New Strategy to Optimize Lean Supply Chain Design by Meta-Heuristic

Corresponding Author: Thi Hong Dang Nguyen Department of Mechanical/ Manufacturing Engineering, École de Technologie Supérieure, Montréal, Québec, Canada Email: thi-hongdang.nguyen.1@ens.etsmtl.ca Abstract: This paper aims at presenting one novel quantitative strategy of optimizing the design of Lean supply chain using Meta-Heuristics. While classifying Lean Manufacturing tools in two categories, namely Functional and Tier Lean tools, we propose a new framework to design the Lean supply chain by implementing the former into a 5-echelon Fat supply chain. As the following step, we investigate the effect of the latter on the mentioned Lean supply chain model. Then, we utilize the tight correlation of Tier Lean tools and priority-based Genetic Algorithm Meta-Heuristics in order to optimize the configuration of the Lean supply chain. Finally, these ideas are illustrated step by step in one numeral example.


Introduction
Supply Chain Management (SCM) is a respected area today, as future competition in the field of business will be based on Supply Chains (SC) system rather than individual enterprises (Rice and Hoppe, 2001). Several models of SC have been studied as part of the incessant efforts taken to improve the competitive advantages of enterprises. Among them, the Lean Supply Chain (LSC) is assessed as an "ideal SC" (Srinivasan, 2012) since it can promptly and economically deliver the final products/services to customers in a seamless manner. The objective of the LSC is to eliminate non-value added activities as well as reduce the required non-value added activities (Anand and Kodali, 2008). Deborah (2005) analyses and compares the characteristics of the Fat Supply Chain (FSC) and LSC, thereby asserting the undeniable benefits and power of the LSC over the FSC.
In the SCM domain, the Supply Chain Design (SCD) directly impacts the performance of the SC since it creates a proper platform for all activities in the chain. Harrison (2001) suggests that approximately 80% of the total product cost may be fixed with SCD decisions. Nonetheless, the design space of the SCD contains a vast number of alternatives (Leukel and Sugumaran, 2013), which makes it hard to define the best solutions. Over time, the developments of information technology and optimization techniques make this difficulty solvable through optimization, simulation, or heuristics (Harrison, 2001). Recently, numerous Meta-Heuristics (MH) which are improved from heuristics, have proven effective in resolving SCD issues.
Inspired by such attractions, we introduce in this study a new quantitative strategy to design LSC by MH. The forthcoming sections in this study are organized into as followings: Literature review; new strategic framework of the Lean Supply Chain Design (LSCD), including the FSC formation, LSC transformation and its optimization by priority-based Genetic Algorithm (pGA); a numerical example; and conclusion.

Literature Review
SCD is a rich domain of SCM. Farahani et al. (2015) classifies SCD into five main rubrics: (1) Network structure; (2) Non-strategic decision of the SC; (3) Technology type/production philosophy; (4) Environmental condition of the model; and (5) Objective of mode, which includes LSC and other kinds of SC. Ugochukwu et al. (2012) states, "When Lean is implemented across the entire SC, the SC is referred as a LSC." Findings from the exhaustive review of Anand and Kodali (2008) show that previous studies concentrated on transforming the current FSC into LSC, rather than building a brand new LSC in its design stage.
Theoretically, the SCD process has been described through various models, in which the 5-stage SC Outline Process (SCOP) proposed by Corominas et al. (2015) profoundly draws out an SCD roadmap. To begin with, the first stage focuses on identifying the environment and objectives of the new SC. Further, stage 2 defines the SC macrostructure. Then, stage 3 identifies the SC mesostructure. Stage 4 specifies the SC microstructure, in which all SC specifications (objectives, parameters, constraints and variables) are formulated into mathematical models. Final stage chooses the optimal SC configuration among obtained results. There are two main solution methodologies in this stage: Exact solution and heuristics or MH (Melo et al., 2008). Tiwari et al. (2010) realize the growing tendency of using MH as they can offer acceptably good solutions with relatively little CPU time. Especially, the application of MH in SCM and SCD is well reviewed by Stanley et al. (2012). The study finds that GA, a globally optimal MH inspired by evolutionary biology (Holland, 1962), is the most prevalent. During the time, GA is modified and hybridised with various algorithms in order to improve its search quality (Jaramillo et al., 2002). Among of which, pGA, proves useful in designing the SC (Mitsuo et al. 2006). It is noteworthy that pGA is superior to Spanning Tree-based GA by using a simpler decoding procedure to generate random feasible chromosomes.

New Strategic Framework of LSCD
The new strategic framework of the LSCD includes three main stages and eight sub-steps ( Fig.  1). To elaborate, suitable LM tools selected among 59 items in review of Anand and Kodali (2008) are implemented into the fourth and fifth stage of the SCOP model (Corominas et al., 2015). These tools are classified into two categories that play a distinct role in the LSCD process: Functional Lean tools (which influence the SC total cost with daily operating functions) and Tier Lean tools (which affect the SC configuration), as depicted in Fig. 2. The entire process is particularly explained in turn below.

Formulate the FSC Model
The objective function of the FSC is to minimize the SC performance -Total Cost (TC), which is apportioned from SC tiers and functions as modified in study of Shretta et al. (2015), (Fig. 3a). The former include the Supplier (S), Plant (P), Distribution Centre (DC), Warehouse (WH) and Customer (C). The latter comprises five basic functions: Procurement, Production, Delivery, Inventory and Quality Assurance, which are described by the SC TC tree (Fig. 3b). Thus, the general FSC TC can be formulated from the five mentioned elements together with the Facility Installation cost. It is noted that all costs that are derived from suppliers are cumulated with the Material cost. Specifically, FSC TC is formulated in Equation 1 as follows:

LSC Transformation
Step 1: Simplify the General Model with Functional Lean Tools (Fig. 4) After a period of time, if these tools are strictly implemented, they can reduce various SC costs to some extent (completely, remarkably, or gradually). For example, Order cost, Setup cost and Holding/work-in-process cost can be almost eliminated by the IT support system, Setup Reduction At the operational level, the objective function Equation 3 can be expressed by mix integer programing as: Where: Unit variable Operating cost of plant j and unit Throughput cost of DC k, warehouse l T jk , T kl , T lm : Unit Transportation cost among adjacent tiers I j , I k , I l : Installation cost of plant j, DC k and warehouse l C j , C k , C l : Capacity of plant j and DC k and warehouse l D j , D k , D l , D m : Demands from plant j, DC k, warehouse l and customer l Variables x j , x k , x l : Binary variable denotes plant j, DC k, warehouse l opened (1) or closed (0) y ij , y jk , y kl , y lm : Quantity of material/product shipped among adjacent tiers Subject to: • Balance between quantities received and amount supplies at each node: ; ; • Satisfy demand from plant, DC, warehouse and customers: ; ; • The quantity delivered from each node is less/equal to its capacity: ; ; • Non-negative conditions: , , 0 ij jk kl y y y ≥ Step 2: Encode the LSC Configuration After simplified, the LSC is encoded by the pGA procedure as in study of Mitsuo et al. (2006) to identify its optimal configuration. The 5-tier SC is encoded through a 7-substring chromosome, in which the first, second and third substrings contain binary variables (open/close plants, DC and WH). The last four adjacent substrings denote transport trees between supplier and plant; plant -DC; DC -WH; then finally, WH and customer. These strings contain |I+J|, |J+K|, |K+L| and |K+M| digits with random values from 1 to |I+J|, |J+K|, |K+L| and |K+M| respectively (Fig. 5a).
Step 3: Modify the Lean Chromosome When Tier Lean tools are applied, they impact the amount of node/tier in the SC, which changes its denoted chromosome. Particularly, the application of Single Sourcing reduces the number of suppliers to one for each component type. Hence, the supplier-plants transport substring is removed because its configuration becomes deterministic (Fig. 5b). Similarly, the Use of Flat Hierarchy can minify the intermediary tiers in the supplier-plant or/and plant-customer substrings. Thus, the correlative substrings of these tiers are deleted. Figure 5c represents the chromosome of the LSC when Single Sourcing is used and the warehouse stage is flatted. LSC objective in Equation 4 becomes: Step 4: Final Lean Chromosome?
The quantity of Tier Lean tools applied depends on the deliberate goals of SC designers. Thereby, the denoted chromosome is correspondingly leaned until the design requirements are met. For instance, other techniques such as Group Technology, Use of Common Part and Modularity are able to change product structure by decreasing the types of components purchased from subcontractors. So, they reduce number of suppliers and genes on chromosomes simultaneously.

Optimise LSC by pGA
Step 5: Generate Lean Population Pool Heuristically, pGA uses the same procedure as GA to randomly generate and handle the offspring in a population pool.
Step 6: Fitness Evaluation After created, each offspring is decoded to the transportation tree in order to calculate the fitness (LSC TC). In pGA, each gene on a chromosome has two factors: Locus and allele. Locus is the position of genes denoting the order of source/destination in the transportation tree. Meanwhile, the gene value of allele bears represents the priority level of nodes assigned to the transportation tree. The decoded procedure determines the highest allele on a chromosome. Its corresponding locus is referred to the node having the priority to be served or delivered. Then, the shipment from this node with its counterpart is established, provided that the transportation cost between them in the cost matrix is the lowest. When any node is completely supplied/ served, its correlative allele is assigned to zero. The assignment repeats until all alleles on the chromosome adopt the null value. At that time, the transportation tree is totally built and the fitness is computed based on this network.
The terminated condition can be set similar to the GA.

Step 8: Define and Decode the Best Chromosome
Finally, the chromosome contributing to the best fitness is defined and then decoded in order to identify the best configuration of the LSC.

Illustrative Example
To illustrate the aforementioned method, one numerical example of the LSC design is described step by step. Assuming that all information in Step 1, 2 and 3 of the SCOP model is defined, the designers outline one potential FSC structure including 7 suppliers, 4 plants, 5 DCs and 8 WHs to serve 8 customers, in which supplier 1 and 2 provide the same components as supplier 6 and 7. While examining three assumptions and collected data in Table 1 and 2, the managers want to lean both the supply side and the demand side, with only 5 suppliers, 3 plants, 4 DCs, 6 WHs selected. Assumptions: • Suppliers' capacities satisfy demands of all plants • Customers' demands are deterministic and must be satisfied completely • All the transportation links between adjacent tiers are available Step 1: Simplify the General Model Designers intend to implement Functional Lean tools in Fig. 3  Step 2: Encode the LSC Configuration With I = 5, J = 3, K = 4, L = 6 and M = 8, the chromosome of the LSC structure is randomly denoted with 7 substrings, 56 digits (Fig. 6).

Step 3: Modify the Lean Chromosome
When Single Sourcing is applied, supplier 6 and 7 are dropped (their material cost higher than competitors'), so their supplies are transferred to supplier 1 and 2 (the forth substring is removed). Since the supply side is leaned, The Use of Flat Hierarchy is then used to clear the warehouse tier (substrings WH and D-W are wiped out). Thus, DCs serve customers directly and the last substring W-C turns out as D-C. The LSC chromosome is then modified as Fig. 7.
In this case, other Tier Lean tools have not been applied. Therefore, the chromosome representing the LSC structure defined in Step 3 is final.
Step 5: Generate Lean Population The mutation and crossover rates are set at 0.1 and 0.8 respectively.
The iteration is set at 1000.
Step 8: Define and Decode the Best Chromosome The best chromosome of the LSC affected by Functional Lean tools in Step 2 is in Fig. 8a, while the optimal one of final LSC is depicted in Fig. 8b. Following this, they are decoded to the best corresponding LSC configurations in Fig. 9a and 9b. The results show that the final structure is much leaner than both FSC and LSC, which are leaned by Functional tools. Concerning fitness, the minimum LSC TC in two situations achieves $6,198,035 and $5,332,175 in turn. On the other hand, the implementation of both Functional and Tier Lean tools reduce the LSC TC by up to 16.24% when compared with the cost of the LSC leaned by Functional tools only.

Conclusion
The paper presents in detail one new quantitative framework to optimise the design of LSC by Meta-Heuristics through three main stages: Forming the FSC model; transforming the FSC into LSC; and optimizing the LSCD with pGA. The particular point of this study is that it classifies LM tools into Functional Lean tools and Tier Lean tools. This classification contributes to two important findings: The framework of the LSC transformation through Functional Lean tools and the integration of Tier Lean tools with pGA to optimise the LSC structure. The solutions from the numerical example prove that this novel approach benefits both the LSC configuration and financial aspects. Moreover, this procedure can clearly draw out a general roadmap for designers, which could assist them in designing their LSC in a quantitative approach. It also offers a reference for the managing cadre in order to flexibly select proper Lean tools that will serve their business objectives.
Along with the selected LM tools in the given instances, other LM techniques related to product design like Modularity, Group Technology and Use of Common Parts also affect the SC structure. Further studies can focus on these areas in order to optimise the conformity of LSC configuration with the product structure.

Funding Information
The authors have no support or funding to report.

Author's Contributions
Thi Hong Dang Nguyen: Conduct the research, prepare the manuscripts and do any revisions.
Thien My Dao: Instruct research directions and qualify the solutions; give final approval of the version to be submitted and any revised versions.

Ethics
This article is original and contains unpublished material. The corresponding author confirms that all of the other authors have read and approved the manuscript and no ethical issues involved.