Integrated strategic and tactical supply chain planning with price-sensitive demands

Abstract

This paper deals with the supply chain network design and planning for a multi-commodity and multi-layer network over a planning horizon with multiple periods in which demands of customer zones are considered to be price dependent. These prices determine the demands using plausible price–demand relationships of customer zones. The net income of the supply chain is maximized, while satisfying budget constraints for investment in network design. In addition, a new approach is considered for capacity planning to make the problem more realistic. In this regard, when production plants are opened and expanded, capacity options are taken into account for manufacturing operations. Furthermore, several aspects relevant to real world applications are captured in the problem. Different interconnected time periods in the planning horizon are considered for strategic and tactical decisions in the problem and then, a mixed-integer linear programming (MILP) model is developed. The performance and applications of the model are investigated by several test problems with reasonable sizes. The numerical results illustrate that obtained solutions after solving the MILP model by using CPLEX solver are acceptable. Moreover, using an alternative pricing approach, a tight upper bound is provided for the problem. In addition, a deep sensitivity analysis is conducted to show the validity and performance of the proposed model.

Appendices

Appendix 1: Pricing parameters

In the pricing framework, in each tactical period, each customer zone has a willingness to pay distribution function for each product. Therefore, a price–demand relation is assumed for any customer in each time period and for each product. The relation between price $(P_{i, k,p, t} )$ and demand $(D_{i, k,p, t} )$ can be generally illustrated as in Fig. 17. This price response function is a special case of logit function. For more detailed explanations, one can refer to Phillips (2005) and Talluri and Ryzin (2006).

Fig. 17

The price-response function

In the test problems, $DMAX_{i, k,p, t} ,a_{i, k,p, t} ,$ and $b_{i, k,p, t}$ are generated as $DMAX_{i, k,p, t} \sim U\left( {500,1200} \right)$, $a_{i, k,p, t} \sim U\left( {140,150} \right)$, and $b_{i, k,p, t} \sim U\left( {190,200} \right)$, successively. Since a unique price for all customers is considered in the optimization problem to avoid cannibalization and arbitrage opportunity, the assumed price levels for all customers are the similar in each time period. Therefore, in each time period and for each product, the price level l is obtained as follows:

$$\begin{aligned} \hbox {PR}_{k, l, p, t}= & {} \frac{\sum \nolimits _{i\in C} {a_{i, k,p, t} } }{\left| C \right| }+\frac{\left( {l-1} \right) }{\left( {\left| L \right| -1} \right) }\left( {\frac{\sum \nolimits _{i\in C} {b_{i, k,p, t} } }{\left| C \right| }-\frac{\sum \nolimits _{i\in C} {a_{i, k,p, t} } }{\left| C \right| }} \right) \nonumber \\&\quad l\in L, k\in K, p\in P/\left\{ 0 \right\} , t\in T, \end{aligned}$$

(50)

In each time period, the customer product demand for every price level should be obtained using the corresponding price-response function. Figure 18 shows the levels of price and demand for customer i and product k in strategic period p and tactical period t.

Fig. 18

The levels of price and demand

Appendix 2

See Table 7.

Table 7 Parameters generation for test problems