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Modelling Of Supply Chain For Financial And Pricing Decisions

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Integrating the various parameters and functionality of all the members which participate to produce/deliver product service in accordance to customers demand is the prime responsibility of the supply chain manager. The delivery performance of such a network can be maximized by synchronizing the work through the system in such a way that the finished products reach the customer, who has a specific demand probability. The following work realizes the implications of this delivery performance in the nodes of the supply chain through various financial parameters. It also proposes a mathematical model to analyze the consequences of a shift in the delivery performance at a particular node in the entire supply chain.

Problem considered:

The problem definition can be given as modeling of a supply chain for financial parameters and their distribution using SPC (Statistical Process Control) techniques.

Objective of the Work

The specific topical aspects of the work include study of the design of the supply chains and application of the concept of statistical process control along with the detailed study of various process indices and relating various costs and pricing decisions to the existing process capability indices to formulate mathematical correlations.

Approach to the solution of the problem

The design of the problem was done in a step-by-step incremental manner.

The methodology followed was,

a) Study of Supply chains

b) Study of research work done in the field of applying six-sigma approach to supply chains.

c) Study of research work done on process capability indices, cost, and pricing functions in the supply chains.

d) Analysis and identification of various key parameters involved in cost and financing decisions in various supply chains.

e) Relating process capability indices to the key parameters.

f) Designing a supply chain that incorporates these key parameters and gives optimal solutions to take the cost and pricing decisions.

g) Collection of real time data from several industries to test the model of the supply chain.

Process Capability Indices

The PCIs Cp, Cpk and Cpm are popular in the areas of design tolerancing and statistical process control. They are the indicators of processes' capability to produce a desired output, though quantifying the process mean, variance and specifications' interrelation.

Indexes Cp, Cpk and Cpm

1) Index Cp: The PCI Cp is defined as

As assumed here, the target value is the mid point of, and can be expressed in the following equivalent form:

Where T= tolerance = (U-L)/2. Cp measures only the potential of a process to produce acceptable products. It does not bother about actual yield of the process where potential and actual yield of any process are defined in the following manner.

Actual Yield: The probability of producing a part within specification limits.

Potential: The probability of producing a part within specification limits, if process distribution is centered at the target value i.e. .

2) Index Cpk: Index Cp does not reflect the impact that shifting the process mean or target value has on a process's ability to produce a product within specification. For this reason, the index Cpk was developed. Cpk is defined as follows:

Index Cpm: Actual yield of the process is related to the fraction of the total number of units produced by the process which are defective, called as fraction defective. The fraction defective is an indicator of process precision and it does not take into account the accuracy of the process. In order to include the notion of accuracy along with precision, we can use the index Cpm as follows:

Lead time estimation

The Lead times of a supply chain can be viewed as random variables drawn from a normal distribution. These lead times occurring at various nodes of the supply chain can be summed up to calculate the total lead time of the supply chain. The resulting Lead time for the overall supply chain is also a normal random variable (Central Limit Theorem), the mean and variance given by,


This is then compared to the customer window of the demand to calculate the actual yield of the process and the cost of inefficiency.

Actual Yield of the process and the Cost of Ineffectiveness:

The actual yield is defined as the part of the production which is sold to the customers. For this the supply should be within the customers demand domain. The overlap of the customer demand distribution and the supply lead time distribution is the actual yield.


P= Profit

V= Production Volume

c= Unit cost of production

y= Actual Yield

p= Profitability

From Sales Profit equations:

Sales Volume = y*V

Profit = price * Sales


= Sales Revenue Ð'- costs

= Sales Volume* Price Ð'- Production* unit costs

= y*V*c*(1+p) Ð'- V*c

Hence the profit margins are proportional to the actual yield.

Since there is a part of production which is not contributing to the sales there is an inherent yield loss associated, this is attributed as the Cost of ineffectiveness (of the supply chain), i.e. the price borne by the Supply chain for



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