Location-based pricing and channel selection in a supply chain: a case study from the food retail industry

Abstract

Many retailers nowadays operate in an Internet-enabled dual-channel supply chain setting, referred to as “click and mortar”. In such a structure, products and services are delivered through both online B2C (business-to-consumer e-tail) and offline B2C (traditional brick and mortar retail) channels. In this paper, we develop and present a unified modeling approach that reflects a real-world dual-channel supply chain in the food retail industry. Motivated by the actual business operations of a case study, we incorporate the spatial locations of customers, as well as other logistics and operational costs, into the service provider’s pricing and the customers’ channel choice decisions. We develop two models, namely the benchmark and proposed models, and conduct extensive numerical experiments with parameter values centered on actual values. The results reveal that the ratio of online and offline profit to the total dual-channel profit vary significantly, depending on the locations of customers and the values of the logistics costs. In addition, our statistical and visual analysis suggest that by jointly optimizing the logistics and operational processes, the service provider can achieve a considerably high profit through both channels, without necessarily expanding the size of its geographical service areas.

Appendices

Appendix A

1.1 A1: Offline-only model

Under the offline-only setting, the customer service area is modeled as a circle with the restaurant at the center. Following Eq. (A1), the customer area is a circle with a radius denoted as l_u, such that the purchase proportion is equal to 0 at a distance of l_u:

$$ \theta \left( {p_{\text{off}} + T_{\text{off}} \left( {l_{u} } \right)} \right) = 0, \quad l_{u} = \left( {p_{ \hbox{max} } - p_{\text{off}} } \right)/C_{t} $$

(A1)

As shown in Eq. (A2), the potential demand for the offline channel can be calculated through integrating over the circle of service with radius l_u:

$$ \begin{aligned} D_{\text{off}} & = \mathop \int \limits_{0}^{\infty } \theta \left( {p_{\text{off}} + T_{\text{off}} \left( l \right)} \right)\,\cdot \,2\pi \,\cdot \,l\,\cdot \,{\text{d}}l = \mathop \int \limits_{0}^{{l_{u} }} \theta \left( {p_{\text{off}} + T_{\text{off}} \left( l \right)} \right)\,\cdot \,2\pi \,\cdot \,l\,\cdot \,{\text{d}}l \\ & = \mathop \int \limits_{0}^{{l_{u} }} \frac{{p_{\hbox{max} } - p_{\text{off}} - C_{t} \,\cdot \,l}}{{p_{\hbox{max} } - p_{\hbox{min} } }}\,\cdot \,2\pi \,\cdot \,l\,\cdot \,{\text{d}}l \\ & = \frac{{\pi \cdot \left( {p_{\hbox{max} } - p_{\text{off}} } \right)^{3} }}{{3C_{t}^{2} \cdot \left( {p_{\hbox{max} } - p_{\hbox{min} } } \right)}} \\ \end{aligned} $$

(A2)

The offline profit function Π_off for this offline-only setting then can be derived, as in Eq. (A3).

$$ \begin{aligned} \varPi_{\text{off}} & = p_{\text{off}} \cdot D_{\text{off}} - \left( {C_{p} + C_{{{\text{of}}f}} } \right)\cdot D_{\text{off}} \\ & = \pi \cdot \left( {p_{\text{off}} - C_{p} - C_{\text{off}} } \right)\cdot \frac{{\left( {p_{\hbox{max} } - p_{\text{off}} } \right)^{3} }}{{3C_{t}^{2} \cdot \left( {p_{\hbox{max} } - p_{\hbox{min} } } \right)}} \\ \end{aligned} $$

(A3)

To find the optimal price for the offline-only setting, we take the derivative of the offline profit function Π_off with respect to the offline price p_off, as shown in Eq. (A4):

$$ \frac{{\partial \varPi_{off} }}{{\partial p_{off} }} = \frac{\pi }{{3C_{t}^{2} \cdot \left( {p_{\hbox{max} } - p_{\hbox{min} } } \right)}}\cdot \left[ {\left( {p_{\hbox{max} } - p_{off} } \right)^{3} - 3\left( {p_{off} - C_{p} - C_{off} } \right)\cdot \left( {p_{\hbox{max} } - p_{off} } \right)^{2} } \right] $$

(A4)

When this equation is solved for price, the optimal offline price $p_{\text{off}}^{*}$ for the offline-only setting is found in Eq. (A5), where purchase proportion is non-negative:

$$ p_{\text{off}}^{ *} = \frac{1}{4}\cdot \left( {3C_{p} + 3C_{\text{off}} + p_{ \hbox{max} } } \right) $$

(A5)

The customers’ travel costs can be obtained through integrating over the potentially infinite circular service area, as given in Eq. (A6):

$$ C_{\text{off}}^{t} = \mathop \int \limits_{0}^{\infty } T_{\text{off}} \left( l \right)\cdot \theta \left( {p_{\text{off}} + T_{\text{off}} \left( l \right)} \right)\cdot 2\pi \cdot l\cdot {\text{d}}l = \frac{\pi }{{6C_{t}^{2} }}\cdot \frac{{\left( {p_{ \hbox{max} } - p_{\text{off}} } \right)^{4} }}{{p_{ \hbox{max} } - p_{ \hbox{min} } }} $$

(A6)

1.2 A2: Online-only model

In the online-only setting, customers can only order online and receive delivery of the product ordered from the service provider, but not visit the restaurant. This setting is particularly suitable for customers who have limited meal time (e.g. office staff) and prefer their meals to be delivered to their locations.

In the online-only setting, the maximum online delivery distance is limited to l_m. In other words, the online demand is 0 for customers at a distance of l_m. The value of l_m can accordingly be obtained through Eq. (A7):

$$ T_{\text{on}} \left( {l_{m} } \right) + C_{p} = p_{\text{on}} + p_{d} ,l_{m} = \left( {p_{\text{on}} + p_{d} - C_{p} } \right)/C_{d} $$

(A7)

Online demand is calculated by integrating the online-only demand over the service area with a radius of l_m, as given in Eq. (A8):

$$ D_{\text{on}} = \mathop \int \limits_{0}^{{l_{m} }} \theta \left( {p_{\text{on}} + p_{d} } \right)\;\cdot \;2\pi \;\cdot \;l\;\cdot \;{\text{d}}l = \pi \cdot \frac{{p_{ \hbox{max} } - p_{\text{on}} - p_{d} }}{{p_{ \hbox{max} } - p_{ \hbox{min} } }}\cdot \left( {\frac{{p_{\text{on}} + p_{d} - C_{p} }}{{C_{d} }}} \right)^{2} $$

(A8)

Substituting demand, price, and delivery costs into Eq. (A9), the online profit can be calculated:

$$ {{\varPi }}_{\text{on}} = \left( {p_{\text{on}} + p_{d} - C_{p} } \right)\;\cdot \;D_{\text{on}} - \bar{T}_{\text{on}} \left( {S_{\text{on}} } \right)\;\;\cdot D_{\text{on}} $$

(A9)

Total delivery cost and an alternative form of online profit function are derived in Eqs. (A10) and (A11), respectively:

$$\begin{aligned}& \bar{T}_{\text{on}} \left( {S_{\text{on}} } \right)\,\cdot \,D_{\text{on}} = \mathop \int \limits_{0}^{{l_{m} }} T_{\text{on}} \left( l \right)\cdot \theta \left( {p_{\text{on}} + p_{d} } \right)\,\cdot \,2\pi \,\cdot \,l\,\cdot \,{\text{d}}l\\ & = \frac{2}{3}\pi \cdot C_{\text{on}} \cdot \frac{{p_{ \hbox{max} } - p_{\text{on}} - p_{d} }}{{p_{ \hbox{max} } - p_{ \hbox{min} } }}\cdot \left( {\frac{{p_{\text{on}} + p_{d} - C_{p} }}{{C_{d} }}} \right)^{3}\end{aligned} $$

(A10)

$$ \begin{aligned} \varPi_{\text{on}} & = \left( {p_{\text{on}} + p_{d} - C_{p} } \right)\,\cdot \,D_{\text{on}} - \bar{T}_{\text{on}} \left( {S_{\text{on}} } \right)\,\cdot \,D_{\text{on}} \\ & = \frac{\pi }{3}\cdot \frac{{p_{\hbox{max} } - p_{\text{on}} - p_{d} }}{{p_{\hbox{max} } - p_{\hbox{min} } }}\cdot \frac{{\left( {p_{\text{on}} + p_{d} - C_{p} } \right)^{3} }}{{C_{d}^{2} }} \\ \end{aligned} $$

(A11)

Finally, the optimal online price is derived in Eq. (A12), when purchase proportion is non-negative:

$$ p_{\text{on}}^{ *} = \frac{1}{4}C_{p} - p_{d} + \frac{3}{4}\;\cdot \,p_{ \hbox{max} } $$

(A12)

Appendix B

See Tables 3, 4, 5, 6.

Table 3 Experimental factors and levels for the comparative experiments

Table 4 ANOVA results showing the significance of factors and interactions with respect to affecting ΔΠ

Table 5 Experimental factors and levels for the proposed model

Table 6 ANOVA results for the proposed model, showing the significance of factors and interactions with respect to affecting ${{\varPi }}_{t}^{*}$