An optimization model for selecting a product family and designing its supply chain

TL;DR: A mixed integer linear programming model is investigated that optimizes the operating cost of the resulting supply chain while choosing the product variants.

About: This article is published in European Journal of Operational Research.The article was published on 2006-03-16 and is currently open access. It has received 146 citations till now. The article focuses on the topics: Supply chain & Supply chain management.

Summary

1. Introduction

• Nowadays, the growing demand for customizable or configurable products involves an increasing number of product variants and a growing complexity of products while controlling the product costs and the customer lead-time.
• These works underlined various interests in adapting the design of a product family in order to enhance the costs and lead-time of a given supply chain.
• But an example of a tool for supporting the bill-of-materials process using the analogy with a configuration process can be found in [14] .
• The authors focus on the second step, and therefore it is necessary to specify: how to depict, through a generic bill-of-materials, the product diversity resulting from the first step (Section 2); the model that enables to make the various choices (Section 3).

Iterative preliminary design processes Detailed design processes

• Family and Bill-of-materials (BOM) preliminary design Supply chain design and family selection family detailed design Supply chain detailed design Fig. 1 .
• A two-step iterative process for product family and supply chain design.

2.1. Modeling the product and design diversities

• Demand diversity can be considered from various points of view: the customer or functional one, the product or physical one, and the supply chain or process one.
• Another consequence is that a product family must at least contain one variant that exactly matches all the functional requirements at the maximal service level so that any demand can be over-satisfied by this variant.
• The design diversity is therefore the diversity of choices in order to define the set of variants, their associated service levels, and their bill-of-materials.
• These design principles are technical and technological choices and the definition of a product family architecture.
• Next sub-sections detail how to describe the result of such design strategies.

2.1.1. Market segment design strategy

• The market segment strategy works on a restricted list of market segments usually defined by a marketing department.
• A market segment is characterized by fixing a specific service level for each of the functional requirements.
• As several design principles can be applied to the same market segment, several admissible variants can be obtained per market segment.
• The bold arrows depict the order relations on the market segments.

Functional and physical decompositions

• Result of a bill-of-materials generation process throughout a market segment strategy.
• A designer may be interested in developing variants for these market segments that share common modular components.
• These approaches can be frequently observed in various markets.
• The design choices that remain finally are: whether to over-satisfy MS123 with a variant designed for MS4; whether to over-satisfy SL1/1 or SL2/1 with a module designed for SL1/2 or SL2/2 if MS123 is not oversatisfied; to select a module or a variant among the designed ones for the not over-satisfied service levels or market-segments.

2.1.2. Modular design strategy

• The second strategy aims at adopting modular principles.
• The principle is to design at least one module variant per functional requirement and per service level so that any demand can be fulfilled with the assembly of the desired module variants.
• In that case, 2 different design principles have been applied to the requirement 2 with the service level 2 (notation: Module V/W-i denotes the design principle number ''i'' for the Requirement V with a service level W).
• The bold arrows represent the order relation on the service levels.
• In the example, an extreme decision can be to only manufacture modules 1/3 and 2/3 in order to satisfy all the market segments.

2.1.4. Consequences on product diversity: Two decisions

• The result of the bill-of-materials design process appears to be a tree decomposition of the market needs (throughout the unbold arrows).
• These nodes correspond with either market segments, or requirements or couples (requirement, service level).
• They depict the functional offer that is proposed to the customers.
• Looking for example at the link between MS123 !.
• Two types of manufacturing decisions must be taken: using the order relation between market segments or service levels, one must choose whether some will be over-satisfied and therefore the corresponding variants or modules will not be manufactured; when several design principles have been applied, one must choose one of the resulting bill-of-materials.

2.2. The generic bill-of-materials (G-BOM)

• During a planning process, the bill-of-materials is used in order to compute net requirement of items given the demand of final products.
• To match the extension of a classical bill-of-materials, the key idea is to add new notions of ''logical item'' versus ''physical item'' and ''exclusive OR'' node versus usual ''AND'' node.
• An ''exclusive OR'' node is introduced to show that one and only one item must be selected among all the child items of the node.
• Therefore, when the ''OR'' choices are made one can express how a market volume induces net requirements on the selected BOM articles.
• So, the market shares do not depend on the choices made.

3. Supply chain and product family optimization

• The authors define a MILP (mixed integer linear programming) model that optimizes the supply chain design, processes a generic bill-of-materials (G-BOM) and therefore identifies the product family.
• The authors assume that the market shares do not depend on the choices made on the G-BOM.
• But before detailing the model, let us depict the notations and variables.

3. Flow conservation constraints

• According to their G-BOM definition: (i) a logical item can neither be manufactured, stored nor shipped, but it can generate a gross requirement in any facility, (ii) a physical item can neither be manufactured nor stored in a customer facility, but it can be shipped to it.
• Inventory constraints Constraint (16) shows that the inventory depends on existence of physical items and production facilities.
• Items with long lead-times require larger safety stocks.
• The flows under question will be the item internal production flow, the item supplying flow from other facilities, and the item delivering flow to customers.

4. Experimental evaluation

• The wiring harness system connects all the electrical components of a car.
• This means that many variants can be designed for a same market segment.
• The solution is depicted in Fig. 10 for the product family and in Fig. 11 for the supply chain layout.
• Computation time decreases with the combinatory, as shown in Fig. 12 , until the duration reaches 115 seconds when combinatory equals 1.

Computer facility

• This last case, the generic bill-of-materials corresponds with the bill-of-materials of the optimal solution.
• Another interest of the proposed model is to investigate the influence of the fixed cost of existence of variants on the diversity level of the product family.
• The diversity level is defined by the number of variants of the product family.
• In order to do so, a set of experiments has been made in which the variant existence costs are multiplied by a coefficient between 0.01 and 150.

5. Conclusion

• In the goal of taking into account demand and product diversity, the two-step approach presented in this paper allows to design a set of product families then to identify one product family and the layout of its supply chain while minimizing the cost compromise ''over equipment cost/references management cost''.
• It has been shown that the result of the first step could be modeled as a generic bill-of-materials (G-BOM).
• Compared to classical Global Supply Chain Models, the proposed constraints and flow conservation equations permit to take into account the proposed G-BOM.
• The proposed approach takes into account three kinds of diversity: the market diversity thanks to requirements and service levels, the product diversity thanks to components and variants, the supply chain layout diversity thanks to logistics aspects.
• In current industrial context where demand, design activities and facilities are more and more worldwide distributed.

Figures

Fig. 4. Example of result of a bill-of-materials generation process throughout a modular strategy.

Fig. 8. A G-BOM for the application case.

Fig. 5. Example of result of a mixed design strategy.

Fig. 1. A two-step iterative process for product family and supply chain design.

Fig. 7. Physical/logical item flows through a manufacturing or a customer facility.

Fig. 2. The design challenge.

Fig. 11. The solution of the supply chain layout.

Fig. 12. Computational times versus the combinatory of the generic BOM.

Fig. 13. Sensibility of the diversity with respect to variant existence cost.

Fig. 6. A generic bill-of-materials.

Fig. 3. Result of a bill-of-materials generation process throughout a market segment strategy.

Fig. 10. Product family solution.

Fig. 9. The supply chain that must be designed.

Frequently asked questions

Q1. What have the authors contributed in "An optimization model for selecting a product family and designing its supply chain" ?

This work is applied to the problem of an automotive supplier. 

Q2. What is the purpose of the bill-of-materials?

During a planning process, the bill-of-materials is used in order to compute net requirement of items given the demand of final products. 

Q3. How many synchronous facilities do you have?

The supply chain gathers: 4 synchronous facilities, each one dedicated to a customer, 7 manufacturing facilities with 3 dedicated to computers and 4 to components. 

Q4. What is the flow of the item?

The flows under question will be the item internal production flow, the item supplying flow from other facilities, and the item delivering flow to customers. 

Q5. What is the purpose of the proposed model?

Another interest of the proposed model is to investigate the influence of the fixed cost of existence of variants on the diversity level of the product family. 

Q6. What are the main strategies used to design the architecture of a product family?

In order to design the architecture of a product family two main strategies are identified which the authors call ‘‘market-segment oriented’’ strategy and ‘‘modular’’ strategy. 

Q7. What is the purpose of the definition of a product family?

From the product point of view, a product family is a set of physical product variants and is defined in order to fulfill the market needs. 

Q8. What is the key idea of a bill-of-materials?

To match the extension of a classical bill-of-materials, the key idea is to add new notions of ‘‘logical item’’ versus ‘‘physical item’’ and ‘‘exclusive OR’’ node versus usual ‘‘AND’’ node.• 

Q9. What is the result of the bill-of-materials design process?

The result of the bill-of-materials design process appears to be a tree decomposition of the market needs (throughout the unbold arrows). 

Q10. What is the definition of a mixed integer linear programming model?

A mixed integer linear programming model is defined in the following as an extension of basic models such as: (i) a single shipping channel is available between any two facilities; (ii) manufacturing or shipping activities have much smaller lead-times than the time period, and thus are supposed continuous. 

Q11. How many experiments have been made to solve the problem once?

In order to do so, a set of experiments has been made in which the variant existence costs are multiplied by a coefficient between 0.01 and 150. 

Q12. What are the main interests of the authors in the design of a product family?

These works underlined various interests in adapting the design of a product family in order to enhance the costs and lead-time of a given supply chain. 

Q13. How long does the combinatory take to complete?

Computation time decreases with the combinatory, as shown in Fig. 12, until the duration reaches 115 seconds when combinatory equals 1. 

Q14. What are the common extensions in global supply chain models?

Many extensions have been introduced in global supply chain models such as financial cost (duties, taxes, exchange rates) or scale economies or choices of technological manufacturing systems or demand instability. 

Q15. What is the difference between the two product families?

As the authors consider an order relation between the service levels of each requirement, a partial order relation also exists between the product variants within a product family: a Variant V1 is greater than a Variant V2, if, for each requirement, the service level of V1 is greater than the service level of V2.