A sustainable pharmaceutical supply chain model for household energy consumption and expiration cost under decision making approach

1. Introduction

This research problem is organized by four decision making approaches with HEC and expiration cost: decentralized, centralized, economic, and social decision-making. In the investigated PSCM, decentralized decision-making is assumed that pharma supplier is the dominating firm over the pharma retailer and consequently interaction between them. Centralized decision-making is an organizational structure where the top management defines decision-making power, and the subordinates need to follow the instructions of their seniors. There are several reasons for using the centralized decision-making. Here, we give some of them such as cost-efficient, enhance work quality, uniformity in action, focus on vision, and proper coordination. There are a few techniques to improve the PSCM: connecting and coordinating using a business network, getting a detailed analysis of the production process, ensuring end-to-end traceability, responding quickly to demand changes, and getting complete inventory visibility. The essential factors of operations research in PSCM were discussed by Ahmadi et al. (2018). The pharmaceutical items pass through various players in an SC to reach the consumers. Since, the complex and competitive nature of these member's relationships, competition and the complexity at various levels of PSCM is advanced but, efficient optimization techniques are needed to provide an excellent suite for informed decision-making. This segment aims to provide valuable information about the PSCM industry's context and fundamental characteristics. For any business, the customer needs the quality of items. For such kind of issue, Chen et al. (2020)addressed the impact of quality regulations in pharmaceutical firms; product quality is essential in developing and protecting company reputation, serving to enhance a firm's competitive advantage. The fundamental differences of centralized and decentralized decision-making cases are shown in Table (1).

Table 1. Key differences of decision making approach.

Basis	Centralized	Decentralized
Connectivity flow	sharp flow	free and unrestricted
Decision making	low and isolated	faster and dispersed
Benefits	quality cooperation and supervision	overload and duty sharing
Power of decision-making	is the responsibility of the senior management	multiple users have the ability to make decisions
Implementation	insufficient management	considerable management
Suitable for	a small kind of company	a large kind of company

Next, the decision-making is the process of identifying alternative sources of action and selecting an appropriate alternative in a given situation. The essential duty of the decision-making is to identify the alternative courses of action means that an ideal solution may not be identifiable. Ding (2018)analyzed the impact of pharma companies in developing countries have begun to introduce specific primary energy management actions that are more focused on individual production machines. This research will help pharma companies to update their inventory system with big data analysis in the multi-production supply chain (SC) problems. The strategic partnership enables suppliers to develop their operations and management to meet the local organization's CSR requirements. Using the decision-making techniques has multiple advantages: gathering necessary details, identifying alternatives, weighing the information, choosing among the alternatives, taking action, and reviewing your decision. We also framed two types of decision-making approaches: coordinated and collaborative decision-making. To maximize profit, the EDM considers major variables such as preferred outcomes and activities, endorsement of the operation, development of choices, evaluation and selection, refinement of alternative solutions, and finalization of recording and evaluation of the process. Household energy consumption accounts for about half of India's total energy consumption. Because of increases in power and petroleum products, the HEC has increased while biomass usage has stayed steady. The HEC considers several factors, including gas and equipment costs, household discretionary income, fuel and equipment accessibility, and particular criteria for each. There are several ways to develop the HEC in PSCM. Here we provide some of the important ways such as the first is reduction, when building new facilities it is vital to focus on your requirements. The second is recover, there are some of the waste water from PSCM manufacturing is much cleaner than the water going into the facility, such as the final rinse of equipment with purified water. The third one is improve energy sources, this could mean looking into where you buy your energy, buying energy that is neutral or producing some of the energy yourself by putting solar panels. Marques et al. (2020) developed the impact of PSCM over time, and at various stages, the PSCM has become substantially inefficient.

The rest of this work is formulated as given below: Section 1.1 presents the literature review for the research issue. Section 2 discusses the mathematical methodology for the profit functions. Sections 2 Mathematical methodology for profit functions, 3 Coordinated decision-making approach are presented to analyze the coordinated and collaborative decision-making approaches. Section 5 illustrates the numerical examples with discussions. The sensitivity analysis and managerial implications are described in Sections 5 Numerical examples and discussions, 6 Sensitivity analysis. Section 8 conclude this study with future research plans.

1.1. Literature review

The main goal of a literature survey is to bring together past and current studies in a particular area and identify the gaps through detailed and novel interpretations. This section provides how the proposed PSCM model is related to prior research in statistics. The PSCM has a long history of dealing with environmental issues stemming from a requirement to secure the environment as an occurrence of health. It has developed a comprehensive management approach that incorporates EDM and SDM environmental challenges.

Ansuategi et al. (2014) developed a green energy and efficiency: an economic perspective. Baboli et al. (2011) framed a joint optimization problem for centralized and decentralized decision making in downstream PSCM. Barcos et al. (2013) introduced the corporate social responsibility (CSR) and inventory policy. Chaudhuri et al. (2018) introduced a cold SC method using different decision-making structures and big-data analysis. Heydari et al. (2016)developed a three-tier SC with lead time aggregation. Hsueh (2015) formulated a sustainable SCM for collaborative bi-level method. Jambulingam and Kathuria (2020) examined the buyer-supplier coordination in PSCM. Kumar et al. (2019)discussed the risks in PSCM: adoption of green SC initiatives in the pharmaceutical industry. Malleeswaran and Uthayakumar (2020) established an integrated SC model for service level constraints and backorder price discount. Milanesi et al. (2020) addressed the wave of sustainability in pharma industries. Narayana et al. (2019) constructed the study on the Indian pharmaceutical industry for the sustainability of market dynamics and reverse logistics. Nematollahi et al. (2017) developed an economic and social collaborative decision-making method in a two-echelon PSCM. Nematollahi et al. (2018) coordinated a PSCM in a periodic review inventory systems. Priyan and Mala (2020) described a game-theoretic inventory model for pharmaceutical products incorporating an expiration date. Putri et al. (2019)introduced a distributor-retailer inventory model for PSCM with expiry cost. Raj et al. (2018) designing a supply contract for the sustainable SC using game theory. Ramandi and Bafruei (2019) analyzed an inventory model for co-ordinating replenishment decisions in a decentralized two-echelon SC. Safarzadeh and Rasti-Barzoki (2019a) introduced a duopolistic SC model with energy productivity and industrial rebound under pricing and government policies. Also, Safarzadeh and Rasti-Barzoki (2019b) framed a game theory method for consumer behavior and energy efficiency programs under government policies. Sazvar et al. (2021) designed the sustainable closed-loop PSCM in a competitive market using waste management. Settanni et al. (2017)examined the synthesis view of operations research in PSCM. Singh et al. (2016)demonstrated the literature of strategic issues in PSCM. Sumrit (2020) classified the supplier selection VMI in healthcare using fuzzy multi-criteria under the decision-making approach. Uthayakumar and Priyan (2013) optimized an inventory management strategies in a PSCM. Whewell (2016) introduced the PSCM industry for strategic influences and SC responses. Weraikat et al. (2019)improved the sustainability in a two-level PSCM via the VMI model.

This literature survey provides additional ideas for improving this manuscript. From the literature discussions, the novelty, research gaps, and objectives of the model are analyzed in the following sections.

1.2. Novelty of the study

1.
This research work discusses the importance of sustainable SC in the pharmaceutical sector. Two methods with four decision-making conditions are developed in this integrated two-echelon pharmaceutical system.
2.
The problem formulation of this sustainable SC model is considered a profit function subject to constraints. The expiration cost is a cost used to reduce the number of defective and unsold drug items.
3.
The household energy consumption is a novel one for this two-echelon pharmaceutical system. It is an additional factor in improving the energy level in the pharma industries. Also, it is used to reduce the GHG emissionsof pharma companies.
4.
The practical and commercial uses of decentralized, centralized, economic, and social decision-making conditions are explained comprehensively. The objectives for all the decision-making approaches in the PSCM are elaborated.
5.
Corporate social responsibility is a business strategy used in the pharmaceutical sector. It integrates the economic and social objectives and is a novel approach to this proposed two-echelon PSCM system. The primary reasons for carrying out this corporate social responsibility in the PSCM are to improve the employee's performance and maximize the profit for the pharma industry.
6.
The service level and visiting interval are the supportive factors for improving the SC process and reducing the drug shortages.

1.3. Significance of the study

There are several ways to build a reliable PSCM in a market. In our research, we provide a few techniques to increase the level of PSCM company's profits as well as the name of the pharma company's. This proposed model has been developed to address the environmental impact of PSCM with the help of multi-approach decision-making structures. The following attributes are used to strengthen the production and quality circles of the PSCM.

1.
Maximize efficiency and flexibility
2.
Improve the life of production assets
3.
Protect data integrity and compliance
4.
Enhance the protection level of pharma industries
5.
Coordinate all the techniques in the pharma sector

The pharmaceutical industry has become more competitive in worldwide. The significance of our research is, to use a business network to connect and collaborate, get a comprehensive overview of production processes, ensure end-to-end traceability, get all inventory visibility, and quickly respond to demand changes. The following elements are the key factors to improve the reliable PSCM in the pharma sector: reliability and sustainability, real-time transparency, compliance and regulations.

1.4. Research gaps and objectives

1.4.1. Research gaps

According to Table 2, the energy sector in the pharmaceutical industry is newly established in this model. The analysis of decision-making approaches in pharmaceutical SC are not addressed in the previous literature.

Table 2. Comparative works in the literature between previous and proposed study.

Authors	Model	Decision Making	Coordination	Energy Sector
Baboli et al. (2011)	Integrated	⊠	Centralized	⊠
Chen et al. (2020)	PSCM	⊠	⊠	⊠
Heydari et al. (2016)	3-Echelon SC	⊠	⊠	⊠
Malleeswaran et al. (2020)	Integrated SC	⊠	⊠	⊠
Nematollahi et al. (2017)	PSCM	Collaborative	⊠	⊠
Safarzadeh et al. (2019a)	SC	⊠	Government policies	Productivity & rebound effect
Sazvar et al. (2021)	PSCM	⊠	⊠	⊠
Weraikat et al. (2019)	VMI	⊠	⊠	⊠
Present model	PSCM	EDM, SDM	Centralized	HEC

2.
Many authors proposed the essential factors of the pharmaceutical supply chain. However, the problem of reducing the defective items and carbon emissions in the pharmaceutical industry is not solved by any existing research work using the optimization tool.
3.
This study is an extension work of Nematollahi et al. (2017) since their work is discussed under decision-making conditions only. Also, no research work was found in the literature for the PSCM using the household energy consumption with expiration cost.
4.
The HEC is developed by Safarzadeh and Rasti-Barzoki (2019a) in the duopolistic supply chain model. Even though, this present work illustrates the practical and environmental uses of HEC in the pharmaceutical supply chains.
5.
The necessity of decision-making structures and HEC in the pharmaceutical model compared with existing literatures are shown in Table 2.

1.4.2. Research objectives

1.
To identify the scope of coordinated and collaborative decision-making conditions in this model and to enhance the profit of the pharma companies.
2.
To incorporate the corporate social responsibility uses in the PSCM.
3.
To secure the periodic review inventory system with visiting frequency and provide a better inter-relationship between pharma supplier and retailer.
4.
To find the maximum profit of the pharmaceutical supply chain for the two testing problems.

1.5. Research questions?

For this study, we examine the following questions based on the pharmaceutical firm's research issues.

RQ.1 What does the regulatory demand for basic requirements have on the decisions and profitability of PSCM?
- Ans: There are several reasons or methods is applicable to improve the regulatory demand for the PSCM. Game theory is a significant role to improve the profit of the PSCM. But, the collaborative decision-making conditions are more familiar than the game theory approach. Since the decision-making approaches provide fluent supply chain interactions between the pharma suppliers and retailers. Also, it gives the maximum profit for the pharma suppliers as well as for the retailers.
RQ.2 How will stockholders improve standard decision-making that will increase the PSCM's economic output and social welfare?
- Ans: Generally, the stockholders and directors make the decisions as owners and managers of the pharma company. In the initial stage of the company, usually, the stockholders and directors are eco-friendly and expect no issues during the decision-making. Here, the corporate social responsibility becomes the supportive factor for the stockholders to improve the economic and social decision-making structures.
RQ.3 What are the essential factors for the improvement of pharmaceutical factory's supply chain performance?
- Ans: The PSC consists of all of the stakeholders involved in the drug production delivery process and which is initially starts with raw materials and ends with the patients. In the present study, the household energy consumption, collaborative decision-making conditions, expiration of the drug, and target filling of the drug are the essential factors for the development of supply chain performances in pharmaceutical companies.

2. Mathematical methodology for profit functions

In this section, we developed the importance of HEC in PSCM and obtained the profit function for pharma supplier and pharma retailer in decentralized decision-making. In centralized decision-making, we obtained the profit function for PSCM. End of the section 3, we constructed an algorithm to optimize the decision variables (k, n, fr, Phe).

3. Coordinated decision-making approach

3.1. Decentralized decision-making

Decentralization is only possible in a collective economic structure and a profit motive will remain in such a structure. It is an ideal way for dealing with emergency situations such as declining sales, decreasing expenses, utilizing resources effectively, driving a competitor to bankruptcy, dealing with government policy changes, and so on. There are multiple reasons to preserve this decentralized decision-making structure, including the dispersion of the executive's freight, increased efficiency and productivity, the ability to expand, etc.

3.2. Pharma retailer profit function

In this case, the visit interval of pharma supplier is Vi. The service level is decided by the pharma retailer and it will be obtained from the reorder point (R). The pharma retailers reorder point is expressed as the sum of visiting interval and lead time, which is defined by μd(Vi + L) and σ(Vi + L).The pharma retailers reorder point is,(1) $R = μ_{d} (V_{i} + L) + k σ \sqrt{(V_{i} + L)}$ Total expected shortage is,(2) $E {(X - R)}^{+} = σ \sqrt{(V_{i} + L)} Γ (k)$ The variables k and Γ(k) are called the safety factor and unit normal loss function,(3) $\begin{align} Γ (k) = \int_{k}^{\infty} (z - k) δ_{z} (k) d z \\ Γ (k) = δ_{z} (k) - k [1 - Δ_{z} (k)] \end{align}$ The pharma retailers total profit function is, $\begin{matrix} ξ_{p r}^{d c} & = (R_{p} - W_{p}) μ_{d} - H_{p r} \{R - μ_{d} L - (\frac{μ_{d} V_{i}}{2}) + f_{s} E {(X - R)}^{+}\} \\ - (\frac{S_{p r} + f_{s} (R_{p} - W_{p}) E {(X - R)}^{+}}{V_{i}}) - E_{r} μ_{d} L E_{c} \end{matrix}$ From equation. (1), The reorder point R is depends on the variable k and the service level is denoted as Δz(k). The total profit of pharma retailer without HEC is,(4) $\begin{align} ξ_{p r}^{d c} (k) & = (R_{p} - W_{p}) μ_{d} - H_{p r} \{(\frac{μ_{d} V_{i}}{2}) + f_{s} σ \sqrt{(V_{i} + L)} Γ (k) + k σ \sqrt{(V_{i} + L)}\} \\ - (\frac{S_{p r} + f_{s} (R_{p} - W_{p}) σ \sqrt{(V_{i} + L)} Γ (k)}{V_{i}}) - E_{r} μ_{d} L E_{c} \end{align}$ The parameters Er and Ec are called the expiry rate and cost.

3.3. Household energy consumption

The major problem of any pharma or chemical industries is to reduce carbon emissions. The household energy consumption (HEC) is also called a domestic energy consumption and it plays a vital role in emission reduction, since the HC's energy consumption is better than the carbon tax policy. In general, the HEC is the total quantity of energy consumed for domestic works in a home. The amount of energy consumed per home varies significantly depends on the life style of every nation, the weather, and etc. But, in this study the duties of HEC is mainly used to empower the energy efficiency in the pharmaceutical sector. This energy consumption is used to discover the behaviors and responsibilities of pharma suppliers and pharma retailers. The energy efficiency becomes a strategic goal for any professional manufacturing working in the drug industry. It usually minimizes the emissions and overtakes a strong foundation for a corporate greenhouse gas management program. The importance of HEC was proposed in many kinds of literature, but no literature work can be found in the drug industries.From the study of Safarzadeh and Rasti-Barzoki (2019a), we have defined the mathematical utility function of the HEC for the PSCM.(5) $U = [U_{h c} - E_{p} P_{h e} (1 + E_{h c})] e_{c} - {(\frac{e_{c}}{2})}^{2}$ The energy price and tax rate opposite reaction on the consumer's utility besides the HEC cost is ${(\frac{e_{c}}{2})}^{2}$ . The optimal value of energy consumption for the HC is, $e_{c}^{*} (U_{h c}) = \{U_{h c} - E_{p} P_{h e} (1 + E_{h c})\}$ Next, we have to find the expected value of the total HEC by using equation (5)and heterogeneity of the consumers in Uhc.(6) $\begin{align} e_{t c}^{*} & = M_{b} \int_{0}^{2 C_{h c}} e_{c}^{*} (U_{h c}) f (U_{h c}) d U_{h c} \\ e_{t c}^{*} & = M_{b} \int_{0}^{2 C_{h c}} \{U_{h c} - E_{p} P_{h e} (1 + E_{h c})\} \frac{1}{2 C_{h c}} d U_{h c} \\ e_{t c}^{*} & = M_{b} \{U_{h c} + E_{p} P_{h e} (1 + E_{h c})\} (\frac{1}{2 C_{h c}} - 1) \end{align}$ The retail price of the HC energy services is obtained from equation. (7),(7) $P_{h e} = \frac{P_{e s}}{2} + \frac{{(C_{h c})}^{2}}{2 E_{p} (1 + E_{h c}) (C_{h c} - 1)}$

Corollary 3.1

The pharma retailers profit function is concave w.r.to k and the optimal SL, $S L_{p r}^{d c^{*}}$ can be obtained from

(8)

S L_{p r}^{d c^{*}} = Δ_{z} (k_{p r}^{d c^{*}}) = 1 - (\frac{H_{p r} V_{i}}{H_{p r} V_{i} f_{s}} + S_{p r} + f_{s} (R_{p} - W_{p}))

Proof:

The 1st and 2nd order partial derivatives of $ξ_{p r}^{d c}$ w.r.to k gives(9) $\frac{\partial ξ_{p r}^{d c} (k)}{\partial k} = - H_{p r} σ \sqrt{(V_{i} + L)} - σ \sqrt{(V_{i} + L)} \{H_{p r} f_{s} + \frac{S_{p r} + f_{s} (R_{p} - W_{p})}{V_{i}}\} (Δ_{z} (k) - 1)$ (10) $\frac{\partial^{2} ξ_{p r}^{d c} (k)}{\partial k^{2}} = - σ \sqrt{(V_{i} + L)} \{H_{p r} f_{s} + \frac{S_{p r} + f_{s} (R_{p} - W_{p})}{V_{i}}\} (δ_{z} (k) - 1)$ Since Rp − Wp > 0, the 2nd order partial derivative of $ξ_{p r}^{d c} (k)$ is $< 0$ . The pharma retailer's expected profit function is concave w.r.to k. □.

The profit function of a pharma retailer is a collection of reorder point, expected shortage, wholesale and selling price, expiration cost, holding cost, and household energy consumption cost.

The annual total expected profit function of a pharma retailer can be written as (from the equations.(4) and (6))(11) $\begin{align} ξ_{p r}^{d c} (k) & = (R_{p} - W_{p}) μ_{d} - H_{p r} \{(\frac{μ_{d} V_{i}}{2}) + f_{s} σ \sqrt{(V_{i} + L)} Γ (k) + k σ \sqrt{(V_{i} + L)}\} \\ - (\frac{S_{p r} + f_{s} (R_{p} - W_{p}) σ \sqrt{(V_{i} + L)} Γ (k)}{V_{i}}) - E_{r} μ_{d} L E_{c} \\ - \{M_{b} \{U_{h c} + E_{p} P_{h e} (1 + E_{h c})\} (\frac{1}{2 C_{h c}} - 1)\} \end{align}$ The parameters $P_{h_{c}}$ , k, and n are called the retail price of the household service, safety factor, and number of replenishment cycle.

3.4. Pharma supplier profit function

In this case, the visit frequency is fixed by the pharma supplier. The order quantity of the pharma supplier is different from one visit to another visit. Further, the order quantity of the pharma supplier will be equal to the expected demand at each visit interval $\bar{Q_{r}} = μ_{d} V_{i} - f_{s} E {(X - R)}^{+}$ .The pharma suppliers expected profit function is, $\begin{matrix} ξ_{p s}^{d c} (T) & = (W_{p} - S_{p}) \{μ_{d} - f_{s} (\frac{E {(X - R)}^{+}}{V_{i}})\} - \frac{O_{p s}}{n V_{i}} \\ - \frac{H_{p s} (n - 1)}{2} (μ_{d} V_{i} - f_{s} E {(X - R)}^{+}) - \frac{d s_{c v}}{V_{i}} \end{matrix}$ Average holding inventory of the pharma supplier is equal to $\frac{(n - 1) \bar{Q_{r}}}{2}$ .

From equation. (2).

The profit function of a pharma supplier is a collection of wholesale and selling price, visiting and distribution cost, expected mean and shortage of the drug demand, and ordering cost.The annual total expected profit function of pharma supplier is,(12) $\begin{align} ξ_{p s}^{d c} (T) & = (W_{p} - S_{p}) \{μ_{d} - f_{s} (\frac{σ \sqrt{(V_{i} + L)} Γ (k)}{V_{i}})\} - \frac{O_{p s}}{n V_{i}} \\ - \frac{H_{p s} (n - 1)}{2} \{μ_{d} V_{i} - f_{s} σ \sqrt{(V_{i} + L)} Γ (k)\} - \frac{d s_{c v}}{V_{i}} \end{align}$

The following algorithm (3.1) is used to find the optimal values for the variables and total profits of decentralized decision making cases from the solution methodology and corollary (3.1).

Algorithm 3.1

3.5. Centralized decision-making

In this case, the central manager has decided everything in the SC. Here, SL and visit interval are simultaneously optimized. A centralized organization is a hierarchical decision-making system in which all decisions and tasks are undertaken directly by the executive level. In the centralized structure, without considering the workers the manager makes the decision about the project and the investment. A centralized organization will delegate decision-making to just the upper executives, while employees will be responsible only for their tasks and not for making decisions.The PSCM expected profit function of the centralized structure is,