Fulfillment mode selection for Indian online sellers under free and flat rate shipping policies

Abstract

In this study, we have examined the performance of an online seller under two distinct fulfillment modes (fulfillment by seller and fulfillment by E-marketplace) under two shipping fee policies (free shipping and flat rate shipping). We have derived closed form analytical expressions for the decision variables of the seller such as sale price, sales volume and profit under the fulfillment modes for the shipping policies under consideration. We have checked the validity of the model by considering a leading Indian E-marketplace. From the case example, we obtained the following results (1) The seller is better off when engaged in a contract with the E-marketplace for inventory storage and order fulfillment (2) The seller is gainful by adopting a free shipping policy than a flat rate shipping policy (3) The impact of referral fee variation by the E-marketplace can significantly affect the profit of the seller whereas the impact of lead time variation has minimal impact on the profit of the seller.

Appendix

1.1 Equilibrium analysis of fulfillment by seller model

In this section, we carry out the equilibrium analysis of FBS model. First, we translate the cost elements to their corresponding symbolic expressions for deriving closed form analytic solutions.

1.1.1 Cost elements of the seller

• (1)
  $${\rm Inventory} \, {\rm holding} \, {\rm cost} \, + \, {\rm Shipping} \, {\rm cost} \, + \, {\rm Packaging} \, {\rm cost} \, = h^{s} \frac{{D_{j}^{s} }}{2} + D_{j}^{s} (x_{1}^{s} f_{1}^{s} + x_{2}^{s} f_{2}^{s} + x_{3}^{s} f_{3}^{s} ) + D_{j}^{s} g^{s}$$

  (15)
• (2)
  $${\rm e-marketplace} \, {\rm fee} \, = \, \text{Referral} \, \text{fee} \, + \, \text{Closing} \, \text{fee} \, = D_{j}^{s} (p_{FS}^{s} \delta + k)$$

  (16)

1.1.2 Profit of the seller under free shipping policy

Profit of the seller = Demand * Margin per product sold − Cost incurred by the seller

$$\pi_{FS}^{s} = (p_{FS}^{s} - r)D_{FS}^{s} - D_{FS}^{s} \left( {\frac{{h^{s} }}{2} + g^{s} + k + p_{FS}^{s} \delta + x_{1}^{s} f_{1}^{s} + x_{2}^{s} f_{2}^{s} + x_{3}^{s} f_{3}^{s} } \right)$$

(17)

The objective of the retailer is to maximize his profit, i.e. ${\text{Max }}\pi_{FS}^{s}$.The F.O.C $\frac{{\partial \pi_{FS}^{s} }}{{\partial p_{FS}^{s} }} = 0$ yields the optimal price as follows

$$\begin{aligned} p_{FS}^{s*} = \frac{{2\left( {1 - \delta } \right)\left( {a - cl^{s} } \right) + b\Delta_{1} }}{{4b\left( {1 - \delta } \right)}} \hfill \\ \hbox{where} \, \Delta_{1} = h^{s} + 2(k + g^{s} + r + x_{1} f_{1}^{s} + x_{2} f_{2}^{s} + x_{3} f_{3}^{s} ) \hfill \\ \end{aligned}$$

(18)

Using the expression of the optimal price, we can derive the expression for optimal sales volume from Eq. (1) as shown below

$$Q_{FS}^{s*} = \frac{{2\left( {a - cl^{s} } \right)\left( {1 - \delta } \right) - b\Delta_{1} }}{{4\left( {1 - \delta } \right)}}$$

(19)

Now by substituting $p_{FS}^{s*}$ and $Q_{FS}^{s*}$, we can obtain the expression for the optimal profit of the seller from Eq. (3) as follows

$$\pi_{FS}^{s*} = \frac{{\left( {b\Delta_{1} - 2\left( {1 - \delta } \right)\left( {a - l^{s} c} \right)} \right)^{2} }}{{16b\left( {1 - \delta } \right)}}$$

(20)

1.1.3 Profit of the seller under flat rate shipping fee policy

The margin per product sold under flat rate shipping is as follows

Margin per product sold = sale price − procurement cost + shipping fee

Hence, the profit of the seller is as follows

$$\pi_{CS}^{s} = \left( {p_{CS}^{s} - r + \omega } \right)D_{CS}^{s} - D_{CS}^{s} \left( {\frac{{h^{s} }}{2} + g^{s} + \delta p_{CS}^{s} + k + x_{1} f_{1}^{s} + x_{2}^{{}} f_{2}^{s} + x_{3}^{{}} f_{3}^{s} } \right)$$

(21)

The optimal price of the seller under flat rate shipping fee policy

$$p_{CS}^{s*} = \frac{{b\left( {\Delta_{1} - 2\omega } \right) + 2\left( {1 - \delta } \right)\left( {a - cl^{s} - \varepsilon \omega } \right)}}{{4b\left( {1 - \delta } \right)}}$$

(22)

The optimal sales volume of the seller can be derived by substituting $p_{CS}^{s*}$ into Eq. (2) as given below

$$Q_{CS}^{s*} = \frac{{2\left( {1 - \delta } \right)\left( {a - cl^{s} - \varepsilon \omega } \right) - b\left( {\Delta_{1} - 2\omega } \right)}}{{4\left( {1 - \delta } \right)}}$$

(23)

Further, substituting the $p_{CS}^{s*}$ and $Q_{CS}^{s*}$ into Eq. (21) will yield the optimal profit of the seller as follows

$$\pi_{CS}^{s*} = \frac{{\left( {b\left( {\Delta_{1} - 2\omega } \right) - 2\left( {1 - \delta } \right)\left( {a - cl^{s} - \varepsilon \omega } \right)} \right)^{2} }}{{16b\left( {1 - \delta } \right)}}$$

(24)

1.2 Equilibrium analysis of fulfillment by E-marketplace model

In this section, we carry out the equilibrium analysis of FBE model. Under FBE model the seller uses E-marketplace partnered logistic services (lower shipping cost) for shipping products to the fulfillment centers. The shipping cost of E-marketplace partnered logistics service is lower than that of a 3PL service provider. We have assumed that the seller replenishes the inventory on a monthly basis, i.e. at the start of a month (selling season), the seller ships the products to the fulfillment centers of the E-marketplace through the E-marketplace partnered logistics service provider.

First, we translate the cost elements of the seller into corresponding mathematical expressions for carrying out the equilibrium analysis. Under FBE, the seller incurs two major types of costs viz. (1) Cost of packing the product at an aggregate level and sending it to multiple fulfillment centers of the E-marketplace, i.e. bulk packing cost (2) The fee to be paid to the E-marketplace for carrying out the fulfillment procedure on behalf of the seller. The cost elements of the seller are shown as follows

$$\begin{aligned} {\text{E-marketplace}} \, {\rm Fee} \, = {\rm Referral} \, {\rm fee} \, + \, {\rm Storage} \, {\rm fee} \, + \, {\rm Pick} \, {\rm and} \, {\rm Pack} \, {\rm fee} \, + \, {\rm Shipping} \, {\rm cost} \, {\rm to} \, {\rm the} \, {\rm fulfillment} \, {\rm center} + {\rm Weight} \, {\rm handling} \, {\rm fee}\; \hfill \\ + {\rm Delivery} \, {\rm service} \, {\rm fee} = D_{j}^{e} (\delta p_{j}^{e} + vh^{e} + g^{e} + x_{1} f_{1}^{e - pc} + x_{2} f_{2}^{e - pc} + x_{3} f_{3}^{e - pc} + y^{e} + \phi p^{e} ) \hfill \\ \end{aligned}$$

(25)

1.2.1 Profit of the seller under free shipping policy

The profit of the seller = Demand * Margin per product sold − Cost incurred by the seller

$$\pi_{FS}^{e} = (p_{FS}^{e} - r^{{}} )D_{FS}^{e} - D_{FS}^{e} (m^{e} + \delta p_{FS}^{e} + vh^{e} + g^{e} + x_{1} f_{1}^{e - pc} + x_{2} f_{2}^{e - pc} + x_{3} f_{3}^{e - pc} + y^{e} + \phi p_{FS}^{e} )$$

(26)

The objective of the seller is to maximize his profit, i.e. ${\text{Max }}\pi_{FS}^{e}$. The F.O.C $\frac{{\partial \pi_{FS}^{e} }}{{\partial p_{FS}^{e} }} = 0$ yields the optimal price as follows

$$\begin{aligned} p_{FS}^{e*} = \frac{{b\Delta_{2} + \left( {1 - \delta - \phi } \right)\left( {a - cl^{e} + un^{e} } \right)}}{{2b\left( {1 - \delta - \phi } \right)}} \hfill \\ {\text{where }}\Delta_{2} = \left( {g^{e} + vh^{e} + m^{e} + r_{{}} + y^{e} + x_{1} f_{1}^{e - pc} + x_{2} f_{2}^{e - pc} + x_{3} f_{3}^{e - pc} } \right) \hfill \\ \end{aligned}$$

(27)

Substitution of $p_{FS}^{e*}$ into Eq. (3) yields the optimal sales volume of the seller as follows

$$Q_{FS}^{e*} = \frac{{\left( {1 - \delta - \phi } \right)\left( {a - cl^{e} + un^{e} } \right) - b\Delta_{2} }}{{2\left( {1 - \delta - \phi } \right)}}$$

(28)

Further, by substituting $p_{FS}^{e*}$ and $Q_{FS}^{e*}$ into Eq. (26), we can obtain the optimal profit of the seller.

$$\pi_{FS}^{e*} = \frac{{\left( {b\Delta_{2} - \left( {1 - \delta - \phi } \right)\left( {a - cl^{e} + un^{e} } \right)} \right)^{2} }}{{4b\left( {1 - \delta - \phi } \right)}}$$

(29)

1.2.2 Profit of the seller under flat rate shipping fee

The margin per product sold under flat rate shipping policy is as follows

Margin per product sold = sale price − procurement cost + shipping fee

In this case, the profit of the seller is given as follows.

$$\pi_{CS}^{e} = (p_{CS}^{e} - r + \omega )D_{CS}^{e} - D_{CS}^{e} (m^{e} + \delta p_{CS}^{e} + vh^{e} + g^{e} + x_{1} f_{1}^{e - pc} + x_{2} f_{2}^{e - pc} + x_{3} f_{3}^{e - pc} + y^{e} + \phi p_{CS}^{e} )$$

(30)

The objective of the seller is to maximize his profit, i.e. ${\text{Max }}\pi_{CS}^{e}$.The F.O.C $\frac{{\partial \pi_{CS}^{e} }}{{\partial p_{CS}^{e} }} = 0$ yields the optimal price as follows.

$$p_{CS}^{e*} = \frac{{\left( {1 - \delta - \phi } \right)\left( {a - cl^{e} + un^{e} - \varepsilon \omega } \right) - b(\omega - \Delta_{2} )}}{{2b\left( {1 - \delta - \phi } \right)}}$$

(31)

We can obtain the optimal sales volume by substituting of $p_{CS}^{e*}$ in Eq. (3) as given below

$$Q_{CS}^{e*} = \frac{{(1 - \delta - \phi )(a - cl^{e} + un^{e} - \varepsilon \omega ) - b(\Delta_{2} - \omega )}}{2(1 - \delta - \phi )}$$

(32)

Now, we substitute $p_{CS}^{e*}$ and $Q_{CS}^{e*}$ into Eq. (30) for obtaining the optimal profit of the seller.

$$\pi_{CS}^{e*} = \frac{{\left( {b(\Delta_{2} - \omega ) - (1 - \delta - \phi )(a - cl^{e} + un^{e} - \varepsilon \omega )} \right)^{2} }}{4b(1 - \delta - \phi )}$$

(33)

Proof of Proposition 1

Sale price under free shipping (FBS) − Sale price under flat rate shipping fee (FBS)

$$p_{FS}^{s*} - p_{CS}^{s*} = \frac{{\omega \left( {b + \varepsilon \left( {1 - \delta } \right)} \right)}}{{2\left( {1 - \delta } \right)b}} > 0$$

Sale price under free shipping policy (FBE) − Sale price under flat rate shipping fee policy (FBE)

$$p_{FS}^{e*} - p_{CS}^{e*} = \frac{\omega }{2}\left( {\frac{1}{1 - \delta - \phi } + \frac{\varepsilon }{b}} \right) > 0$$

Proof of Proposition 2

Sales volume under flat rate shipping fee policy (FBS) − Sales volume under free shipping policy (FBS)

$$Q_{CS}^{s*} - Q_{FS}^{s*} = \frac{{\omega \left( {b - \varepsilon \left( {1 - \delta } \right)} \right)}}{{2\left( {1 - \delta } \right)}} > 0 \, \;\;\;{\text{if }}\frac{b}{\varepsilon } > (1 - \delta )$$

Proof of Proposition 3

Profit of the seller under flat rate shipping fee policy (FBS) − Profit of the seller under free shipping policy (FBS)

$$\pi_{CS}^{s*} - \pi_{FS}^{s*} = \frac{{\omega \left( {b - \varepsilon \left( {1 - \delta } \right)} \right)\left( {\left( {1 - \delta } \right)\left( {2a - 2l^{s} c - \varepsilon \omega } \right) - b\left( {\Delta_{1} - \omega } \right)} \right)}}{{4b\left( {1 - \delta } \right)}}$$

Proof of Proposition 4

Sales volume under flat rate shipping fee policy (FBE) − Sales volume under free shipping policy (FBE)

$$Q_{CS}^{e*} - Q_{FS}^{e*} = \frac{{\omega \left( {b - \varepsilon \left( {1 - \delta - \phi } \right)} \right)}}{{2\left( {1 - \delta - \phi } \right)}} > 0{\text{ if }}\frac{b}{\varepsilon } > \left( {1 - \delta - \phi } \right)$$

Proof of Proposition 5

Profit of the seller under flat rate shipping fee policy (FBE)  −  Profit of the seller under free shipping policy (FBE)

$$\pi_{CS}^{e*} - \pi_{FS}^{e*} = \frac{{- \left({\left({a - cl^{e} + nu} \right)\left({- 1 + \delta + \phi} \right) + b\Delta_{2}} \right)^{2} + \left({\left({- 1 + \delta + \phi} \right)\left({a - cl^{e} + n^{e} u - \epsilon\omega} \right) + b\left({\Delta_{2} - \omega} \right)} \right)^{2}}}{{4b\left({1 - \delta - \phi} \right)}}$$

After simplification of the expression.

$$\pi_{CS}^{e*} - \pi_{FS}^{e*} = \frac{{\left( {b - \varepsilon \left( {1 - \delta - \phi } \right)} \right)\omega \left( {\left( {b - \varepsilon \left( {1 - \delta - \phi } \right)} \right)\omega + 2\left( {a - cl^{e} + n^{e} u} \right)\left( {1 - \delta - \phi } \right) - 2b\Delta_{2} } \right)}}{{4b\left( {1 - \delta - \phi } \right)}}$$

Inorder to have $\pi_{FS}^{e*} > \pi_{CS}^{e*}$(proposition 5), we can derive the following expression.

$$0 > b - \varepsilon (1 - \delta - \phi ) > \frac{{2b\Delta_{2} - 2(a - cl^{e} + un^{e} )(1 - \delta - \phi )}}{\omega }$$

Proof of Proposition 6

Impact of referral fee variation on the sale price under FBS and free shipping policy

$$\frac{{\partial p_{FS}^{s*} }}{\partial \delta } = \frac{{2k + 2g^{s} + h^{s} + 2r + 2x_{1} f_{1}^{s} + 2x_{2} f_{2}^{s} + 2x_{3} f_{3}^{s} }}{{4\left( {1 - \delta } \right)^{2} }} > 0$$

Impact of referral fee variation on the sales volume under FBS and free shipping policy

$$\frac{{\partial Q_{FS}^{s*} }}{\partial \delta } = - \frac{{b\left( {2k + 2g^{s} + h^{s} + 2r + 2x_{1} f_{1}^{s} + 2x_{2} f_{2}^{s} + 2x_{3} f_{3}^{s} } \right)}}{{4\left( {1 - \delta } \right)^{2} }} < 0$$

Impact of referral fee variation on the sale price under FBS and flat rate shipping policy

$$\frac{{\partial p_{CS}^{s*} }}{\partial \delta } = \frac{{2k + 2g^{s} + h^{s} + 2r - 2\omega + 2x_{1} f_{1}^{s} + 2x_{2} f_{2}^{s} + 2x_{3} f_{3}^{s} }}{{4\left( {1 - \delta } \right)^{2} }} > 0$$

Impact of referral fee variation on the sales volume under FBS and flat rate shipping policy

$$\frac{{\partial Q_{CS}^{s*} }}{\partial \delta } = - \frac{{b\left( {2k + 2g^{s} + h^{s} + 2r - 2\omega + 2x_{1} f_{1}^{s} + 2x_{2} f_{2}^{s} + 2x_{3} f_{3}^{s} } \right)}}{{4\left( {1 - \delta } \right)^{2} }} < 0$$

Impact of referral fee variation on the sale price under FBE and free shipping policy

$$\frac{{\partial p_{FS}^{e*} }}{\partial \delta } = \frac{{g^{e} + vh^{e} + m^{e} + r + y^{e} + x_{1} f_{1}^{e - pc} + x_{2} f_{2}^{e - pc} + x_{3} f_{3}^{e - pc} }}{{2\left( {1 - \delta - \phi } \right)^{2} }} > 0$$

Impact of referral fee variation on the sales volume under FBE and free shipping policy

$$\frac{{\partial Q_{FS}^{e*} }}{\partial \delta } = - \frac{{b\left( {g^{e} + vh^{e} + m^{e} + r + y^{e} + x_{1} f_{1}^{e - pc} + x_{2} f_{2}^{e - pc} + x_{3} f_{3}^{e - pc} } \right)}}{{2\left( {1 - \delta - \phi } \right)^{2} }} < 0$$

Impact of referral fee variation on the sale price under FBE and flat rate shipping policy

$$\frac{{\partial p_{CS}^{e*} }}{\partial \delta } = \frac{{g^{e} + vh^{e} + m^{e} + r + y^{e} + x_{1} f_{1}^{c - pc} + x_{2} f_{2}^{c - pc} + x_{3} f_{3}^{c - pc} - \omega }}{{2\left( {1 - \delta - \phi } \right)^{2} }} > 0$$

Impact of referral fee variation on the sales volume under FBE and flat rate shipping policy

$$\frac{{\partial Q_{CS}^{e*} }}{\partial \delta } = \frac{{b\left( {\omega - g^{e} - vh^{e} - m^{e} - r - y^{e} - x_{1} f_{1}^{c - pc} - x_{2} f_{2}^{c - pc} - x_{3} f_{3}^{c - pc} } \right)}}{{2\left( {1 - \delta - \phi } \right)^{2} }} < 0$$

Proof of Proposition 7

Impact of referral fee variation on the profit of the seller under FBS and free shipping policy

$$\frac{{\partial \pi_{FS}^{s*} }}{\partial \delta } = \frac{{b^{2} \Delta_{1}^{2} - 4\left( {1 - \delta } \right)^{2} \left( {a - l^{s} c} \right)^{2} }}{{16b\left( {1 - \delta } \right)^{2} }} < 0$$

Impact of referral fee variation on the profit of the seller under FBS and flat rate shipping policy

$$\frac{{\partial \pi_{CS}^{s*} }}{\partial \delta } = \frac{{\left( {b\left( {\Delta_{1} - 2\omega } \right)} \right)^{2} - \left( {2\left( {1 - \delta } \right)\left( {a - cl^{s} - \varepsilon \omega } \right)} \right)^{2} }}{{16b\left( {1 - \delta } \right)^{2} }} < 0$$

Impact of referral fee variation on the profit of the seller under FBE and free shipping policy

$$\frac{{\partial \pi_{FS}^{e*} }}{\partial \delta } = \frac{{b^{2} \Delta_{2}^{2} - \left( {1 - \delta - \phi } \right)^{2} \left( {a - cl^{e} + un^{e} } \right)^{2} }}{{4b\left( {1 - \delta - \phi } \right)^{2} }} < 0$$

Impact of referral fee variation on the profit of the seller under FBE and flat rate shipping policy

$$\frac{{\partial \pi_{CS}^{e*} }}{\partial \delta } = \frac{{b^{2} \left( {\Delta_{2} - \omega } \right)^{2} - \left( {1 - \delta - \phi } \right)^{2} \left( {a - cl^{e} + un^{e} - \varepsilon \omega } \right)^{2} }}{{4b\left( {1 - \delta - \phi } \right)^{2} }} < 0$$

The rationale underlying the deductions corresponding to proposition 7 is high magnitude of base demand compared to the other parameters of the model.

Proof of Proposition 8

Impact of shipping fee variation on the profit of the seller under FBS

$$\frac{{\partial \pi_{CS}^{s*} }}{\partial \omega } = \frac{{\left( {2b - 2\varepsilon \left( {1 - \delta } \right)} \right)\left( {b\left( {2\omega - \Delta_{1} } \right) + 2\left( {1 - \delta } \right)\left( {a - cl^{s} - \varepsilon \omega } \right)} \right)}}{{8b\left( {1 - \delta } \right)}} > 0$$

Impact of shipping fee variation on the profit of the seller under FBE

$$\frac{{\partial \pi_{CS}^{e*} }}{\partial \omega } = \frac{{\left( {b - \varepsilon \left( {1 - \delta - \phi } \right)} \right)\left( {b\left( {\omega - \Delta_{2} } \right) + \left( {1 - \delta - \phi } \right)\left( {a - cl^{e} + un^{e} - \varepsilon \omega } \right)} \right)}}{{2b\left( {1 - \delta - \phi } \right)}} > 0$$

Proof of Proposition 9

Impact of lead time variation on the profit of the seller under free shipping policy

$$\frac{{\partial \pi_{FS}^{s*} }}{\partial l} = \frac{{c\left( {b\Delta_{1} - 2\left( {1 - \delta } \right)\left( {a - cl^{s} } \right)} \right)}}{4b} < 0$$

Impact of lead time variation on the profit of the seller under flat rate shipping policy

$$\frac{{\partial \pi_{CS}^{s*} }}{\partial l} = \frac{{c\left( {b\left( {\Delta_{1} - 2\omega } \right) - 2\left( {1 - \delta } \right)\left( {a - cl^{s} - \varepsilon \omega } \right)} \right)}}{4b} < 0$$

Proof of Proposition 10

Impact of lead time variation on the profit of the seller under free shipping policy

$$\frac{{\partial \pi_{FS}^{e*} }}{\partial l} = \frac{{c\left( {b\Delta_{2} - \left( {1 - \delta - \phi } \right)\left( {a - cl^{e} + un^{e} } \right)} \right)}}{2b} < 0$$

Impact of lead time variation on the profit of the seller under flat rate shipping policy

$$\frac{{\partial \pi_{CS}^{e*} }}{\partial l} = \frac{{c\left( {b\left( {\Delta_{2} - \omega } \right) - \left( {1 - \delta - \phi } \right)\left( {a - cl^{e} + un^{e} - \varepsilon \omega } \right)} \right)}}{2b} < 0$$