An optimization model of supplier selection and order allocation with transportation mode alternatives under carbon cap and trade policy

Abstract

This research develops an optimization model of supplier selection and order allocation with transportation mode alternatives under carbon cap and trade policy. The objective function of the model is to maximize the manufacturer’s total profit. Total revenue comes from the selling of both good items and imperfect items. Total cost in this research consists of purchase cost, transportation costs from supplier to manufacturer and from manufacturer to retailer, transaction cost, holding cost, inspection cost and carbon emission cost. Transaction cost is applied for each selected supplier in each period without considering the type and quantity of the item. This research considers a supply chain with multiproducts, multiperiods, multisuppliers and multiretailers. We assumed that the manufacturer inspects all the products come from the suppliers and some of the products are defective. Those defect items are sold in a lower price at a secondary market. This research has a contribution in the inclusions of carbon emission and defect product in the model. Hence, the model is in line with the sustainability issue and closer to the real condition in terms of imperfect manufacturing. A mixed integer linier programming (MILP) model is developed in this research, and the model was solved using Lingo 15.0 software with branch and bound method. The result of sensitivity analysis shows that the objective function is sensitive to the changes of demand, selling price of good item, transportation cost, purchasing cost and holding cost. While the decision variables of order allocation and the number of transportation mode are sensitive to the changes of demand, transportation cost and purchasing cost.

Keywords:

• Supplier selection
• order allocation
• imperfect quality
• transportation mode alternatives
• carbon cap and trade

REVIEW EDITOR:

• Pratama Danang Miftahudin
• Alumni of Universitas Sebelas Maret, Industrial Engineering, Universitas Sebelas Maret, Jalan Ir. Sutami 36 A, Surakarta, Jawa Tengah 57126, Indonesia

SUBJECTS:

• Engineering & Technology
• Industrial Engineering & Manufacturing
• Operations Research
• Production Systems
• Production Engineering
• Operations Research

1. Introduction

Supply Chain Management (SCM) has been recognized as an effective tool and strategy to improve company’s business performance. According to a research by Parilla (2020), from 258 companies under investigations, more than 70% of them got 26%–75% profit margin by adopting effective SCM. Another study by Lee (2021) revealed that SCM strategies and organizational competencies has a significant effect on the operational and financial performance of the companies under research. With the pressures of globalization and intense competition, manufacturing companies have to make continuous improvements to increase their competitive advantage over their competitors. In addition to policies regarding global sourcing, supplier selection and order allocation (SSOA) are very important and complex decisions (Basa et al., 2018). Hence, it gets a great attention in various business and management literature (Rezaei & Davoodi, 2007). According to Ebrahim et al. (2009), the purpose of supplier selection is to determine the best combination of suppliers that can provide the best goods or services for the company and be part of important decisions in the company’s supply chain.

An effective supplier selection strategy will directly impact supply chain performance in terms of productivity and profitability. A study by Ekiyor et al. (2019) showed that supplier selection criteria had a positive effect on company profitability of about 49%. While in the study of Van der and Ntshingila (2020), supplier selection and development had a positive impact on company business performance. There are two types of supplier selection problems, namely single sourcing and multisourcing. In single sourcing, the supplier can meet all the demands of the manufacturer, whereas in the case of multisourcing, no single supplier can fulfill the demand as required by the manufacturer. In this case, the manufacturer has to make decisions in supplier selection and the respective order allocation (Ghodsypour & O’Brien, 1998).

Many researches have been conducted in the field of SSOA. Commonly, due to the nature of the problems, supplier selection involved multicriteria decision making using various multicriteria decision techniques. While the order allocation decision is solved using both linear and nonlinear mathematical programming. Environmental impact and disruption risks have become the major concern in SSOA and become the important aspects in supply chain decision makings. In terms of environmental impact, one of the quantitative measures commonly used in supply chain is the carbon emissions. According to the data from International Energy Agency, transportation sector consumed of about 29% of energy and shared about 25% of the total carbon emissions and 20% of global gas house emission (Jiang et al., 2024; Wang et al., 2023). Hence, both transportation cost and its impact on environment should be considered in SSOA.

SSOA has been recognized as complex and challenging task. Despite of many models have been developed in the area of SSOA, few attempts have been made to provide a mathematical model to address the existence of alternative carriers in raw materials and finished goods delivery as well as product defects under carbon cap and trade policy. The rest of the article is structured as follows. Section 2 provides a review of the related literature. Section 3 provides the system description. Section 4 focuses on model development and detail explanation of the objective function and constraints of the model. Section 5 provides the numerical example to show the model application. Section 6 provides the results and discussion including the sensitivity analysis of the model. Section 7 concludes the research and gives some directions for further research.

2. Literature review

There is many research that have been conducted to solve SSOA problems. Basnet and Leung (2005) developed a supplier selection model and determined the optimal lot size to meet the demand of raw materials using a basic model developed by Wagner and Whitin (1958). Benson (2005) proposed supplier capacity limit by considering multi-supplier supply chain to determine the optimal procurement strategy. Mohammed et al. (2018) developed a model to solve SSOA problems in two separate stages. In the first stage, supplier selection was solved using Fuzzy Analytic Hierarchy Process (FAHP) and Fuzzy TOPSIS (FTOPSIS). In the second stage, order allocation problem was solved using multiobjective optimization involving several objective functions in terms of cost, carbon emission and total value purchasing. The final solution was obtained using TOPSIS based on the results of nondominated solution of the model. Gören (2018) developed a sustainable SSOA model. He employed Fuzzy Decision-Making Trial and Evaluation Laboratory (FDEMATEL) was employed to determine the weight of the sustainable criteria. The weight was then used as the input for the Taguchi loss function to determine the rank of each supplier. Finally, the results became the input for bi-objective integer linear programming optimization model to determine the optimal order allocation. Mohammed et al. (2019) also employed FAHP and FTOPSIS to determine the criteria weight of the suppliers and the order allocation problem was solved using $\epsilon$ constraints approach.

Environmental impact and disruption risks have become the major concerned and the important aspects in supply chain decision makings. Hence, some researchers developed models to determine the environmental impact of order allocation decisions and the impact of disruptive events on supply chain decisions. In terms of environmental impact, one of the quantitative measures commonly used in supply chain is the carbon emissions. Lamba and Singh (2019) and Lamba et al. (2019) developed models to study several policies regarding the implementation of carbon emission costs. Three policies were studied, namely cap and trade, strict cap and carbon tax policies. Feng and Gong (2020) proposed linguistic entropy weight method to select several qualified green suppliers and employed multiobjective programming to determine the order allocation. The model considered multiproduct and multiperiod allocation problem to simultaneously minimize several objectives consisting costs, energy consumption and carbon emission. In terms of disruption, Hosseini et al. (2019) developed an SSOA model considering the supplier resiliencies. The model simultaneously considered additional supplier capacity, supplier reliability, back-up suppliers and geographic segregation. Moreover, Kaur and Singh (2021) proposed a model considering not only traditional disruption risks, but also disruptive technology.

According to Chopra and Meindl (2007), transportation becomes one of the important aspects in supply chain. Hence, transportation cost and its impact on environment should be considered in the SSOA. In many studies, the transportation cost has been included in the total cost of supply chain (Mendoza & Ventura, 2009). The inclusion of transportation cost in the SSOA will further improve supply chain efficiency. Blumenfeld et al. (1985) discussed the need to analyze the relationship between supply chain and transportation cost. The objective of the model is to minimize the total inventory and routing costs simultaneously in determining the optimal route and shipping size of the vehicles used as the carriers. The simultaneous determination of supplier selection, order allocation and carrier selection can help to avoid the suboptimal solutions that might result from completing three separate decisions. Dullaert et al. (2005) considered a combinatorial optimization method to determine the optimal outcome of a mixed alternative modes of transportation to minimize the total logistics costs when goods are shipped from suppliers to customers. The total logistics costs included ordering costs, transportation costs and inventory costs. Pazhani et al. (2015) developed a model for the selection of suppliers and supplies at multiple levels in the supply chain by considering purchasing costs, setup costs, storage costs and transportation costs. Chan et al. (2015) developed a bi-objective model for three echelon supply chains by taking into consideration the decision of carrier selection. Further, Wicaksono et al. (2019) considered dynamic supplier in their model to allow for the raw materials to be provided by different supplier at each period.

Filcek and Józefczyk (2012) considered a model consisting of suppliers, production and retailers to determine optimal raw material allocation and transportation. Basa et al. (2018) developed a multisource problem model for one item involving lot sizing, order allocation and carrier selection decisions by considering quantity discounts. The model involved storage costs, ordering costs, transportation costs and goods prices with several constraints including waiting time, supplier capacity and truck capacity. Hu et al. (2018) developed an integrated model of SSOA to determine optimal supplier’s configuration and its order allocation, as well as selecting the appropriate logistics service providers. Yaghin and Darvishi (2020) developed an order allocation and transportation planning model under uncertainty in apparel industry environment. The model considered multisources, multiproducts and multicarriers with price discount to minimize total logistic cost, late delivery and value purchasing. Heinold and Meisel (2020) developed an intermodal freight transportation planning model considering emission limits and allocation. Two transportation modes were considered, namely road and railway transportation services. A bi-objective optimization model was developed by Sobhanolahi et al. (2020) to solve SSOA problem. The model involved single product sold with discounts considering transportation cost and solved using nondominated sorting genetic algorithm (NSGA II). Similar to Sobhanolahi et al. (2020), the research of Abrishami et al. (2020) developed a model to solve SSOA problem for multi raw materials sold with discount to minimize total cost including transportation cost. Using the same objective function to minimize total cost, the research of Ghorbani and Ramezanian (2020) included carrier selection and transportation cost to solve SSOA in humanitarian logistics.

In a production environment, it is often found that not all products are of good quality. Some of them are defective products which cannot be sold directly to consumers. They have to be repaired or reworked according to the conditions of the products. A considerable cost should be expensed by the company to withdraw the products which has reached the consumer. Hence, it is more appropriate to consider quality-related costs in determining the optimal ordering policy. Rezaei and Davoodi (2007) developed a supplier selection model taking into account the imperfect quality of goods and storage capacity. Salameh and Jaber (2000) argued that products that are not perfect or below the specified quality standards are not always a defective product. However, it can be used in certain conditions with a lower level of quality standards. A total inspection can be carried out to determine the good quality items and the imperfect ones.

Table 1 shows the summary of literature review and the relative position of this research. From the table, this article contributes to the inclusions of defect, transportation mode selection and its corresponding cost under carbon cap and trade policy. Hence, an SSOA model is developed for a three echelon supply chain environment consisting of suppliers, manufacturers and retailers. The model considers the existing of several choices of suppliers with one manufacturer to meet the demands of several retailers. The manufacturer will order a certain number of each type of raw materials from suppliers who produce the materials. The manufacturer then transforms the raw materials into final products to meet the retailers’ demand. The model involves transportation modes selection to deliver raw materials from suppliers to the manufacturer and from manufacturer to retailers under carbon cap and trade policy. A mixed integer linear programming (MILP) model is proposed in this research to solve the problem.

Table 1. Literature review.

Study	Objective function		Price		Product		Transportation		Defect	Carbon policy
	Single	Multi	Normal	Discount	Single	Multi	Selection	Cost
Basnet and Leung	–	∗	∗	–	–	∗	–	–	–	–
Basa et al.	∗	–	–	∗	∗	–	–	∗	–	–
Rezaei and Davoodi	–	∗	∗	–	–	∗	–	–	∗	–
Ebrahim et al.	–	∗	–	∗	∗	–	–	–	∗	–
Ghadsypour and O’Brien	∗	–	∗	–	∗	–	–	–	∗	–
Mohammed et al. (2018)	–	∗	∗	–	∗	–	–	–	–	∗
Gören (2018)	–	∗	∗	–	–	∗	–	–	∗	–
Mohammed et al. (2019)	–	∗	∗	–	∗	–	–	∗	–	∗
Lamba and Singh (2019)	–	∗	∗	–	–	∗	–	∗	–	∗
Lamba et al. (2019)	–	∗	∗	–	–	∗	–	∗	–	∗
Feng and Gong (2020)	–	∗	∗	–	–	∗	–	–	–	∗
Hosseini et al. (2019)	–	∗	∗	–	∗	–	–	–	–	–
Kaur and Singh (2021)	∗	–	∗	–	∗	–	–	∗	–	–
Chopra and Meindl (2007)	∗	–	∗	–	∗	–	–	∗	–	–
Pazhani et al. (2015)	∗	–	∗	–	∗	–	∗	∗	–	–
Chan et al. (2015)	–	∗	∗	–	–	∗	∗	∗	–	–
Wicaksono et al. (2019)	∗	–	∗	–	–	∗	∗	∗	∗	–
Filcek and Józefczyk (2012)	∗	–	∗	–	∗	–	–	∗	–	–
Hu et al. (2018)	∗	–	∗	–	∗	–	–	∗	–	–
Yaghin and Darvishi (2020)	–	∗	–	∗	–	∗	∗	∗	–	–
Sobhanolahi et al. (2020)	–	∗	–	∗	∗	–	–	∗	–	–
Abrishami et al. (2020)	∗	–	–	∗	–	∗	∗	∗	–	–
Ghorbani and Ramezanian (2020)	∗	–	∗	–	∗	–	∗	∗	–	–
This study	∗	–	∗	–	–	∗	∗	∗	∗	∗

3. System description

We consider a supply chain consisting of multisupplier, single manufacturer and multiretailer. The supply chain planning involves multiproducts, multiperiods and multitransportation modes. A certain number of suppliers is available to supply the required products. Each supplier may provide more than one product, and each product may be provided by more than one supplier. Hence, the manufacturer has to select a subset of suppliers from the set of available suppliers. After selecting the suppliers, the manufacturer has to determine the optimal order allocation of each product to the selected suppliers. Afterward, the manufacturer will make the inspections for the incoming products. The good products will be sold in normal price, while the defect products will be sold in a lower price at a secondary market. Finally, the final products are then used to fulfill the demand of retailers. Several carriers are available to deliver the products from the suppliers to manufacturer and from manufacturer to the retailers. Figure 1 depicts the description of the general system, while Figure 2 shows the more detail description of the system.

Figure 1. System under consideration.

Figure 2. Detail system description.

The manufacturer needs to maximize the total profit which is obtained by subtracting the total revenues from the total cost. The total costs considered by the manufacturer consist of the cost of purchasing the product, the cost of transportation from supplier to manufacturer and from manufacturer to retailer, transaction costs, storage costs, costs of quality inspection and carbon emission costs. The carbon emission costs come from the activities of transportations, product orders and storage.

4. Model development

4.1. Assumptions

The following assumptions are used in the development of the model:

1. Transaction cost is independent of the types and quantities of the products.

2. Demands of product i in period t for all of retailer (DR) are known over a planning horizon.

3. Shortage and backorder are not allowed.

4.2. Notations of the model

4.2.1. Index

I: index for product (i = 1, 2, …, I)

j: index for supplier (j = 1, 2, …, J)

p: index for retailer (p = 1, 2, …, P)

r: index for carrier (r = 1, 2, …, R)

t: index for time period (t = 1, 2, …, T)

4.2.2. Decision variables

$$\mathit{\text{Zj}},t:\{\begin{array}{l}1,\mathit{\text{\hspace{0.5em}if supplier j is selected in period}} t \\ 0,\mathit{\text{\hspace{0.5em}otherwise}} \end{array}$$

X_i,j,t,r: order quantity for product i from supplier j in period t with carrier r.

Inv_i,t: inventory of product i in period t.

Num_j,t,r: the number of carrier r to deliver from supplier j in period t.

Numwr_p,t: the number carrier to deliver to retailer p in period t.

4.2.3. Parameters

Sg_i: unit selling price of good quality of product i

Sd_i : unit selling price of defect product i

H_i: unit holding cost of product i

V_i: unit inspection cost of product i

O_j: unit transaction cost of supplier j

TCwr_p: unit transportation cost from manufacture to retailer p

Eo_t: unit carbon emission of placing an order in period t

Eh_t: unit carbon emission of holding a unit product in inventory at period t

Ev_t: unit variable carbon emission in each order at period t

Cc_r: unit capacity of carrier r

maxnum_r: available units of carrier r

PR_ij: average percentage of defective product i from supplier j

UP_ij: unit price of product i from supplier j

SC_ij: capacity of product i at supplier j

D_it: demand accumulation of product i at period t for all retailer

TC_jr: unit transportation cost of carrier r from supplier j

DR_ipt: demand for product i from retailer p at period t

W: manufacturer storage capacity

C: carbon cap during the planning horizon

4.3. Objective functions and constraints of the model

With the above parameters and decision variables, the MILP model is expressed as follows: (1) $$\mathrm{\text{Maximize}}\mathrm{ }Z=Z_1+Z_2-Z_3-Z_4-Z_5-Z_6-Z_7-Z_8-Z_9$$(1) where (1a) $$Z_1=\sum _i\sum _j\sum _t\sum _r{X}_{\mathit{\text{ijtr}}}\times \left(1-{\text{PR}}_{\mathit{\text{ij}}}\right){\times \text{Sg}}_i$$(1a) (1b) $$Z_2=\sum _i\sum _j\sum _t\sum _r{X}_{\mathit{\text{ijtr}}}{\times \text{PR}}_{\mathit{\text{ij}}}\times {\text{Sd}}_i$$(1b) (1c) $$Z_3=\sum _i\sum _j\sum _t\sum _r{X}_{\mathit{\text{ijtr}}}{\times \text{UP}}_{\mathit{\text{ij}}}$$(1c) (1d) $$Z_4=\sum _j\sum _t\sum _r{\text{num}}_{\mathit{\text{jtr}}}\times {\text{TC}}_{\mathit{\text{jr}}}$$(1d) (1e) $$Z_5=\sum _p\sum _t{\text{numwr}}_{\mathit{\text{pt}}}\times {\text{TCwr}}_p$$(1e) (1f) $$Z_6=\sum _j\sum _t{O}_j\times Z_{\mathit{\text{jt}}}$$(1f) (1g) $$Z_7=\sum _i\sum _t{H}_i\left(\sum _j\sum _t\sum _r{X}_{\mathit{\text{ijtr}}}\times \left(1-{\text{PR}}_{\mathit{\text{ij}}}\right)-\sum _{k=1}^t{D}_{\mathit{\text{ik}}}\right)$$(1g) (1h) $$Z_8=\sum _i\sum _j\sum _t\sum _r{X}_{\mathit{\text{ijtr}}}{\times V}_i$$(1h) (1i) $$Z_9=\sum _t\mathit{\text{Cp}}\times \left(\mathit{\text{Ep}}-\mathit{\text{Em}}\right)$$(1i)

Equation (1)(1) $$\mathrm{\text{Maximize}}\mathrm{ }Z=Z_1+Z_2-Z_3-Z_4-Z_5-Z_6-Z_7-Z_8-Z_9$$(1) is the objective function of the MILP model with the aim of maximizing the total profit which consists of nine parts. Equations (1a)(1a) $$Z_1=\sum _i\sum _j\sum _t\sum _r{X}_{\mathit{\text{ijtr}}}\times \left(1-{\text{PR}}_{\mathit{\text{ij}}}\right){\times \text{Sg}}_i$$(1a) and (1b)(1b) $$Z_2=\sum _i\sum _j\sum _t\sum _r{X}_{\mathit{\text{ijtr}}}{\times \text{PR}}_{\mathit{\text{ij}}}\times {\text{Sd}}_i$$(1b) express the revenue comes from selling good quality products and defect products, respectively. Equation (1c)(1c) $$Z_3=\sum _i\sum _j\sum _t\sum _r{X}_{\mathit{\text{ijtr}}}{\times \text{UP}}_{\mathit{\text{ij}}}$$(1c) is the formulation of purchase cost, Equations (1d)(1d) $$Z_4=\sum _j\sum _t\sum _r{\text{num}}_{\mathit{\text{jtr}}}\times {\text{TC}}_{\mathit{\text{jr}}}$$(1d) and (1e)(1e) $$Z_5=\sum _p\sum _t{\text{numwr}}_{\mathit{\text{pt}}}\times {\text{TCwr}}_p$$(1e) show, respectively, the cost of transportation from suppliers to the manufacturer and from the manufacturer to retailers. Equations (1f)–(1i) express, respectively, the transaction cost, holding cost, inspection cost and carbon emissions cost.

The following constraints are imposed to the model:

1. Demand fulfillment: Because shortage is not allowed in this model, the number of orders for each type of product to suppliers for each period cannot be less than the number of each type of product ordered by the retailer for each period. (2) $$\sum _j\sum _{k=1}^t\sum _r{X}_{\mathit{\text{ijkr}}}\times \left(1-{\text{PR}}_{\mathit{\text{ij}}}\right)-\sum _{k=1}^t{D}_{\mathit{\text{ik}}}\ge 0$$(2)

2. There is a transaction cost for each selected supplier. This transaction cost does not consider the number of products ordered or the type of product ordered at the supplier. (3) $$\left(\sum _{k=1}^t{D}_{\mathit{\text{ik}}}\right)\times Z_{\mathit{\text{jt}}}-X_{\mathit{\text{ijtr}}}\times \left(1-{\text{PR}}_{\mathit{\text{ij}}}\right)\ge 0$$(3)

3. Storage capacity: Because every product of imperfect quality is assumed to always be bought from outside the system, the only products stored in the warehouse are of good quality. (4) $$\sum _i\sum _j\sum _{k=1}^t\sum _r{X}_{\mathit{\text{ijkr}}}\times \left(1-{\text{PR}}_{\mathit{\text{ij}}}\right)-\sum _i\sum _{k=1}^t{D}_{\mathit{\text{ik}}}\le W$$(4)

4. Capacity of transportation mode from supplier to manufacture. The number of all products ordered does not exceed the total capacity of each type of transportation multiplied by the number of units available. (5) $$\sum _i{X}_{\mathit{\text{ijtr}}}\le {\text{Cc}}_r\times {\text{maxnum}}_r$$(5)

5. Capacity of transportation mode from manufacturer to retailer. The number of demands received does not exceed the total transportation capacity multiplied by the number of units available. (6) $$\sum _i{\text{DR}}_{\mathit{\text{ipt}}}\le \text{Ccwr}\times \text{maxnumwr}$$(6)

6. Supplier capacity: The number of products ordered to suppliers for each type does not exceed the supplier’s capacity to produce that type of product. (7) $$\sum _r{X}_{\mathit{\text{ijtr}}}\le {\text{SC}}_{\mathit{\text{ij}}}$$(7)

7. Carbon emission constraint: The amount of carbon emitted plus the amount of carbon sold must equal the allowable carbon limit plus the amount of carbon purchased. $$\sum _j\sum _t{\text{Eo}}_t\times Z_{\mathit{\text{jt}}}+\sum _i\sum _t{\text{Eh}}_t\times {\mathit{\text{Inv}}}_{\mathit{\text{it}}}+\sum _i\sum _j\sum _t\sum _r{X}_{\mathit{\text{ijtr}}}\times {\mathit{\text{Ev}}}_t+\mathit{\text{CFT}}\times$$ (8) $$\sum _j\sum _t\sum _r{\mathit{\text{num}}}_{\mathit{\text{jtr}}}+\mathit{\text{Em}}=C+\mathit{\text{Ep}}$$(8)

8. Demand accumulation for each product in t period for all retailer. (9) $$D_{\mathit{\text{it}}}=\sum _p{\text{DR}}_{\mathit{\text{ipt}}}$$(9)

9. The number of transportation mode that used to deliver from supplier to manufacture. (10) $${\text{num}}_{\mathit{\text{jtr}}}=\sum _i{X}_{\mathit{\text{ijtr}}\mathrm{ }}÷{\text{Cc}}_r$$(10)

10. The number of transportation mode that used to deliver from manufacture to retailer. (11) $${\text{numwr}}_{\mathit{\text{pt}}}=\sum _i{\text{DR}}_{\mathit{\text{ipt}}\mathrm{ }}÷\text{Ccwr}$$(11)

11. Non-negative and integer constraints (12) $${\text{num}}_{\mathit{\text{jtr}}},{\text{numwr}}_{\mathit{\text{pt}}}\ge 0$$(12)

12. Binary variables constraint (13) $$Z_{\mathit{\text{jt}}}\in \left\{\mathrm{0,1}\right\}$$(13)

5. Numerical example

In this section, we present a numerical example with the purpose to show how the proposed model works. We consider three products, four suppliers, four retailers and three carriers alternative over six periods of planning horizon. The input parameter was generated randomly and set in such a way to satisfy all the constraints of the model. Table 2 shows the demand from the retailers in six consecutive periods. Table 3 shows the parameters for each supplier in terms of unit price, transaction cost, capacity and defect percentage of each product at each supplier. Table 4 shows the carrier parameters to deliver the products from supplier to the manufacturer and the maximum number and capacity of each carrier. The transportation cost from manufacturer to each retailer is assumed to be $4000, $4200, $4900 and $4550, respectively.

Table 2. Retailer demand.

Product	Retailer	Period
		1	2	3	4	5	6
1	1	205	176	175	200	190	245
	2	230	210	175	214	180	235
	3	191	170	175	220	195	229
	4	200	160	180	210	210	225
2	1	195	210	165	215	200	210
	2	195	220	165	210	200	215
	3	195	205	155	215	200	215
	4	195	222	176	210	202	210
3	1	186	195	215	216	230	169
	2	176	205	220	185	220	220
	3	171	181	230	210	213	180
	4	166	155	222	195	230	210

Table 3. Parameters of the suppliers.

Product	Supplier	Unit price ($)	Transaction cost ($)	Capacity (units)	Imperfect quality (%)
1	S1	31	350	600	6
	S2	32	300	1000	6
	S3	35	375	500	2
	S4	32	325	800	1
2	S1	28	350	1000	9
	S2	24	300	700	5
	S3	27	375	500	1
	S4	26	325	800	2
3	S1	33	350	1200	7
	S2	32	300	600	5
	S3	31	375	500	2
	S4	31	325	1000	9

Table 4. Carrier parameters.

Parameters	Supplier	Carrier
		1	2	3
Delivery cost	S1	5500	4000	3275
	S2	6000	4200	4125
	S3	6000	4900	3025
	S4	6500	4550	4125
Maximum number		2	2	5
Capacity		1000	700	550

The selling price of each product both good quality and defect product, unit holding cost and unit inspection cost are shown in Table 5. Table 6 shows the carbon emission parameters in each period. The carbon emissions come from placing an order, holding the inventory and transportation are assumed to be the same in each period with the values of 100, 3 and 0.1, respectively. The carbon emission cap is set at 35,850.

Table 5. Price and cost parameters for each final product.

Parameters	Product
	1	2	3
Good quality product price	50	34	60
Imperfect product price	20	25	40
Unit holding cost	5	3.5	8
Unit inspection cost	2	1.5	1.8

Table 6. The results of optimization.

Product	Supplier	T1			T2			T3			T4			T5			T6
		R1	R2	R3	R1	R2	R3	R1	R2	R3	R1	R2	R3	R1	R2	R3	R1	R2	R3
1	1	0	600	0	0	600	0	0	600	0	0	600	0	0	600	0	0	600	0
	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
	3	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
	4	162	468	0	0	0	0	0	0	0	400	399	0	0	0	0	0	0	0
2	1	0	100	0	0	65	0	0	0	0	0	0	0	0	0	0	0	0	0
	2	0	700	0	0	700	0	0	700	0	0	700	0	0	700	0	0	700	0
	3	0	0	50	0	0	50	0	0	50	0	0	50	0	0	50	0	0	50
	4	69	0	0	0	0	0	0	0	0	0	300	0	0	0	0	0	0	0
3	1	0	0	0	0	340	0	0	100	0	0	100	0	0	100	0	0	100	0
	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
	3	0	0	500	0	0	500	0	0	500	0	0	500	0	0	500	0	0	500
	4	768	231	0	0	0	0	0	0	0	200	399	0	0	0	0	0	0	0

6. Results and discussion

LINGO 15.0 software with the embedded branch and bound algorithm was selected to solve the model. Under a standard computer specification with Intel Core i3 and 4 GB of RAM, the optimal results were found after 41,127 iterations in 18.68 s. Table 6 shows the optimal results of the model. The table shows the selected supplier for each product, along with the order allocation and the selected carrier at each period. For example, in period 1, product 1 is supplied by supplier 1 and supplier 4 using carriers 1 and 2. For product 2, orders in period 1 are supplied by all suppliers with different transportation modes. With this optimal decision, the manufacturer get the total profit of $181,305. The entries in Table 7 shows the inventory of good quality product over six planning periods. From the table, we conclude that there are no shortages for each product demand in each period and no inventory exists in the last period.

Table 7. Inventory of good quality product.

Product	Period
	1	2	3	4	5	6
1	362	210	69	581	370	0
2	93	10	64	223	135	0
3	701	487	183	506	196	0

Sensitivity analysis is performed to determine how the model responds to the changes of the input parameters. The sensitivity analysis scenario conducted in this research involves of the changes in demand (D_it), the selling price of good and defect products (Sg_i and Sd_i), transportation costs (TC_jr), product purchase prices (UP_ij), holding costs (H_i) and transaction costs (O_j). Table 8 shows the results of sensitivity analysis. The table shows the changes in the objective function when the parameters change according to the developed scenarios. From the table, we can see that the most sensitive parameter is the price of good quality product, followed by unit purchasing price, demand, unit holding cost and unit transportation cost. While the selling price of defect product and transaction cost are not sensitive to the profit of the manufacturer.

Table 8. The results of sensitivity analysis.

Scenario	Parameters
	Dit	Sgi	Sdi	TCjr	UPij	Hi	Oj
+30%	28.52%	113%	3.37%	−14.73%	−70.9%	−31.45%	−1.12%
+20%	18.97%	76.8%	2.06%	−9.86%	−46.82%	−21.18%	−0.75%
+10%	9.6%	37.01%	1.16%	−5.11%	−22.54%	−10.26%	−0.45%
0%	–	–	–	–	–	–	–
−10%	−9.47%	−37.06%	0.96%	5.23%	22.66%	10.91%	0.37%
−20%	−19.55%	−76.8%	2%	10.20%	47.87%	21.18%	0.75%
−30%	−29.53%	−113%	2.9%	15.43%	72.40%	32.10%	1.12%

Although the model was solved in short computational time, the solving duration will be much more longer when the problem becomes more complex and larger. The addition of products, periods, suppliers and carrier alternatives will significantly increase the computational time. Chen and Tan (2023) divide the optimization problems into two categories, namely Type S and Type R. Type R problems were considered to be more complex as the decision variables have strong dependencies, while for Type S problem, the decision variables were fully independent. The implementation of metaheuristic algorithms will increase the computational efficiency. Many metaheuristic algorithms have been proposed in the literature to solve large and complex problems through single metaheuristic algorithm or hybridization. Several metaheuristic algorithms have been used to solve large and complex problems such as nondominated sorting genetic algorithm, simulated annealing, tabu search and variable neighborhood search. Several new metaheuristic algorithms have been proposed such as self-adaptive fast fireworks algorithm, adaptive polypoid memetic algorithm (Chen & Tan, 2023; Dulebenets, 2021, 2023). Based on the research of Pasha et al. (2022), the hybrid version of those metaheuristic algorithms consistently outperformed their nonhybridized versions. Hence, for future research, it is interesting to determine the performance of the hybrid version of the above algorithms to solve the larger and more complex version of the developed model in this research.

7. Conclusions

In this research, we developed a MILP model for SSOA with carrier selection by considering defect product, carbon emissions and the capacity of each supplier to maximize total profits. The results of the sensitivity analysis show that the objective function is sensitive to the changes of demand parameters, good product selling prices, transportation costs, product purchase prices and storage costs. Meanwhile, the changes in the selling price of defect products and transaction costs have no significant effect on the profit. For further research, a more complex model can be developed by adding the considerations of common and noncommon parts, shortage, unreliable delivery performance or lead time delivery. Another further research can be directed to solve the more complex and larger model using some hybrid metaheuristic algorithms.

Disclosure statement

No potential conflict of interest was reported by the authors.