Incorporating Emerging Economies in the Supply Chain

Amiya K. Chakravarty

doi:10.1007/978-3-642-41911-9_7

Supply Chain Transformation pp 203-235 | Cite as

Incorporating Emerging Economies in the Supply Chain

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Amiya K. Chakravarty

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First Online: 31 December 2013

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Part of the Springer Texts in Business and Economics book series (STBE)

Abstract

The ripples from the rapid pace of change in emerging economies are being felt worldwide. In the next 15 years, 85% of the world’s population, and 57% of the nearly one billion households with purchasing power will live in these economies. This scenario not only provides opportunities for multinationals, it also creates a sense of urgency. Unilever, GE, and P&G, among others, already conduct a large percent of their R&D and business transactions in these economies. Therefore, formulating a strategy that incorporates emerging economies has become the top priority for many companies. That notwithstanding, global companies do face a complex set of challenges in penetrating these markets: unstable economic environment, poor infrastructure, and lower price expectations. Therefore, changes in supply chains would necessitate going beyond just tweaking the strategies framed primarily for mature economies. At the same time, it would not be feasible to manage multiple country-specific supply chains. The answer may lie in agility; a supply chain that can adapt to different environments, or a meta-supply-chain for coordinating several country-specific supply chains.

Keywords

Supply Chain Expected Profit Innovative Product Functional Product Mature Economy

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Appendix 1

The company’s revenue with Q units of the assembled product can be expressed as $ \pi =p\left\{{\displaystyle \underset{\xi \le Q}{\int}\xi f\left(\xi \right) d\xi}+Q{\displaystyle \underset{\xi \ge Q}{\int }f\left(\xi \right) d\xi}\right\} $, where Q = Min(γ _E q _E, γ _M q _M), and p is the unit sales price. Note that Q = γ _E q _E if γ _E ≤ γ _M q _M/q _E, and Q = γ _M q _M if γ _M ≤ γ _E q _E/q _M. Therefore, with g _E(⋅) and g _M(⋅) as the pdf of γ _E and γ _M respectively, the expected revenue is expressed as

$$ \mathrm{Rev}=p\left[\underset{\gamma_M}{E}\underset{\gamma_E\le \frac{\gamma_M{q}_M}{q_E}}{E}\underset{\xi }{E} Min\left\{{\gamma}_E{q}_E,\xi \right\}+\underset{\gamma_E}{E}\underset{\gamma_M\le \frac{\gamma_E{q}_E}{q_M}}{E}\underset{\xi }{E} Min\left\{{\gamma}_M{q}_M,\xi \right\}\right] $$

Assuming unit procurement costs of c _E and c _M, and unit assembly cost of c _A, the component procurement cost is expressed as $ {c}_E{q}_E\underset{\gamma_E}{E}{\gamma}_E+{c}_M{q}_M\underset{\gamma_M}{E}{\gamma}_M $. Next, note that the expected number of units assembled is expressed as $ {q}_E\left\{\underset{\gamma_M}{E}\left(\underset{\gamma_E\le \frac{\gamma_M{q}_M}{q_E}}{E}{\gamma}_E\right)\right\}+{q}_M\left\{\underset{\gamma_E}{E}\left(\underset{\gamma_M\le \frac{\gamma_E{q}_E}{q_M}}{E}{\gamma}_M\right)\right\} $. Therefore, the cost of assembly would be $ {c}_A\left[{q}_E\left\{\underset{\gamma_M}{E}\left(\underset{\gamma_E\le \frac{\gamma_M{q}_M}{q_E}}{E}{\gamma}_E\right)\right\}+{q}_M\left\{\underset{\gamma_E}{E}\left(\underset{\gamma_M\le \frac{\gamma_E{q}_E}{q_M}}{E}{\gamma}_M\right)\right\}\right] $.

Therefore, the expected profit would be

$$ \pi =\left|\begin{array}{l}p\left[\underset{\gamma_M}{E}\underset{\gamma_E\le \frac{\gamma_M{q}_M}{q_E}}{E}\underset{\xi }{E} Min\left\{{\gamma}_E{q}_E,\xi \right\}+\underset{\gamma_E}{E}\underset{\gamma_M\le \frac{\gamma_E{q}_E}{q_M}}{E}\underset{\xi }{E} Min\left\{{\gamma}_M{q}_M,\xi \right\}\right]\\ {}-\left\{{c}_E{q}_E\underset{\gamma_E}{E}{\gamma}_E+{c}_M{q}_M\underset{\gamma_M}{E}{\gamma}_M\right\}-{c}_A\left[{q}_E\left\{\underset{\gamma_M}{E}\left(\underset{\gamma_E\le \frac{\gamma_M{q}_M}{q_E}}{E}{\gamma}_E\right)\right\}+{q}_M\left\{\underset{\gamma_E}{E}\left(\underset{\gamma_M\le \frac{\gamma_E{q}_E}{q_M}}{E}{\gamma}_M\right)\right\}\right]\end{array}\right. $$

Appendix 2

For given w ₁, w ₂, and R, retailer determines her reaction function (Stackelberg game) by maximizing her profit in Q. Supplier 1 determines w ₁, and supplier 2 determines w ₂ and R by maximizing their respective profit functions, subject to the retailer’s reaction function.

The retailer’s expected profit is expressed as

$$ \pi =p\left\{{\displaystyle \underset{\xi \le Q+R}{\int}\xi f\left(\xi \right)}+\left(Q+R\right){\displaystyle \underset{\xi \ge Q+R}{\int }f\left(\xi \right)}\right\}-{w}_2\left\{{\displaystyle \underset{Q\le \xi \le Q+R}{\int}\left(\xi -Q\right)f\left(\xi \right)}+R{\displaystyle \underset{\xi \ge Q+R}{\int }f\left(\xi \right)}\right\}-{w}_1Q. $$

From the first order condition in Q, we express retailer’s decision as (p − w ₂)F(Q + R) + w ₂ F(Q) = p − w ₁.

Supplier 1’s profit is expressed as π ₁ = (w ₁ − c ₁)Q. From first order condition in w ₁, given the retailer’s reaction function (p − w ₂)F(Q + R) + w ₂ F(Q) = p − w ₁, we have w ₁ = w ₂ Qf(Q) + (p − w ₂)Qf(Q + R) + c ₁.

Supplier 2’s profit is written as $ {\pi}_2={w}_2\left\{{\displaystyle \underset{Q\le \xi \le Q+R}{\int}\left(\xi -Q\right)f\left(\xi \right)}+R{\displaystyle \underset{\xi \ge Q+R}{\int }f\left(\xi \right)}\right\}-{c}_2R $, so that from the first order condition in w ₂, given the buyer’s reaction function, is expressed as

$$ \frac{w_2}{\left(p-{w}_2\right)f\left(Q+R\right)+{w}_2f(Q)}=\frac{{\displaystyle \underset{Q\le \xi \le Q+R}{\int}\left(\xi -Q\right)f\left(\xi \right)}+R{\displaystyle \underset{\xi \ge Q+R}{\int }f\left(\xi \right)}}{{\left\{F\left(Q+R\right)-F(Q)\right\}}^2}. $$

Similarly, the first order condition in R leads to,

$$ \frac{w_2f(Q)F\left(Q+R\right)+\left(p-{w}_2\right)f\left(Q+R\right)F(Q)}{\left(p-{w}_2\right)f\left(Q+R\right)+{w}_2f(Q)}=1-\frac{c_2}{w_2}. $$

Appendix 3

Assume F(ξ) to be the continuous distribution of demand ξ.

Retailer’s Profit

As the retailer can only sell an amount that does not exceed either supply or demand, her expected revenue will be $ p\underset{\xi }{E}\left\{ Min\left(Q,\xi \right)\right\} $. Retailer’s expected payment to the bank is expressed as $ \underset{\xi }{E} Min\left( p\xi, wQ\right) $. Hence, retailer’s expected profit will be $ p\underset{\xi }{E}\left\{ Min\left(Q,\xi \right)\right\}-\underset{\xi }{E} Min\left( p\xi, wQ\right) $.

Bank’s Profit

Amount received from the retailer = $ {\displaystyle \underset{\xi \le \frac{ wQ}{p}}{\int } p\xi f\left(\xi \right) d\xi}+ wQ{\displaystyle \underset{\xi \ge \frac{ wQ}{p}}{\int }f\left(\xi \right) d\xi} $

Payment to the supplier on day 30 = $ \alpha wQ\left(1-\frac{r}{12}\right) $

Payment to the supplier on day 60 = $ wQ\left(1-\alpha \right){\displaystyle \underset{\xi \ge \frac{ wQ}{p}}{\int }f\left(\xi \right) d\xi}+{\displaystyle \underset{\xi \le \frac{ wQ}{p}}{\int } Max\left( p\xi -\alpha wQ,0\right)f\left(\xi \right) d\xi} $

Therefore, the Bank’s expected profit is written as

$$ {\pi}_B=\left|\begin{array}{l}\left\{{\displaystyle \underset{\xi \le \frac{ wQ}{p}}{\int } p\xi f\left(\xi \right) d\xi}+ wQ{\displaystyle \underset{\xi \ge \frac{ wQ}{p}}{\int }f\left(\xi \right) d\xi}\right\}\\ {}-\left\{\alpha wQ\left(1-\frac{r}{12}\right)+ wQ\left(1-\alpha \right){\displaystyle \underset{\xi \ge \frac{ wQ}{p}}{\int }f\left(\xi \right) d\xi}+{\displaystyle \underset{\xi \le \frac{ wQ}{p}}{\int } Max\left( p\xi -\alpha wQ,0\right)f\left(\xi \right) d\xi}\right\}\end{array}\right. $$

Supplier’s Profit

Manufacturer’s profit would be equal to the amount received from the bank less manufacturing cost. Therefore the supplier’s expected profit is expressed as

$$ {\pi}_M=\left\{\alpha wQ\left(1-r\right)+ wQ\left(1-\alpha \right){\displaystyle \underset{\xi \ge \frac{w}{p}Q}{\int }f\left(\xi \right) d\xi}+{\displaystyle \underset{\xi \le \frac{w}{p}Q}{\int }{\left( p\xi -\alpha wQ\right)}^{+}f\left(\xi \right) d\xi}\right\}- cQ $$

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Amiya K. Chakravarty
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1.DM School of Business Northeastern UniversityBostonUSA

Incorporating Emerging Economies in the Supply Chain

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