an integrated system. Supply management[2] refers to the management of the relations of all the organizations at different levels in the marketing channels. It is a technique which makes sure that all the enterprises in the chain can keep up with the whole chain. It is able to arrange properly the behavior of every enterprise in the chain. To make sure the natural running of the whole circulation of materials,
Received by the editors January 1, 2004 and, in revised form, March 22, 2004. 2000 Mathematics Subject Classification. 35R35, 49J40, 60G40.
This research was supported by national natural science foundation of China (serial number: 60274024).
as manufacturers the manufacturing enterprise should guarantee the safety of its high-speed efficient operation.
As for the problem of store management for production enterprise, there are two kinds of stores: one is stores of material, semi-manufactured goods, and the other is stores of spare part. For large enterprise, the store management of spare part is of notable importance. It can ensure the safety of the operation of equipment. The stores of spare part can influence the production process and current capital working. For instance, in the metallurgy industry, the spending of spare part is about six percent of the total cost, the fund for spare part stores is seven percent of the active capital[3]. So how to optimize the store of spare part is a very important issue for production enterprise, especially the large manufacture enterprise
Unfortunately, in the daily operations, the amount of spare part in stores is usually greater than the number we need indeed. It will be very severe if we ignore it. We will meet the following three typical problems:
(1) the store of spare part will occupy active capital chronically, and will affect the capital working.
(2) overstock will augment the store cost meaninglessly, which contains the accrual active capital and other store costs.
(3) overstock will augment the waste of spare part in storage, especially some exact and damageable instruments which would become bad or rusty with time going by.
The perfect situation of the spare part store is that the store is just in the balanced level. But in the actual case, we always find that the part is overstock. We have two ways to remedy it: 1. let it be consumed unaffectedly and don’t stock any part when the store is still in overstock. 2. dispose of or abandon some stores, but if we dispose of or abandon the stores to the normal level, some time later we need to buy them again.
So we need to find the way to manage the stores of spare part properly. The level of the management affects the usage efficiency and the capital working. There are various types of spare parts in enterprises, some of them are baroque or awkward. Hence the workload about manufacture, purchasing, store and management are very big, and that the occupied active capital is very large to affect the produce cost and the economic benefit.
One of the common methods for store management is taxonomy of ABC[4], MRP, JIT and so on. In this paper we use the taxonomy of ABCcontrolling the key spare parts. Through analysis we class all the parts to three species as ABC, and use corresponding strategies to control them.
In long-term practical experiments, we employ the “3 managing and 4 regulating” (planning management, ration management, store management, consume ration, capital ration, affirmative reserve and regular assign managing) method for spare part planning management.
In the actual optimization of management, we emphasize the control of class A which has very large proportion in the year cost. If we can reduce the store amounts as more as possible, we can speed the velocity of the current capital.
As is Common to realize the modernization, standardization and rationalization of the management, we should do as follows:
(1) ensuring the early management of equipment, the early days of the equip-ment are very important to the equipequip-ment. We should not only make sure that it can run adequately in this period but also make preparations for
the equipment’s evening operation management. Recently with the devel-opment of technology, the updating of equipments is fast-stepping, so we needn’t focus on how to maintain the equipment’s usage life, we should bend ourselves to ensure the high-efficiency operation of the equipment, as is the emphasis of the spare part management.
(2) finding out the rule of enterprises’ using life, checking and evaluating the status of equipments. The factual criterion which show the status is the status of the major parts. Knowing and noting the security rule and relative data of major parts, we can mater the spare part’s using life and get the consume rule.
(3) concentrating on the management of the spare part. Nowadays the kind and the amount of equipments increase very fast, so how to manage their storage becomes very important. Managing all the spare parts together turns out quite difficult and uneconomical, so we classify the spare parts logically, finding out the most important ones. This can be realized based on the ABC taxonomy, but here we don’t only consider the parts’ occupied capital proportion, but also the parts’ usage life and security. Then we use the networks or other information methods to implement the management. Thus the concentration is not only the parts’ and capital’s concentrations, but also the concentration of management (that’s the most important). (4) making sure the spare parts’ store management can let the production
security assort with the economical benefit. In the past, our enterprise always emphasizes the security of production, ignoring the expected profit, thus leading to high cost of the produce and that the enterprise couldn’t grow very well. So the management of spare parts is not only the method to keep the security of production but also a direct factor affecting the economic advantage.
(5) establishing a management information system, which can gets and treats the requirement of spare parts in time. There are so many varieties of spare parts that it’s easy to be erroneous if we deal with them by hand. If we could set up a information system we would be able to run it appropriately, and reduce the cost of spare parts’ storage.
The spare parts’ scientific and logical management is a very important work for us. We should improve it and ensure the equipments run reliably and highly efficiently.
Up to know, the current management in our country is underdeveloped. There are problems even if we just consider the most important part. For example, there are numerous spare parts required to be considered, the traditional method is very extensive, and the stock decision is always speculative and easily be affected by authority, as can easily make unnecessary overstock and some spare parts may be invalid, so that there are always some meaningless capital waste. To solve these problems and get the optimal quantity of spare part storage, and discuss the application of the intelligent optimization in spare part management, this paper presents an improved genetic algorithm.
2. Optimization of Spare Part Store Based on an Improved Genetic Al-gorithm
2.1. A Genetic Algorithm of Deuce Symmetrical Crisscross Based on the Real Value(GADSC).
Genetic algorithm(GA) was first proposed by Holland in 1975[5]. It represents an approach of global optimization search which is based on the mechanics of natural selection and natural genetics. It combines survival of the fittest among string structures with a structured yet randomized information exchange to form a search algorithm with the expected ever-improving performance. Due to its capabilities of directed random search for global optimization, it has drawn broad attention in various fields[10].
GA provides a universal model for solving a class of complex optimization prob-lems, and it has strong robustness for all kinds of probprob-lems, so it can be applied to a variety of fields. For example, in function optimization, we can use GA to solve the nonlinear, multi-model, model-object functions; Combinatorial optimiza-tion based on GA, such as TSP, knapsack problem, bin-packing problem, layout optimization, figure partition, etc[11−13]; GA is also applied in single production workshop scheduling, production line workshop scheduling, production planning, duty distribution and others production scheduling problems[10]; In the field of au-tomatic control, GA is used to optimize the aviation control systems and design the space rendezvous controllers and identify process parameters. Moreover, optimized designing of fuzzy controllers, learning fuzzy control rules, structure optimization and weight learning of neural network[11] etc can also be attacked based on GA; For robotics, GA is an important in route layout of moving robots, the motion tracking layout of articulation robots, solving inverse kinematics for robots, the structure optimization and action harmonization of cell robots, etc [12,13]. GA has also played a major part in image optimization. It has found applications in pattern recognition, image restoration and edge image feature extraction[14]. GA has shown primary application capacity in the aspects of Artificial Life such as evolutionary prototyping, learning model, behavior model and self-organization model.
As one of the effective methods to solve complex problem, the genetic algorithm can be used to find the answers of those problems that can not be solve by traditional ways. It is a directional stochastic search method, which is simple, maneuverable, robust. But the typical GA is not a complete searching MARKOV processwith low convergence speed, early convergence, bad stability and bad controllability[56]which affect the optimum. The search ability and the convergence character are important for judging the performance of GA. Factors affecting the search ability and the convergence character contain genetic algorithm operators, genetic coding methods, evolution strategies and so on[15]. Searching the new points from the given points, the genetic operators implement the jump in the searching space from the old one to the new one, as is the basic search strategy for GA[8]. Large numbers of experiments have proved that the traditional cross operator(one point crossover, two point crossover) can make the genetic value in the fore and caudal local of each unit of the colony all the same, when they are in the early iterative decades, that the cross operation are nullification, the genetic value of these positions are only changed by mutation, which greatly reduces the convergence performance and the search ability of the algorithm, especially in the pocket and small scale cases, that could make the algorithm not find the real optimum value.
The traditional GA usually uses two point crossover to improve the convergence speed. The main procedure is shown below:
(1) randomly setting two crossover points in each unit of the selected couples. (2) exchanging the parts between the two points of the two individuals. Unfortunately the traditional GA’s crossover could only get the genetic informa-tion of the units’ middle part, they can’t do anything with the head and the tail of
every unit. The traditional simple GA’s search capability seems not so good as we expect. Some researchers use some corresponding coding way top remedy this, they put the decisive variable in the middle of every unit and put the less important one to the head or tail. But actually the coding way is not practical, the programming work is very difficult. So in this paper we improve it, so that the algorithm can handle more problems.
In this paper we use the Genetic Algorithm of Deuce Symmetrical Crisscross based on the real value[4]real value coding operate in some real number bound.
The real coding GA initializes every unit by real number Xi ∈ s(i = 1, 2, · · · , m).
The dimension of the real vector is decided by the actual parameter number. Ran-dom choosing the units X1, X2 and selecting two cross points, the algorithm ran-domly generates an integer from 0 to 2. The deuce symmetrical crisscross operator is defined as follows: when the random is 0, we cross the heads of X1and X2; when it’s 1, we cross the middles of X1 and X2; when it’s 2, we cross their tails.
Figure 1. The crossover when the random number is 0 The main process of this improved genetic algorithm is described below:
(1) randomly create a set of initial units to form a population, and evaluate the fitness of every unit.
(2) quit, if the defined criterion is satisfied; else go to the next step. (3) select the value of evaluation.
(4) do the cross using probability. (5) do the mutation using probability. (6) go to step2.
2.2. Optimization of Spare Part Store Based on GADSC.
In this paper the uncoil of the optimum value of spare part stores is denoted as a real value. There are many kinds of spare parts. The arrive time and the additional charge (store management cost, traffic cost and other corresponding cost) of each part is different. Here we only need to control the stock number
If the equipment needs several kinds of spare parts (denote the ith part as i), and the corresponding prices are p1, p2 ,...,pm. The function of in-and-out is given
by function (1):
(1) Z(i) = I(i) + S(i) − U (i)
where I(i) is the ith part’s store at the beginning of a produce period; S(i) stands for the ith part’s stock in a produce period; U (i) denotes the number of the ith part’s be consumed in a produce period and Z(i) is the ith part’s store at the end of a produce period, respectively.
Function (2) refers to the total cost of the ith part in a single period:
(2) [I(i) + Z(i)
2 × pi× h(i) + S(i) × pi]
where h(i) is the expense coefficient(decided by traffic cost, store management cost and outage) and I(i)+ Z(i)2 × pi× h(j) stands for the store cost of the ith part’s.
The minimum object function for the store cost is given be equation (3): (3) min m X i=1 [I(i) + Z(i) 2 × pi× h(i) + S(i) × pi]
Because the limit of depot’s cubage and other factors, there is an upper limit to every part in any period.
(4) S(i) ≤ G(i)
where G(i) denotes the upper limit to buy.
For the stocks one should ensure the stock number of every part is above a guard line.
(5) Z(i) ≥ I(i)min
All the part safety coefficients are n1, n2,..., nm (the coefficients are decided by
experience and traffic condition).
In the produce process, the stocks should ensure the safety degree as high as possible:
(6) max[Z(1) × n1+ Z(2) × n2+ · · · + Z(m) × nm]
From the above, we get a two-objective optimization model which aims at getting the minimum of the capital cost and the maximum of the safety degree.
(7)
J = { min
m
P
i=1
[I(i)+ Z(i)2 × pi× h(i) + S(i) × pi] max[Z(1) × n1+ Z(2) × n2+ · · · + Z(m) × nm]
s.t.{
Z(i) = I(i) + S(i) − U (i) Z(i) ≥ I(i)min
S(i) ≤ G(i)
3. Simulation
we have got a spare part store model to optimize the store of a certain steel-group. By using GA to get the minimum of the cost, the model can satisfy the need of continuous production. Here we optimize five kinds of major parts, table 1 shows the basic demand information of these parts and the optimal results. Table 2 shows the expense in some traditional method.
To implement the algorithm above, the popular size is set to be 80iterative number be 100, cross probability be 0.6, and mutation probability be 0.01.
Table 3 shows the comparison of the two ways in terms of the safety degree and the cost. we can see that to ensure high safety degree, the optimal model gets the optimal cost 60132 (Chinese Yuan) and the traditional cost 83702 (Chinese Yuan). The optimization has saved 39.2 percents of all the cost. Therefore, we see that this method can not only ensure the safety of produce, but also avoid the waste of capital, thus improve the operation efficiency.
Figure 2 shows the traces of the capital cost and the degree of production safety, figure 3 shows the trace of finding the optimum of the five kinds of parts. The two pictures show that in a short time and few iterative steps, the algorithm can converge to the optimal value in an exact bound, and these two figures also show the celerity and accuracy of the algorithm. The new method has overcome the shortcoming of the traditional method, and it can improve the circulating efficiency, bring more economic benefit and social value. It’s clear that the new approach has a promising future.
part I(i) U(i) pi(RMB) h(i) I(i)min G(i) S(i) 1 1678 1548 20 0.001 150 1800 950 2 58 49 385 0.003 15 80 6 3 2190 2180 15 0.001 180 2500 170 4 73 66 156 0.003 9 100 100 5 450 397 81 0.0015 170 600 117
Table 1. the basic part demand information of the enterprise and the result of the optimal method
part Cost(RMB) pi(RMB) Requirement Total(yuan)
1 2164 20 387 9935
2 3856.4 385 25 10510
3 2654.7 15 1000 19800
4 1060 156 34 5570.8
5 7652 81 400 37886
Table 2. data statements of the traditional method in the corre-sponding period
Total cost Security degree
GA 60132 (yuan) 105.5
tradition 83702 (yuan) 109.2
Table 3. the comparison between the optimal way and the tradi-tional method
Figure 2. The traces of cost and safety degree 4. Conclusion
In this paper, we have discussed a direction of marketing and investigated the problem of spare part store management in a typical supply chain background. Here we focused on the manufacturing enterprise’s spare pare store management, which is very important for the whole produce operation. To implement this, we construct a multi-objective optimal model and single-period spare part store management optimal model.
The optimization of spare parts of enterprise in a supply chain guarantees high security of the product system, and reduces the outage and cost of store. The
Figure 3. The trace of the five best solution values
genetic algorithm of deuce symmetrical crisscross based on the real value provides a new method to optimize the storage of spare parts, so that we can effectively settle the problem of part stores which is very complex. It is very important to improve safety of production and the efficiency of the use of production expenses. By experiments, we saw that the method is effective.
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Faculty of Information Science and Engineering, Northeastern University, ShenYang, P.R.China, 110004
