Supply chain network design models

There have been a lot of studies conducted from different perspective for the supply chain network design. The emphasized decision variables can be classified as facility selection, production/shipment quantities and supplier selections, etc.

According to Vial and Goetschalckx (1997), the most comprehensive strategic problems is the optimization of the complete supply chain. The strategic design of a supply chain requires managers to determine:

the number, location, capacity, and type of manufacturing plants and warehouse to use;

the set of suppliers to select;

the transportation channels to use;

the amount of raw materials and products to produce and ship among suppliers, plants, warehouses, and customers; and

the amount of raw materials, intermediate products, and finished goods to hold at various location in the inventory.

Many critical reviews of supply chain network design with emphasize on different perspective can be found. Vidal and Goetschalckx (1997) reviewed strategic production-distribution models. The review was classified into four sections: previous reviews, optimizations models, additional issues for modeling, and case studies and applications. Geoffrion and Powers (1995) reviewed the evolution of the strategic production and distribution models since 1970. Beamon (1998) reviewed strategic, stochastic, simulation, and economic models in the supply chain literature. Meixell and Gargeya (2005) focused on the model-based literature that addresses the global

supply chain design problems. In their paper, they mentioned that global supply chain models need to address the composite supply chain design problem by extending models to include both internal manufacturing and external supplier locations.

Arntzen et al. (1995) developed a mixed integer programming (MIP) model considering multiple products, facilities, time periods, and transportation modes. The model aimed at minimizing a composite function of activity days and total production costs, inventory, transportation costs, etc. All the costs considered in the objective function are weighted by a factor α . The objective function represents a weighted combination of time and cost so that either measure or both can be used to derive recommendations (Meixell and Gargeya, 2005). As Vidal and Goetschalckx (1997) mentioned, the main contribution of the study is the inclusion of offset trade, local content, and duty considerations in an international supply chain model that also includes bill of material (BOM) constraints.

Nagurney et al. (2002, 2003, 2005) considered many decision-makers and their independent behaviors in the supply chain and developed network equilibrium models for a competitive supply chain comprised of manufacturer, retailers and customers. In the model, transportation links are associated with different costs. Their models used a variational inequality formulation to derive product shipments and price pattern in the network.

Santoso et al. (2005) proposed a stochastic programming model and solution algorithm for solving supply chain network design problems under uncertainty. The proposed method integrates an accelerated decomposition scheme along with the developed sample average approximation (SAA) method. Goetschalckx et al. (2002) integrated the design of strategic global supply chain network with the determination of tactical production-distribution allocations and transfer prices. The results showed that

more savings in computing times can be achieved by simultaneously determining strategic and tactical decisions as compared to the sequential decision process where first the plants are located and then the tactical production-distribution flows are determined.

Eskigun et al. (2005) considered the design of an outbound supply chain network considering lead times, location of distribution facilities and choice of transportation mode. The objective function is to minimize total cost, given by the sum of transportation cost, lead-time cost and fixed cost. In the model, the varying capital and production costs of plants in different regions are neglected and the impacts of spatial distance between two locations on transit time and transportation cost are not mentioned.

From reviewing the literature about supply chain network design to date, the mixed integer programming (MIP) formulation has been intensively used to investigate strategic issues of supply chain management (e.g. Brown et al. 1987; Goetschalckx et al., 2002). Due to large-scale models have been proven to be extremely difficult to solve optimality, solution methods and computational experiences are necessary. Brimberg and ReVelle (1998) formulated a bi-objective plant location models for analyzing the trade-off between total cost and the proportion of the market to be served. In this study, partial satisfaction of demand is considered rather than serving all demand in the traditional plant location problem. The weighted method approach is investigated for obtaining efficient solutions of the model. Jayaraman and Pirkul (2001) extended the plant location problem to incorporate the tactical production-distribution problem for multiple commodities. In the model, a facility or warehouse is constrained to serve one single customer. Miranda and Garrido (2004) proposed a simultaneous approach to incorporate inventory control decision into typical facility location models. Crama

et al. (2004) constructed a nonlinear MIP model to determine the optimal procurement decisions in the presence of total quantity discounts and alternative product recipes.

Several studies have recognized the benefits of centralized production. Cohen and Moon (1990) analyzed the impacts of scale and scope cost behavior on the optimal design of supply chain systems. The results showed that there are trade-offs between various costs, such as the fact that the effect of decreasing the fixed cost on the number of plants is largely offset by an increase in inbound cost. Cohen and Moon (1991) formulated a MIP model to determine the optimal assignment of product lines and volumes to a set of capacitated plants. In the model, the capacity of plants is given and fixed and the production cost functions exhibit concavity with respect to each product line volume to reflect economies of scale. Moreover, correlation and regression analyses are employed to analyze the relationship between the cost parameters. The results indicate that focused plants arise in situations with high economies of scale.

However, although the capacity utilization of different-size plants will result in various influences on their total cost, its extent is seldom discussed. The models constructed are usually large-scale linear or nonlinear MIP formulations, which are difficult to solve.

Therefore, these studies focused mainly on developing an approximation procedure and compared the efficiency of their proposed heuristics with others.

Many solution algorithms have been developed for handling linear MIP models, such as linear approximation, Lagrangian relaxation, branch-and-bound, Benders decomposition and primal decomposition methods (e.g. Jayaraman and Pirkul, 2001;

Miranda and Garrido, 2004). Goetschalckx et al. (1994, 1995) presented a generic model for the strategic design of production-distribution systems, including visual capabilities. Based on the generic model, they introduced algorithm components that significantly reduce the solution times compared to standard MIP solutions by a

commercial solver. Cohen and Moon (1991) provided an algorithm to solve production-distribution models with piecewise linear concave costs of production. In the algorithm, a variant of the generalized Benders Decomposition technique was applied. Table 2.2 summarizes main issues and features and important results in the existing literature on supply chain network design models.

Table 2.2 Main issues, features and results in literature on supply chain network design models

Authors Main issues and features Important results Vidal and

Goetschalckx (1997), Geoffrion and Power (1995), Gargeya (2005)

Review supply chain design models

Global supply chain models need to address the composite supply chain problem by extending models to include both internal manufacturing and external supplier locations Arntzen et al.

(1995)

Develop a MIP model

considering multiple products, facilities, time periods and transportation modes

The main contribution is the inclusion of offset trade, local content and duty considerations

Nagurney et al.

(2002, 2003, 2005)

Consider many decision-makers and independent behaviors for a competitive supply chain

Use a variational inequality formulation to derive product shipments and price pattern in the network

Santoso et al.

(2005)

Propose a stochastic

programming model and solution algorithm for supply chain design problems under uncertainty

Focus on developing efficient algorithms in solving the proposed models

Goetschalckx et al.

(2002)

Integrate the design of strategic global supply chain network with the determination of tactical production-distribution allocations

Focus on developing efficient algorithms in solving the proposed models

Eskigun et al.

(2005)

Design an outbound supply chain network, considering lead times, location and choice of

transportation modes

Focus on developing efficient algorithms in solving the proposed models

Cohen and Moon

(1990) Analyze the impacts of scale and scope cost behavior on the optimal design of supply chain systems

The effect of decreasing fixed cost on the number of plants is largely offset by an increased inbound costs

Cohen and Moon (1991)

Determine the optimal

assignment of product lines and volumes to a set of capacitated plants

Focused plants arise in

situations with high economies of scale

Source: this study

Summary:

There is vast literature conducting supply chain network problems. The majority of this research focused on the production-distribution models. And the mixed integer programming (MIP) method has been extensively used to investigate the problems.

Because these models constructed are usually large-scale linear or nonlinear MIP formulations, which are difficult to solve. These studies focused mainly on developing and approximation procedure and comparing the efficiency of their proposed heuristics with others. In addition, though the capacity utilization of different-sized plants will result in various influences on their cost, its extent is seldom discussed. The impacts of high capacity cost on the optimal plant capacity and production among manufacturing plants with different sizes are seldom discussed. Though optimal flows between demand and supply nodes have been discussed and have been included in the supply chain design problems, the shipping frequency and shipment size between different combinations of suppliers and manufacturing plants have not been discussed yet. Furthermore, production and shipping economies and their tradeoff relationships are seldom discussed when designing a supply chain network.