# A comparative study of three different SCM approaches

*R. Meenakshi
Sundaram, Sameer G. Mehta*

R. Meenakshi Sundaram, Sameer G. Mehta,
A comparative study of three different approaches on a hypothetical supply chain model is presented. The three approaches investigated are: independent; semi-integrated; and integrated. In the independent approach, it is assumed that decisions are made independently at three different levels. Decisions are assumed to be made at two different levels in the semi-integrated approach. In the integrated approach, all decisions are assumed to be made at a single level |

## Introduction

The advent of economic globalization in the past 20 years has had two major impacts in manufacturing. A global market has evolved very rapidly as more and more companies are embracing e-commerce. The competition has become fierce as companies can go beyond national borders. Manufacturing companies are under intense pressure to produce quality products faster and inexpensively. Innovative new technologies and techniques are evolving to meet the demand for cost reduction and quality improvements. Techniques such as lean manufacturing, Kanban systems, total quality management, just-in-time, and kaizen have been proven to be extremely effective on the shop floor. Manufacturers are continuously striving to improve the internal operations and are beginning to focus on the external operations as well. The unrelenting task of cutting costs to improve the profit margin has resulted in the management of all upstream operations as well as downstream operations external to manufacturing. These downstream operations are responsible for delivery of the products to the market. This has led to connecting both upstream and downstream companies culminating in the concept of supply chain management (SCM).

Thus a supply chain may be
defined as a network of facilities and distribution operations to perform the
functions of procurement of materials, transformation of these materials into
intermediate and finished products, and the distribution of these finished
products to customers (Ganeshan, 1999). SCM constitutes a set of approaches
utilized to efficiently integrate suppliers, manufacturers, warehouses, and
retailers, so that merchandise is produced and distributed in the right
quantities, to the right locations, and at the right times, in order to
minimize system-wide costs while satisfying service level requirements
(Simchi-Levi *et al.*, 2000).
Logistics is defined as "the process of planning, implementing, and
controlling the efficient, effective flow and storage of materials, finished
goods, services, and related information from origin to the location where they
are used or consumed" (Fawcett and Clinton, 1997).

A typical supply chain has a linear structure with links connecting one constituent to the next. Raw materials are procured and products are made at one or more plant locations. The products are then either stored locally or shipped to warehouses/distribution centers for intermediate storage. This description essentially represents a traditional brick-and-mortar supply chain.

Depending on the market demand, the products are shipped either to distributors or retailers directly. Thus a network of suppliers, manufacturers, distribution centers, and retailers communicate for the manufacture and distribution of products in a supply chain. Each member of the supply chain operates independently without very many interactions with members farthest in the hierarchy. The interaction between two immediate members is limited to just transfer of information and materials.

In a traditional supply chain, members are concerned with decisions that directly affect their bottom line. Many manufacturing operations were designed in the past to maximize throughput and lower costs with little consideration for the impact on inventory levels and distribution capabilities. The result of these factors is that there was not a single, integrated plan for the entire supply chain. Independent and conflicting plans were made by each of the supply chain members to achieve individual goals. Therefore, there exists a need to integrate these different functions. SCM is a strategy through which such integration can be achieved. The primary focus is on manufacturing and logistics so that manufactured products can be delivered as required on a timely basis and cost-effectively. Collaborative efforts among supply chain members are leading to improvement in supply chain efficiency. The end-user benefits since this results in an attractive price, improved quality and better service.

## Review of literature

Early studies related to SCM were fragmented, with focus on improving functions such as purchasing, distribution, materials management, and logistics. The role of planning in the supply chain was totally independent between production and distribution. The independent approach results in higher cost due to inventory at different levels.

Glover *et al.* (1979) developed a network model
for production scheduling and distribution operations at Agrico Chemicals. In
the model, a decision support system was embedded to analyze both short-term
and long-term planning decisions, which involved determining the size and
location of distribution centers and the volume and mode of shipping.

Lawrence and Burbridge (1976) developed a multi-objective linear programming approach to determine alternative production schedules for groups of products in a two-echelon supply chain. The model helped determine what products to make, how much to produce, and where to produce these products. The model attempted to achieve coordinated production and distribution schedules subject to stated objectives of the firm.

The objectives considered in the model presented by Lawrence and Burbridge were:

- maximization of the total sales revenue for specific locations;
- minimization of the total cost of production and distribution;
- maximization of the production volume of a particular item at a specific location.

These conflicting objectives radically affect the operations of a company. Therefore, instead of optimizing each of the objectives independently, the goal programming technique was used to simultaneously satisfy the three objectives by assigning priorities. The goal programming technique tries to satisfy the first goal with the highest priority first, then the second and so on until the last goal is satisfied. This provides the decision maker some flexibility in compromising the goals.

Cohen and Lee (1988) developed a decision model that linked management control and system performance in the supply chain using several submodels. The submodels were linked by inventory and scheduling decisions. Each submodel was optimized subject to a defined level of customer service. With the help of heavy traffic queuing theory, Arreola-Risa (1989) demonstrates that by assuming an exponential distribution for the manufacturing lead time, the accuracy of the operating characteristics of the model by Cohen and Lee (1988) could be improved.

Blumenfield *et al.* (1986) considered the problem of
scheduling the production and distribution for a manufacturing company
supplying parts to assembly plants. A model was proposed that included the
following limitations:

- a single destination for each part type;
- identical production cycles for each part;
- fixed transportation costs for each shipment.

It was concluded that
simultaneous consideration of the production and distribution schedules would
result in reduced costs. It was also found that cost saving for a given
production-distribution schedule was maximized when the demand, item value, and
variable costs were the same for each product. The model, reportedly
(Blumenfield *et al.*, 1987)
implemented at General Motors Delco electronics division, resulted in a savings
of $2.9 million per year in logistics cost.

Chen *et al.* (1994) presented a
production-planning model for a system composed of a central factory and
several satellite factories. Each satellite factory specialized in the
production of specific part types and supplied them to other plants in the
network as required. Only the central factory dealt with outside customers.
Material flow within the network was to satisfy the customer demands at the
central factory. The production-planning problem was to minimize total cost.
This included transportation, processing, holding raw materials, and
manufacturing products in a network of factories. Two nonlinear mathematical
programming models were developed to determine the best production and
procurement policies. Heuristic algorithms were developed for solving the
models.

Ozdamar and Yazgac (1999) defined a production system as a chain of subsystems from the supplier subsystem to the distribution subsystem. They concluded that it was impossible to separate the subsystems and achieve the goal of minimizing total costs. Therefore, an integrated production-distribution model was proposed to solve the production and distribution problems. The model was based on the operating system of a multinational company producing detergents in a central factory. Products were distributed to geographically distant warehouses. The overall system costs included factory and warehouse inventory costs as well as transportation costs. A hierarchical approach was used to schedule the weekly fluctuating demand.

Cachon and Zipkin (1999) investigated a supply chain that consisted of a supplier and a retailer. Stationary stochastic demand and fixed transportation times were assumed. Inventory and backorder costs were considered at both stages. Two types of games were developed for the solution. The games minimized the total costs but differed in the way each operated. In the first game, the firms tracked inventory levels along echelons; in the other game, each firm tracked only local inventory. In the first case, there was an effort to reduce the total supply chain costs while the other focused on reducing the local costs, thus inducing competition. Solutions to the test problems showed a difference between the two approaches. The competition introduced by the second approach reduced the efficiency of the operation. For some specific cases, competition increased total cost only by a fraction of 1 percent; in others, the increase was much greater. Hence it was concluded that the supply chain approach was better.

From the above discussions, it can be concluded that the investigations demonstrated the importance of cooperation among different functions of the supply chain. While some studies focused on combining the inventory and transportation functions, others combined the production and distribution decisions to reduce costs. Methods such as Benders decomposition, goal programming, non-linear programming, linear programming, and heuristics have been used. Different configurations of supply chains were used in these studies. While some used the single warehouse-multiple retailer configuration, others used the multiple manufacturers-retailers configuration. In most of these studies, only two stages were considered. Though proven to be cost-effective, the production-distribution models lacked the element of complete integration of the supply chain. Therefore it is worth investigating the integration of a supply chain with more than two stages.

Currently, SCM is receiving significant attention. Newer models and methodologies are being developed for integrating many functions in the entire supply chain. A review of some recent studies is presented in the next few paragraphs.

Ganeshan (1999) presented a near optimal type of inventory-logistics cost minimizing model. The model considered a production distribution network with a single distribution center receiving consignments from several suppliers. The consignments were distributed to a number of lower echelon retailers. The model addressed the following issues in the system:

- the inventory analysis at the retailers;
- the demand process at the warehouse;
- the inventory analysis at the warehouse.

Cost components in the model were inventory and transportation costs. Solutions for the test problems were verified using simulation. The following inferences were made from the study:

- The model was accurate in estimating the service levels at the retailer as well as the warehouse level. It was recommended that the model could be used to determine stock levels at each center.
- The model was flexible enough to include the changes in supply chain configuration.

The author recognized the following shortcomings of the model:

- The model assumed that the supplier always had sufficient capacity to satisfy demand. The model did not extend beyond two echelons.
- The model assumed identical suppliers and retailers for simplicity.

Matta and Sinha (1995) investigated a two-echelon system, which included a warehouse, a system of suppliers, and a set of downstream retailers. The model considered the ordering costs only at the warehouses, not at the retailers. A cost model was developed to derive an optimal ordering-distribution policy for the distribution system. However, the model had its shortcomings. Although it extended beyond a manufacturing echelon into multiple echelons, it failed to integrate production-scheduling decisions in the model.

Simchi-Levi and Chan (1998) considered the problem of integrating inventory control and vehicle routing to develop an optimal cost strategy for a distribution system. The system consisted of a single outside vendor, a fixed number of warehouses, and a set of geographically dispersed retailers. Demands at the retailers were assumed to be constant. In addition, inventory-holding charges were applicable at the warehouses and retailers. The authors emphasized the strategy of cross-docking for distribution planning in the system. Cross-docking is a strategy in which warehouses receive fully loaded trucks from suppliers. Warehouses coordinate the delivery to retailers but never hold inventory. Using this strategy, a model was developed to coordinate the distribution process.

Another study related to
integrated decision making in a supply chain is the inventory planning at
Libbey-Owens-Ford. Martin *et al.*
(1993) developed a model called FLAGPOL. This large-scale mathematical model
simultaneously considered the production and distribution, as well as inventory
operations in the flat glass business of Libbey-Owens-Ford. The model was used
to make decisions in a supply chain covering four plants, over 200 products,
over 40 demand centers, and a planning period of 12 months.

Fumero and Vercellis (1999) aimed to coordinate important and interrelated logistics decisions such as capacity management, inventory allocation, and vehicle routing. An optimization model that accounted for the various production and distribution capabilities of the system was developed.

The model was solved using the three approaches; Lagrangian relaxation, Lower bound solutions, and Heuristic solution. The computational results on test problems demonstrated the effectiveness of the model. The model was solved for a single plant, multi-period, and multi-product configuration. The capacities were assumed to be infinite. Back orders were not allowed. The model ignored the effects of suppliers and warehouses in the system.

Recent literature reviews demonstrate the increasing emphasis on synchronization of decision processes throughout the supply chain. Inventory and routing problems have been investigated under deterministic as well as stochastic assumptions, but most studies have ignored production decisions. Models that considered the production processes at different facilities failed to include the distribution plans. Ideal conditions such as single product, single plant, single period, and no back orders are the assumptions in most of these models. There is a need for developing more realistic models relaxing these assumptions over a wide range of conditions with total integration.

## Proposed method

The major objective of the research reported here is to develop mathematical approaches that would aid decision making at various levels in the supply chain. Three approaches are presented incorporating varying degrees of integration of the decision processes.

Integration in a supply chain can be defined as an association of customers, retailers, distribution centers/warehouses, and manufacturers using techniques enabling them to work together to optimize their collective performance in the creation, distribution, and support of the end product (NRC, 2000). There are basically two types of integration processes: namely, internal integration, involving coordinated management of a company's internal operational activities like production scheduling, labor allocation, inventory holding, job sequencing, shipping, etc., and external integration, which refers to integration of activities external to the company across the supply chain. Less than 5 percent of companies have achieved total integration with others (Copacino, 1997). The importance of supply chain integration for developing successful and competitive strategies has been stressed.

*Independent approach*

In this approach, it is assumed that links of the supply chain operate independently as detailed in Figure 1. Decision-making occurs through a series of modules operated by various members of the supply chain. There are separate modules for decision making such as production planning and shipping at every echelon of the supply chain. Modules focus on local optimization. This type of supply chain represents the segregated association of businesses where decisions are localized in the form of "silos". The forecast demands from retailers are consolidated into the distribution-planning module maintained by the distributor. The module indicates replenishment is shipped from each distribution center/warehouse to each retailer. The module considers stocks on hand at each distribution center/warehouse and the capacity of the trucks. The module also determines the replacement volume of products needed at each distribution center/warehouse. The manufacturer's plant-production-planning module receives the quantity requirements from the distribution centers/warehouses. The module develops production plans for the plants and the master production schedule required by the upstream tier-1 supplier. The plant-shipping module develops the shipping plan from the production plan.

The tier-1 supplier-production-planning module receives the master production schedule from the manufacturer's plants. The module develops a desegregated production plan for supplier plants. In addition, it develops a master production schedule for the material-requirements-planning module of tier-1 suppliers. It also determines the quantities of material to be supplied by each tier-2 supplier to the tier-1 supplier plants. The tier-1 supplier-shipping module develops a logistics plan for shipment of components from the tier-1 suppliers to the manufacturer's plants.

*Semi-integrated
approach*

Unlike the independent approach, the semi-integrated approach involves some degree of coordination among the constituents of the supply chain. The decision processes are illustrated in Figure 2. Like the independent approach, the demand forecasts from each retailer are consolidated and sent to the distributor. The distributor passes on these requirements to the integrated plant-supplier-planning (IPSP) module residing at the manufacturer and accessible to the tier-1 suppliers. This module is used to develop production plans at the manufacturing plants and the tier-1 supplier plants. It is also used to develop the shipping plan for the tier-1 supplier plants.

When the distribution-planning module receives the plant production plans, the module determines the product-shipping schedule from the manufacturing plants to the distribution centers and to the retailers. The module also considers the stock levels of the distribution centers/warehouses and the capacities of the trucks available. The tier-1 supplier, upon receiving the master production schedule, develops the material requirement plan. The requirements are sent to the tier-2 supplier for material procurement.

*Integrated approach*

In the integrated approach shown in Figure 3, total collaboration among the various links of the supply chain is achieved. Unlike the previous two approaches, the integrated-supply-chain-planning (ISCP) module makes all the decisions using a single module. Each facility is connected to the decision-making process through the integrated-supply-chain-planning module or the ISCP module. In this process, once the retailers place their orders with the ISCP module, the planning across the whole supply chain occurs.

The ISCP module helps in making the following decisions in the supply chain:

- Quantity of products to supply to each retailer from each distribution center/warehouse.
- Levels of stocks to be maintained at the distribution centers/warehouses.
- Production plans for the manufacturing plants.
- Shipping plans from plants to the distribution centers/warehouses.
- Quantity of components required at the plants.
- Production plans for the tier-1 suppliers.
- Shipping plans from the tier-1 suppliers to the plants.
- Material requirements at the tier-1 suppliers.
- Quantity of material to be supplied to each tier-1 supplier by each tier-2 supplier.

## Discussion

Mathematical models were developed for each of the three approaches. For each of the supply chain approaches using the demand and resource limitations, the developed models were solved. The mathematical models developed are included in the Appendix.

The following assumptions were made in developing the mathematical models for all three approaches:

- A fixed number of echelon levels exists in the supply chain. A supply chain can involve any number of entities at the same level.
- The mathematical models are multi-product and multi-period type.
- Manufacturing operations are assumed at the manufacturer and tier-1 supplier level.
- Tier-2 suppliers are assumed to have fixed capacity to supply materials. No production or inventory decisions are involved at tier-2 supplier level.
- All products in a category have the same shipping costs.
- There is no material flow between entities at the same level.
- Less than partial truckload shipments are allowed in the supply chain.
- There are no location decisions involved in the supply chain.
- Lead times are ignored in the formulation of the supply chain models.
- Back orders are allowed at the retailers. No back orders are allowed at other levels.
- The truckload decisions in the supply chain are weight-constrained. This is contrary to the real world situation where both weight as well as volume constraints are considered in making shipping decisions.

These solutions provided a detailed plan for each of the following functions:

- Quantity of each product manufactured at each plant.
- Quantity of product shipments from manufacturers to distribution centers/warehouses.
- Quantity of product shipments from distribution centers/warehouses to the retailers.
- Component requirements at the manufacturer.
- Component production plans for each tier-1 supplier facility.
- Quantity of components shipped from tier-1 suppliers to manufacturers.
- Material requirements at tier-1 supplier facilities.
- Material procurement quantities from each tier-2 supplier.

*Model performance*

Several test problems were developed for the supply chain described. Further, the results obtained were tested statistically to assess the effect of supply chain integration. The hypothetical supply chain configuration used in the tests is described in Table I. The supply chain consists of an organization that owns and operates two manufacturing plants. Both plants are assumed to manufacture two products. It is also assumed that the two plants have different production capacities and, consequently, different production costs.

The manufacturers ship products to the distribution centers/warehouses based on the demand schedule. The distributors place purchase orders with the manufacturers, who in turn develop the production plans. Each distribution center/warehouse has a specific capacity to handle each product and ships units to retailers upon receipt of orders.

Three retailer outlets are assumed in the supply chain investigated and all three are assumed to be operated by the same company. It is assumed that the company has demand forecasts to place orders with the distributor.

The manufacturers use two component parts in production. Component orders are placed with the tier-1 suppliers. The tier-1 suppliers level includes two production facilities to meet the component demands. Both the facilities are assumed to be operated by a single company. The tier-1 suppliers develop their production plans based on the master production schedule provided by the manufacturer.

The suppliers are assumed to use two different raw materials for making the two components. The material orders for the tier-1 supplier are placed with two second-tier suppliers for replenishment.

*Experimental design*

Having formulated the mathematical models for the three different approaches, it was necessary to assess the benefits of an integrated decision-making process. Also it was necessary to investigate the effect of various supply chain parameters on the benefits of supply chain integration. An analysis of variance (ANOVA) was performed to test the statistical significance of the factors. An experiment with two levels of each parameter was designed.

The first step in the design was to identify factors that influence cost. The cost reduction that can be achieved was of interest in this experimental analysis.

The following factors were chosen:

- the distribution center/warehouse capacity;
- the manufacturing plant capacity;
- the tier-1 supplier production capacity;
- total shipping cost in the supply chain;
- model type.

The factor levels selected for the experiment are tabulated in Table II. The models were tested for different combinations of the factors at high and low levels. A high level indicates a capacity utilization of 80 percent for all three capacity factors. In other words, 80 percent of the total capacities available at the distribution centers/warehouses, plants, and tier-1 suppliers are utilized to meet the retailer demands. The low level is 60 percent capacity utilization. Shipping cost was also tested at high and low levels. The high level represents shipping costs as 10 percent of the total costs. The high level for the model type indicates cost reduction achieved by using the integrated approach as compared to the independent approach; the low level indicates the cost reduction achieved when the semi-integrated approach is used as compared to the independent approach.

*Comparison of test
runs for each of the approaches*

The objective of conducting the test runs was to compare the supply chain costs for each of the three approaches and to assess the benefits of integrating the decision-making processes in a supply chain.

Total supply chain cost was obtained by solving the mathematical models developed for each of the following three approaches:

(1) Independent approach - six decision levels.

(2) Semi-integrated approach - three decision levels.

(3) ntegrated model - one decision level.

The total supply chain cost for each approach is shown in Table III.

The mathematical models were utilized to determine the following:

- volume of each product manufactured at each plant;
- volume of product shipments from manufacturers to distribution centers/warehouses;
- volume of product shipments from distribution centers/warehouses to the retailers;
- component requirements at the manufacturer;
- component production plans for each tier-1 supplier facility;
- quantity of components shipped from tier-1 suppliers to manufacturers;
- material requirements at tier-1 supplier facilities;
- material procurement quantities from each tier-2 supplier;
- number of truckload trips between manufacturers and distribution centers/warehouses;
- number of truckload trips between distribution centers/warehouses and retailers;
- beginning and ending inventories at each location.

From results of the test runs, supply chain costs for decision making using the independent approach are the highest followed by the semi-integrated approach. The integrated supply chain approach had the least total cost. This supports the contention that increased collaboration within the supply chain ensures better supply chain performance.

*Experimental design
characteristics*

Having confirmed that the
integrated approach produced better results than the independent approach, an
investigation needed to be carried out to assess the effect of various supply
chain parameters on the benefits of supply chain integration. Thus, the
response variable in the experiment was the percentage cost reduction that was
achieved using the semi-integrated approach and integrated approach as compared
to the independent approach. The experiment was a 2^{5} factorial
design with five factors at two levels, as shown in Table
IV. With each run a unique combination of only one replicate for a given
treatment set, this experiment was an unreplicated factorial for a 2^{5}
design. The data for the percentage cost reduction achieved by supply chain
integration were obtained from all the test runs tabulated in Table III. The
experimental design data are not included in the paper.

*Analysis*

The factors found to have significant influence on the percentage of cost reduction were the following:

- distributor capacity utilization;
- plant capacity utilization;
- supplier capacity utilization;
- shipping cost;
- model type;
- interaction between distributor capacity utilization and shipping cost;
- interaction between distributor capacity utilization and model type.

The following inferences were made from the analysis of variance. These conclusions apply only to the data tested. No inferences can be made about supply chains in general.

(1) It can be seen from the results that as the shipping cost in the supply chain changes from high to low, the mean percentage cost reduction drops from an average of 3.5 percent to a value of 1.6 percent. Thus, the higher the shipping costs, the more beneficial it is to integrate the decision-making process in the supply chain.

(2) It can be seen from the results that as the shipping cost in the supply chain changes from high to low, the mean percentage cost reduction drops from an average of 3.5 percent to a value of 1.6 percent. Thus, the higher the shipping costs, the more beneficial it is to integrate the decision-making process in the supply chain.

(3) The integrated supply chain approach results in greater cost reduction than the semi-integrated approach as compared to independent approach. This result supports the contention that the model costs decrease as the degree of supply chain integration increases.

(4) It can be inferred from Table V that supply chain integration benefits are much higher when the supply chain is less constrained in resources available at each level. The semi-integrated approach and the integrated approach take a system-wide view of the decision-making process in the supply chain and provide globally optimized solutions for the given assumptions. Since decisions in the independent approach are made at several levels, they tend to generate localized optimum solutions at each level. The greater the available capacities at each level of supply chain, the more localized are the decisions generated by the independent approach, and thus the greater the supply chain cost resulting from the independent approach as compared to the globally optimizing integrated supply chain approaches.

(5) There is a significant effect of shipping costs-distributor capacity utilization interaction and model type-distributor capacity utilization interaction on the benefits of supply chain integration. It can be inferred from the cost reduction achieved by integrating the supply chain is high for the following conditions:

- shipping costs in the supply chain are high;
- capacity utilization at the distributor level is low;
- an integrated supply chain approach is used.

The manufacturers use two component parts in production. Component orders are placed with the tier-1 suppliers. The tier-1 level includes two production facilities to meet the component demands. Both the facilities are assumed to be operated by a single company. The tier-1 suppliers develop their production plans based on the master production schedule provided by the manufacturer.

The suppliers are assumed to use two different raw materials for making the two components. The tier-1 material orders are placed with the two second-tier suppliers for replenishment.

The objective for the test runs is to compare the supply chain operation costs for each of the three approaches and validate the benefits of integrating the decision-making process for different processes across the whole supply chain.

As reported earlier, the integrated approach involves integration of all the decision-making processes across the supply chain. The semi-integrated supply chain approach includes integration of decision processes at the plant-supplier level and plant-retailer logistics level thus providing for some degree of integration in the supply chain. The independent approach involves independent decision making at each level of the supply chain as an example of minimum collaboration.

From the results obtained for the test runs, it is evident that the supply chain cost for decision making using the independent approach are the highest followed by the semi-integrated supply chain approach. The integrated supply chain approach resulted in a plan with the least cost along the supply chain as compared to the other two approaches. This supports our contention of better supply chain performance with increased collaboration across the supply chain.

## Conclusion

For each of the three supply chain approaches, linear programming models were formulated and the models for one of the approaches are shown in the Appendix. Linear programming is a well-known mathematical technique to optimize a linear function subjected to several linear constraints. Also the decision to formulate the above models as linear programming models was largely influenced by the availability of a linear programming software package.

The models formulated are all five echelons, multi-facility, multi-period, multi-product type. The models can only be applied to a supply chain representing five levels, namely, the retailers, the warehouses, the plants, the suppliers, and the second-tier suppliers. However the model can support any number of facilities at each level. Actual production occurs only at the plants and the suppliers.

Models for each of the three formulated supply chain approaches were solved for a set of 16 test problems. For a given supply chain configuration, the formulated models were solved and the total cost across the supply chain was computed. The Linear Interactive Discrete Optimizer (LINDO) optimization software tool was used to solve the models. The mainframe version was used due to the magnitude of the supply chain formulation at hand. Each of the formulated models incorporated varying degrees of integration of the decision-making process for the various functions across the supply chain. From the results obtained for the test runs, it is evident that the supply chain costs for decision making using the independent supply chain approach are the highest followed by the semi-integrated supply chain approach. The integrated supply chain approach resulted in a plan with least costs along the supply chain as compared to the other two approaches. The integrated supply chain approach represents a system, which involves integration of all the decision-making processes across the supply chain. It represents a synchronized supply chain where decisions at each level of plants, warehouses, suppliers and retailers are taken simultaneously under a single decision system. The semi-integrated supply chain approach includes integration of decision processes at the plant-supplier level and plant-retailer logistics level thus providing for some degree of integration in the supply chain. It represents collaboration between the plants and the suppliers on one hand and the plants and the warehouses on the other. The independent approach involves independent decision making at each level of the supply chain and thus displays minimum collaboration. Each module herein can be thought of as a decision system that optimizes the specific processes for which it is developed such as production planning, logistics, and others. Thus it can be concluded from the results that increased collaboration across the supply chain results in improved performance of the supply chain. In general, optimizing each process of the supply chain in isolation from other process does not guarantee optimization for the whole supply chain. Considering the advancements in technology, manufacturers should try to achieve optimality in the supply chain by integrating the decision making processes across the supply chain under a single system.

*Figure 1.** Independent approach*

*Figure 2.** Semi-integrated approach*

*Figure 3.** Integrated approach*

*Table** I.*

*Supply chain configuration*

*Table II.** Factor levels*

*Table III.** Comparison of total supply chain
costs*

*Table IV.** Experimental design characteristics*

*Table V.** Response to variation in capacity
utilization*

*See equation (1)*

*See equation (2)*

*See equation (3)*

*See equation (4)*

*See equation (5)*

*See equation (6)*

*See equation (7)*

*See equation (8)*

*See equation (9)*

*See equation (10)*

*See equation (11)*

*See equation (12)*

*See equation (13)*

*See equation (14)*

*See equation (15)*

*See equation (16)*

*See equation (17)*

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Simchi-Levi,
D., Kaminsky, P., Simchi-Levi, E., 2000, Designing and Managing the Supply
Chain: Concepts, Strategies, and Case Studies, Irwin McGraw-Hill, Boston,

## Appendix. Formulation of mathematical models

The notations used for the various parameters, cost components and decision variables are as follows:

*Parameters*

i - Plant.

j - Distribution center/warehouse.

k - Retailer.

p - Product type.

q - Material type.

r - Component type.

s - Tier-1 supplier.

t - Planning period in a planning horizon.

v - Tier-2 supplier.

CD_{pkt} - Demand
for product "p" at retailer "k" in planning period
"t".

MP_{pi} - Maximum
production capacity of plant "i" for product "p" in any
given period.

MO_{pi} - Maximum
overtime production capacity of the plant "i" for product
"p" in any given period.

N_{rp} - Component
determination factor. It is the number of components "r" required to
make product "p".

NR_{qr} - Material
determination factor. Quantity of material "q" required for component
"r".

QV_{qr} - Maximum
capacity of tier-2 supplier "v" to supply component "q".

SP_{rs} - Maximum
production capacity of tier-1 supplier "s" for component
"r".

SO_{rs} - Maximum
overtime production capacity of tier-1 supplier "s" for component
"r".

VWpj - Maximum quantity of product "p" which can be handled at distribution center/warehouse "j" in any given period.

W_{p} - Weight of
the product "p".

WX_{ij} - Weight
capacity of trucks operating between plan "i" and distribution
center/warehouse "j".

WZ_{jk} - Weight
capacity of trucks operating between distribution center/warehouse
"j" and retailer "k".

*Decision variables*

Decision variables at manufacturing plants

D_{rit} - Quantity
of component "r" needed for production at plant "i" in the
planning period "t".

I_{pit} - Inventory
of product "p" to be held at plant "i" in planning period
"t".

P_{pit} -
Production in units for product "p" at plant "i" in
planning period "t".

PW_{ijt} - Number
of truckload trips required from plant "i" to distribution
center/warehouse "j" in planning period "t".

P_{it} - Overtime
production in units for product "p" at plant "i" in
planning period "t".

Ra_{rity} -
Inventory of component "r" to be held at plant "i" in
planning period "t".

Sa_{pient} -
quantity of product "p" to be shipped from plant "i" to
distribution center/warehouse 'j' in planning period 't'.

Decision variables at tier-1 suppliers

DQ_{qst} - Quantity
of material "q" required for production at tier-1 supplier
"s" in the planning period "t".

IQ_{qst} - Number
of units of ending inventory of material "q" at tier-1 supplier
"s" in planning period "t".

R_{rsit} - Quantity
of component "t" shipped from tier-1 supplier "s" to plant
">i" in the planning period "t".

RP_{rst} -
Production in units for component "r" at tier-1 supplier
"s" in planning period "t".

RO_{rst} - Overtime
production in units for component "r" at tier-1 supplier
"s" in period "t".

SI_{rst} - Number
of units of ending inventory of component ">r" at tier-1 supplier
"s" in planning period "t".

Decision variable at tier-2 suppliers

Q_{qvst} - Quantity
of material "q" to be supplied by tier-2 supplier "v" to
supplier "s" in planning period "t".

Decision variable at distribution centers/warehouses

SC_{pjkt} -
Quantity of product "p" shipped from distribution center/warehouse
"j" to retailer outlet "k" in the planning period
"t".

WC_{jkt} - Number
of truckload trips from distribution center/warehouse "j" to retailer
outlet "k" in the planning period "t".

WD_{pjt} - Demand
for product "p" at distribution center/warehouse "j" in
planning period "t".

WI_{pjt} - Inventory
of product "p" to be held at distribution center/warehouse
"j" in planning period "t".

Decision variable at retailers

B_{pkt} - Units of
product "p" backordered at retailer "k" in planning period
"t".

*Cost components*

CB_{pk} - Backorder
cost for a unit of product "p" at retailer "k".

CI_{pi} - Inventory
holding cost per period for a unit of product "p" at plant
"i".

CIQ_{qs} -
Inventory holding cost per period for a unit of material "q" at
tier-1 supplier "s".

CP_{pi} -
Production cost for a unit of product "p" at plant "i".

CPW_{ij} - Shipping
cost for a truckload from plant "i" to distribution center/warehouse
"j".

CO_{pi} - Overtime
production cost for a unit of product "p" at plant "i".

CQ_{qvs} - Cost of
a unit of material "q" supplied by tier-2 supplier "v" to
tier-1 supplier "s".

CR_{rsi} - Shipping
cost of component "r" from tier-1 supplier "s" to plant
"i".

CRI_{rsi} -
Inventory holding cost per period for a unit of component "r" at
plant "i".

CRP_{rs} -
Production cost for a unit of component "r" and tier-1 supplier
"s".

CRO_{rs} - Overtime
production cost for a unit of component "r" at tier-1 supplier
"s".

CSI_{rs} -
Inventory holding cost per period for a unit of component "r" at
tier-1 supplier "s".

CW_{pj} - Inventory
holding cost per period for a unit of product "p" at distribution center/warehouse
"r".

CWC_{jk} - Shipping
cost for a truckload from distribution center/warehouse "j" to
retailer "k".

Formulation of mathematical model for integrated approach

In the integrated approach as shown in Figure 3, all supply chain links are connected through the integrated supply chain planning (ISCP) module. It utilizes supply chain constraints to determine the following:

- Distribution centers/warehouses' shipping plans.
- Distribution centers/warehouses' stock requirements.
- Production planning at the manufacturers.
- Manufacturers' shipping plans.
- Manufacturers' component requirements.
- Tier-1 supplier production planning.
- Tier-1 supplier shipping plans.
- Tier-1 supplier material shipping plans.
- Tier-1 supplier material requirements.
- Tier-1 supplier shipping plans.

*Objective function*

The objective function for the ISCP module is to minimize the following costs:

- Manufacturer production costs.
- Manufacturer overtime production costs.
- Manufacturer inventory costs.
- Tier-1 supplier shipping costs.
- Tier-1 component production costs.
- Tier-1 overtime production costs.
- Tier-1 supplier inventory costs.
- Backorder costs.
- Manufacturer-distribution center/warehouse shipping costs.
- Distribution center/warehouse-retailer shipping costs.
- Distribution center/warehouse inventory costs.
- Tier-1 supplier material procurement cost.
- Tier-1 supplier inventory costs for materials.

*Minimize* &Sgr;* _{t}* &Sgr;

*&Sgr;*

_{p}

_{i}*CP*+&Sgr;

_{pi}P_{pit}*&Sgr;*

_{t}*&Sgr;*

_{p}

_{i}*CO*+&Sgr;

_{pi}O_{pit}*&Sgr;*

_{t}*&Sgr;*

_{p}

_{i}*CI*+&Sgr;

_{pi}I_{pi}*&Sgr;*

_{t}*&Sgr;*

_{r}*&Sgr;*

_{s}

_{i}*CR*+ &Sgr;

_{rsi}R_{rsit}*&Sgr;*

_{t}*&Sgr;*

_{s}

_{r}*CRP*

_{rs}*RP*+&Sgr;

_{rst}*&Sgr;*

_{t}*&Sgr;*

_{s}

_{r}*CRO*

_{rs}*RO*+&Sgr;

_{rst}*&Sgr;*

_{t}*&Sgr;*

_{s}

_{r}*CSI*

_{rs}*SI*+ &Sgr;

_{rst}*&Sgr;*

_{t}*&Sgr;*

_{p}

_{k}*CB*

_{pk}*B*+&Sgr;

_{pkt}*&Sgr;*

_{i}*&Sgr;*

_{j}

_{t}*CPW*

_{ij}*PW*+ &Sgr;

_{ijt}*&Sgr;*

_{t}*&Sgr;*

_{j}

_{k}*CWC*

_{jk}*WC*+ &Sgr;

_{jkt}*&Sgr;*

_{t}*&Sgr;*

_{p}

_{j}*CW*

_{pj}*WI*+&Sgr;

_{pjt}*&Sgr;*

_{t}*&Sgr;*

_{s}

_{q}*CIQ*+&Sgr;

_{qs}*&Sgr;*

_{t}*&Sgr;*

_{q}*&Sgr;*

_{v}

_{s}*CQ*

_{qv}*Q*

_{qvst}*Constraints*

(1) *Product consumption*.
For each period, beginning inventory at all DCs/warehouses + beginning
manufacturing plant inventory + regular production + overtime production -
retailer demand - previous period backorders + current period backorders =
ending inventory at all DCs/warehouses + ending manufacturing inventory(see
equation 1)

(2) *Manufacturer
production capacity - regular time*. For each period, regular
production <=*q* maximum
production capacity.(see
equation 2)

(3) *Manufacturer
production capacity - overtime*. For each period, overtime
production <=*q* maximum
overtime capacity.(see
equation 3)

(4) *Component
requirements at manufacturing*. For each period, component demand =
component determination factor* (regular + overtime production scheduled)(see
equation 4)

(5) *Manufacturing demand*.
For each period, quantity of components shipped by tier-1 suppliers =
manufacturing component demand(see
equation 5)

(6) *Tier-1 shipping
quantities*. For each period, beginning inventory + regular
production + overtime production - quantity shipped to the manufacturing plants
= ending inventory(see
equation 6)

(7) *Tier-1 production
capacity - regular time*. For each period, regular component
production <=*q* maximum
component production(see
equation 7)

(8) *Tier-1 production
capacity - overtime*. For each period, overtime component production
<=*q* maximum overtime
production(see
equation 8)

(9) *Manufacturing-DC/warehouse
shipping quantities*. For each period, beginning inventory +
manufacturing plant regular production + manufacturing overtime production =
quantity shipped to all DCs/warehouses = ending inventory(see
equation 9)

(10) *Distribution
centers/warehouse inventory*. For each period, beginning inventory +
quantity received by DC/warehouse - quantity to be shipped by DC/warehouse =
ending inventory(see
equation 10)

(11) *Retailer demand*.
For each period, retailer demand + previous period backorder = quantity
received from DC's/warehouses + current period backorder(see
equation 11)

(12) *Truckload trips
between manufacturing plants-DC/warehouses.* For each period, weight
of the product * quantity supplied from manufacturing plants <=*q* weight capacity of truck * number of
truckload trips(see
equation 12)

(13) *Number of truckload
trips between DC/warehouse-retailers*. For each period, weight of
the product * quantity supplied from DC/warehouse <=*q* weight capacity of truck * number of
truckload trips(see
equation 13)

(14) *Distribution
center/warehouse capacity*. For each period, quantity received by
DC/warehouse + ending inventory <=*q*
DC/warehouse capacity(see
equation 14)

(15) *Tier-1 material
requirements*. For each period, tier-1 supplier demand = material
determination factor * (tier-1 regular + overtime production scheduled)(see
equation 15)

(16) *Tier-1 material
replenishment*. For each period, tier-1 supplier beginning inventory
+ quantity of material received from tier-2 suppliers - material demand at
tier-1 supplier = ending inventory at a tier-1 supplier(see
equation 16)

(17) *Tier-2 supplier
capacity*. For each period, quantity of material shipped by tier-2
supplier <=*q* maximum tier-2
supplier capacity(see
equation 17)