Analysis of Current Practice

In the current practice of IT industries, the third-party players cooperated with manufacturers are usually authorized by those manufacturers for collection work. We use the Dell’s recycling system in the Europe which simply shows the concept of third-party player collection to represent the current practice model as shown in Figure 2.

Figure 2: Current Recycling System Manufacturer

A (collection service fee) (profits of handling)

ψ =Fτ

Reverse Flow Forward Flow

Contract Relationship

In this model, we assume that the third-party player decides the products return rate, τ , the retailer decides the retail price, p, in the market, and the manufacturer decides the wholesale prices, w . The contract is provided by the manufacturer to the third-party player, so the contract variable, F, is a decision variable of the manufacturer. Other notations in Figure 2 are the same as described in Section 4.1. We denote Π^C_i as a profit function for member i in the current recycling system, where subscript i takes value M, R, or 3P, which denotes the manufacturer, the retailer, or the third-party player, respectively. Therefore, the profit functions of the manufacturer, the retailer, and the third-party player are

( - )( - ) ( )

The sequence of decision-making of associated players is depicted in Figure 3. After observing the unit manufacturing cost, the manufacturer determines the wholesale price, w , and the contract variable, F . Then the retailer decides the retail price, p, and the third-party player determines the return rate, τ, simultaneously based on the wholesale price and the contract information revealed by the manufacturer.

Figure 3: The Timeline of the Current Recycling Model

STAGE 1 STAGE 2

PLANNING HORIZON Manufacturer determines contract

variable, F, and wholesale price, w.

Retailer determines retail price, p, and third-party player decides

return rate, τ.

Manufacturer observes unit cost, c.

Contract variable and wholesale price are revealed to retailer and

third-party player.

Market clears.

In practice, the manufacturer who is the first mover in decision timeline has sufficient bargaining power to act as a Stackelberg leader. When making decisions, the manufacturer considers the retailer’s and the third-party player’s best responses to its decisions. The retailer and the third-party player, making decision after observing the manufacturer’s decision, act as followers in the model. We solve this two-stage sequential game by using backward induction moving from the second stage, retailer and third-party player’s decisions, to manufacturer’s decision problem in the first stage.

Step 1. The retailer’s decision in the second stage:

The retailer maximizes its profits from selling new products as shown in (4.4).

Max ( - )( - )^C_R

first-order conditions hold. From the first-order conditions, the retailer sets the retail price as

*

2 p φ+w

= . (4.5)

Step 2. The third-party player’s decision in the second stage:

The profits of the third-party player are the income from those recycling services and the contract minus the collection effort as shown in (4.6).

* 2

Max ( -3^C_P A p ) F -C_L

τ Π = τ φ + τ τ (4.6)

From the second-order conditions, we have

2 By using the first-order conditions to derive the best response to the return rate, it gives

( - *)

2 _L 2 _L

A p F

C C

τ = φ + . (4.7)

For any value of p, the third-party player determines the return rate as above. In Stage 2, the retailer or the third-party player solves its problem simultaneously. Then we substitute (4.5), the optimal retail price, into (4.7) to obtain the optimal return rate as follows:

* ( - ) that the optimal return rate, τ^*, is bounded between zero and one, we impose the condition of

3

Assumption 1 The parameter, C , defined in the collection effort is assumed to be _L

sufficiently large such that τ^*<1, i.e., 16C_L >(b A+ )²+(φ+c b A)( + ). Step 3. The manufacturer’s decision in the first stage:

The manufacturer solves the problem to maximize its total profit which is the sum of the revenue from selling new products and those recycled hardware minus the cost on the contract relationship with the third-party player.

* * * *

Max ( -, ^C_M )( - ) ( - )

-w F Π = φ p w c +bτ φ p Fτ (4.9)

When making the decision, the manufacturer would consider the retailer’s and the third-party player’s best responses to its decisions. Substituting (4.5) and (4.8) into the manufacturer’s profit function, we have

,

To ensure Π^C_M is concave in w and F , the Hessian Matrix of (4.10),

, must be negative semidefinite. Then it should satisfy the conditions,

-1 0

maximized when first-order conditions hold. We take the partial derivative of Π^C_M with respect to w and F as shown below:

From the first-order conditions, the manufacturer decides the wholesale price w and the contract variable F as follows:

* 2 ( - ) *( - )

Solving the two equations for two unknown variables, the final results of w and F, which simultaneously satisfy the first-order conditions, are

*

Substituting the optimal wholesale price w^* and the contact variable F in (4.10), the ^* manufacturer’s profits are given by

2

The optimal unit market price and return rate can be obtained by substituting the w^* and F into (4.5) and (4.8). The total profits of the current practice model can be easily ^* found by summing up profits of the manufacturer, the retailer, and the third-party player.

However, a closed-loop channel with collection in retailers is the most efficient model in Savaskan et al. (2004). Savaskan et al. (2004) investigate the recycling systems with products remanufacturing. In the retailer collection model, the retailer collects those returned products and sells them back to the manufacturer for remanufacturing processes.

We integrate this concept of collection in retailers into the current practices. Then, we develop a model where the retailer engages in returned products collection to improve the current practice. In this retailer collection model, the retailer collects those obsolete products returned by customers. The manufacturer cooperates with a third-party firm to handle those recycled products which are collected by the retailer. We analyze the retailer collection model in the next section.