Sustainable Procurement

Sourcing strategy for sustainable ATO: a mathematical approach

Due to price competition, many companies are manufacturing in low-cost countries and selecting such a location by considering manufacturing costs, corporate tax rate, export incentives, the presence of key suppliers or duty-free imports, infrastructure, the political situation and skilled labour. In ATO base product are expected to be manufactured at low-cost countries/locations and final configurations as well packaging are expected to be made at the distribution point near to the customer.

Stage-1: selection of supplier for the base product

In this proposed model, shown in Figure 1, we assumed that the base product is manufactured at the manufacturing site and stored at the centralized warehouse in generic form. Once order is arrived, base product is shipped with the bill of material (BOM), shown in Figure 2, to retailer's site where auxiliary part/module is prepared and assembled. In closed loop supply chain, shown in Figure 1, used products are collected from the collection site and sent to the disassemble site where products are disassembled completely or partly. After processing, disassembled parts/sub-assembly is sent to the manufacturer site where they are reused as new parts/sub-assembly. Disassembly cost varies with level of disassembly. Hence, up to a certain level product should be disassembled.

Figure 1 The proposed 2-stage supply chain model for sustainable ATO.

Figure 2 The bill of material. Source: Elaborated by the author.

In the proposed AHP model, shown in Figure 3, flexibility encompasses volume flexibility, routing flexibility, material handling flexibility, machine flexibility, operation flexibility, expansion flexibility, process flexibility. Proposed AHP model encompasses three main criteria to select suppliers for the base product through the sustainable procurement process.

Figure 3 The AHP model of supplier selection for the base product.

Deterministic order allocation model for the base product

The following assumptions are considered to prepare objective functions for supplier selection.

Assumptions

Multiple items are purchased from selected suppliers.
Quantity discounts are not taken into consideration.
No shortage of item is allowed for any supplier.
Demand of base product for the planned horizon is constant and known with certainty.

$C_{ij}$ = the purchase cost of product j from ith supplier.
$TC_{ij}$ = the transportation cost of product j from ith supplier.
$CC_i$ = the overall performance index of ith supplier.
$CO_{ij}$ = the ordering cost of jth product from ith supplier.
$α_i$ = the reliability of ith supplier.
$X_{ij}$ = the order quantity of product j to ith supplier.
$LD_{ij}$ = the percentage late delivery of product j from ith supplier.
$V_{ij}$ = the capacity of ith supplier for jth product.
$D_j$ = the demand for jth product
$H_j$ = the handling cost per ton of product j.
$B$ =Total allocated budget for all products.
$λ_j$ = percentage of jth product disposed at disposal site
$ξ_j$ = Level of disassembly of jth product at disassembly site
$β_i$ = GHG emission factor per weight unit distance due to the use of transportation mode.
$d_i$ = the distance of ith supplier from the manufacturing/retailing site
alpha = probability value of chance constraint
$i$ = 1,2,3……… n of suppliers
$j$ =1,2,3……. m no of products

The total cost of purchase (TCP) consists of purchase, transportation, order/setup, and holding cost.

Min TCP:

$\sum_{i=1}^{n} \sum_{j=1}^{m} C_{i j} X_{i j}+\sum_{i=1}^{n} \sum_{j=1}^{m} T C_{i j} X_{i j}+\sum_{j=1}^{m} H_{j} \sum_{i=1}^{n} X_{i}+\sum_{i=1}^{n} \sum_{j=1}^{m} C_{O i j} X_{i j}$

(11)

In the second objective function total value of reliable purchase (TVRP) is considered instead of total value of purchase (TVP) proposed by Ghodsypour & O'Brien (1998). The reliability of supply, $\alpha_i$ , of each supplier is obtained from supplier's reliability measurement data sheet, Table 2, to form TVRP equation.

Table 2 Supplier data sheet.

Name	Cost (INR)		Ordering Cost (INR/tonne)		Capacity (Tonne)		% late delivery	Distance (Km)	Mode of Transport
Name	Prod A	Prod B	Prod A	Prod B	Prod A	Prod B	% late delivery	Distance (Km)	Mode of Transport
Supp. 1	100	150	2000	3000	1000	2000	0.2	190	1. By HGV 2. 100 Km by rail and 90 Km by HGV
Supp. 2	102	149	2000	3000	1000	1500	0.15	200	1. By Large container
Supp. 3	101	150	2000	3000	1000	1500	0.2	180	1. By HGV
Supp. 4	100	151	2000	3000	1000	1500	0.15	200	1.160 Km by rail and 40 Km by HGV. 2. By HGV
Supp. 5	103	152	2000	3000	1000	1500	0.1	240	1.200 Km by rail and 40 Km by HGV.
Supp. 6	102	150	2000	3000	1000	2000	0.2	240	1. By HGV 2.200 Km by rail and 40 Km by HGV.

Maximize TVRP:

$\sum_{i=1}^{n} \sum_{j=1}^{m} \alpha_{i} C C_{i} X_{i j}$

(12)

Minimize number of late deliveries:

$\sum_{i=1}^{n} \sum_{j=1}^{m} LD_{i j} X_{i j}$

(13)

Minimize GHG emission for inbound logistics:

$\sum_{i=1}^{n} \beta_i d_i \sum_{j=1}^{m} X_{i j}$

(14)

Subject to

Capacity constraint:

$\sum_{j=1}^{m} \sum_{i=1}^{n} X_{i j} \leq \sum_{j=1}^{m} \sum_{i=1}^{n}$

$v_{i j }$ for

$i=1,2,3.........n$ and

$j=1,2,3….m$ (15)

Demand constraint:

$\sum_{j=1}^{m} \sum_{i=1}^{n} X_{i j}=\sum_{j=1}^{m} D_{j}-\sum_{j=1}^{m}\left(1-\lambda_{j}\right) \xi_{j} D_{j}$

(16)

Cost constraint:

$\sum_{j=1}^{m} \sum_{i=1}^{n} C_{i j} X_{i j} \leq B$

(17)

Non-negativity constraint:

$X_{ij} ≥ 0$ for

$i=1,2,3........n$ and

$j=1,2,3…m.$ (18)

Stage-II: supplier selection for auxiliary parts

Higher priority is given to flexibility and technical capability of suppliers to tackle high volatile demand at retailer's site. In this regard, an AHP model of supplier selection for auxiliary parts/sub-assembly is prepared, shown in Figure 4, to augment sustainable procurement process at retailer's site.

Figure 4 The AHP model of supplier selection for the auxiliary parts/sub-assembly.

Mathematical model for stochastic demand

A multi-objective stochastic model is considered at retailers' site to deal with uncertainty in demand. It is assumed that suppliers are very close to the retailer's site. Therefore, transportation cost as well GHG emission through transportation is very negligible.

Min TCP:

$\sum_{i=1}^{n} \sum_{j=1}^{m} C_{i j} X_{i j}+\sum_{j=1}^{m} H_{j} \sum_{i=1}^{n} X_{i}+\sum_{i=1}^{n} \sum_{j=1}^{m} C_{O i j} X_{i j}$

(19)

Maximize TVRP:

$\sum_{i=1}^{n} \sum_{j=1}^{m} \alpha _{i} CC_{i} X_{i j}$

(20)

Minimize number of late deliveries:

$\sum_{i=1}^{n} \sum_{j=1}^{m} LD _{iJ} X_{i j}$

(21)

Subject to

Demand constraint:

$Pr \left[\sum_{i=1}^{n} x_{i j} \geq D_{j}\right] \geq \text { alpha }$

(22)

Above chance constrained can be converted to a deterministic constraint as follows

$\sum_{i=1}^{n} \sum_{j=1}^{m} X_{i j} \geq u {j} + \Phi^{-1}(\text { alpha }) \sigma_j$

(23)

Where,

$\Phi(X)=\frac{1}{\sqrt{2 \pi} \sigma} \int_{-\infty}^{X} e^{-\frac{(X-u)^{2}}{2 \sigma^{2}}} d X=\operatorname{alph} a, \Phi^{-1}(\text { alpha })=X$

(24)

Capacity constraint:

$\sum_{j=1}^{m} \sum_{i=1}^{n} X_{i j} \leq \sum_{j=1}^{m} \sum_{i=1}^{n} v_{i j }$

(25)

Cost constraint:

$\sum_{j=1}^{m} \sum_{i=1}^{n} C_{i j} X_{i j} \leq B$

(26)

Non-negativity constraint:

$X_{ij} ≥ 0$ for

$i=1,2,3........n$ and

$j=1,2,3…m$ (27)