# A production recovery plan in manufacturing supply chains for a high-demand item during COVID-19

Sanjoy Kumar Paul (UTS Business School, University of Technology Sydney, Sydney, Australia)
Priyabrata Chowdhury (School of Accounting, Information Systems and Supply Chain, RMIT University, Melbourne, Australia)

ISSN: 0960-0035

Publication date: 22 June 2020

## Abstract

### Purpose

A recent global pandemic, known as coronavirus disease 2019 (COVID-19), affects the manufacturing supply chains most significantly. This effect becomes more challenging for the manufacturers of high-demand and most essential items, such as toilet paper and hand sanitizer. In a pandemic situation, the demand of the essential products increases expressively; on the other hand, the supply of the raw materials decreases considerably with a constraint of production capacity. These dual disruptions impact the production process suddenly, and the process can collapse without immediate and necessary actions. To minimize the impacts of these dual disruptions, we aim to develop a recovery model for making a decision on the revised production plan.

### Design/methodology/approach

In this paper, the authors use a mathematical modeling approach to develop a production recovery model for a high-demand and essential item during the COVID-19. The authors also analyze the properties of the recovery plan, and optimize the recovery plan to maximize the profit in the recovery window.

### Findings

The authors analyze the results using a numerical example. The result shows that the developed recovery model is capable of revising the production plan in the situations of both demand and supply disruptions, and improves the profit for the manufacturers. The authors also discuss the managerial implications, including the roles of digital technologies in the recovery process.

### Originality/value

This model, which is a novel contribution to the literature, will help decision-makers of high-demand and essential items to make an accurate and prompt decision in designing the revised production plan to recover during a pandemic, like COVID-19.

## Keywords

#### Citation

Paul, S.K. and Chowdhury, P. (2020), "A production recovery plan in manufacturing supply chains for a high-demand item during COVID-19", International Journal of Physical Distribution & Logistics Management, Vol. ahead-of-print No. ahead-of-print. https://doi.org/10.1108/IJPDLM-04-2020-0127

### Publisher

:

Emerald Publishing Limited

## 1. Introduction

Statistics show a strong increasing trend of unexpected and catastrophic events that firms have experienced in the recent past. For example, according to a recent report (Elliott et al., 2019), recording and reporting of such incidents by organizations at its highest level – 76.7% – in the last years. These events, which are popularly known as disruptions (Tang, 2006; Chen et al., 2013), range from less severe to more severe (Pavlov et al., 2019). These disruptions have substantial negative consequences on the return on sales, return on profit, stock return, brand image, employment in the firms, buyers' safety and overall supply chain performance (Hendricks and Singhal, 2003, 2005; Zsidisin, 2003; Thun and Hoenig, 2011; Chowdhury et al., 2019; Elliott et al., 2019). All these negative consequences are the results of immediate impacts on the supply chain network as one or more components of the network, such as supply, production, distribution or transportation links, become unavailable (Norrman and Jansson, 2004; Shao, 2012; Hishamuddin et al., 2014; Vergragt et al., 2014; Fan and Stevenson, 2018; Ivanov, 2020a). While firms are struggling to manage these firm- or supply chain-specific disruptions, they also have been increasingly experiencing extraordinary outbreaks such as epidemics or pandemics. For example, 1,438 epidemics have been reported by the World Health Organization (WHO) between 2010 and 2018 (Hudecheck et al., 2020). The impact of these major outbreaks are more severe for their unique features such as long-term existence of the disruptions, ripple effect on other activities, i.e. disruption propagations, high uncertainty and simultaneous impacts on supply, demand and infrastructure (Choi, 2020; Ivanov, 2020a).

Most recently, since December 2019, firms have been experiencing the major extraordinary outbreak of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), also known as coronavirus disease 2019 (COVID-19). Almost all the nations of the world have affected by this outbreak; hence, WHO declared this COVID-19 as a pandemic on March 11, 2020 (WHO, 2020). The current impact of this outbreak on the manufacturing firms is already very severe and medium-to-long-term impacts are predicted to be higher than that of any other previous major outbreaks such as 2003 SARS and 2009 H1N1 (Haren and Simchi-Levi, 2020; Koonin, 2020; Laing, 2020; Mogaji, 2020). For example, all the largest 1,000 companies in the world have been severely impacted as they all have multiple facilities in the quarantine areas (Linton and Vakil, 2020). Even before declaring this outbreak as a pandemic, production and material supply of 938 of the Fortune 1,000 companies have been severely affected given that their tier 1 or tier 2 suppliers are located in Wuhan, China, from where it is generally believed that the COVID-19 originates (Fortune, 2020). Moreover, the severe spread of the virus into Europe and the United States has blocked the movement of the products and materials worldwide (Lee et al., 2020). As such, it has become extremely challenging to continue the operations of supply chains as the operations of some parts of the supply chain has stopped (Breen and Hannibal, 2020; Ivanov, 2020b). While almost all manufacturing firms across various industries have affected by COVID-19 (Linton and Vakil, 2020), the specific nature of the effects varies depending on the nature of the products, e.g. high-demand items or low-demand items. For example, the demand of some products such as toilet paper, hand wash and sanitizers, food items, and medicines goes up expressively while the demand of some other products such as garments and sports items fall drastically (Bagshaw and Powell, 2020; Haren and Simchi-Levi, 2020). During a pandemic, the impacts on the high-demand items are more immediate and visible, given that these products are essential for daily life and, in some cases, for survival (Koyuncu and Erol, 2010; Dasaklis et al., 2012; Ivanov, 2020b). Moreover, while firms experience an immediate and sharp increase in demand for these products, they also face a substantial shortage of raw material supply during this pandemic (Ivanov, 2020a; Koonin, 2020; Linton and Vakil, 2020).

Just take an example of a Nowra-based Australian hand sanitizer manufacturing company, Nowchem, which faces both supply and demand disruptions during this COVID-19. While just a few months ago, from December 2019 to February 2020, the company faced a financial hit due to South Coast Bushfire; the company faced unprecedented demand of its product both locally and globally during early March in the face of COVID-19 (Clifford and Huntsdale, 2020). The company ramps up production by utilizing its full capacity and increasing the working and overtime hours of the staffs. However, soon after increasing its capacity, the company started facing shortages of required raw materials such as alcohol, bottles, caps, labels and other ingredients (Alexander, 2020). In fact, not only Nowchem, three-quarters of Australian hand-sanitizer manufacturers reported shortages of key materials such as ethanol, bottle pumps and sprays. In contrast, more than 50% reported shortages of gelling agents, bottles and pouches (Alexander, 2020). By mid-April of 2020, Nowchem had to stop the production of hand sanitizer due to the shortage of thickening agents. Even, according to the same article (Alexander, 2020), before the complete shutdown of production, the company had been producing 60% of its total capacity, 60,000 L out of 100,000 L per week. Because of having both supply and demand disruptions, the manufacturing company, Nowchem, should formulate appropriate strategies and recovery plan to recover from this unprecedented event. On the other hand, current literature on disruption recovery strategies and modeling considering an epidemic or pandemic outbreak is mostly limited to humanitarian logistics (Ivanov, 2020a). Therefore, these studies are unable to provide appropriate production recovery model and strategies for commercial products and their supply chains. Considering the inadequacy of research on production recovery modeling considering a major outbreak, this study investigates the following research questions.

1. How can manufacturers make an optimal decision on their production recovery to tackle both supply and demand disruptions caused by a major epidemic or pandemic outbreak like COVID-19?

2. What are the managerial implications of the developed recovery model?

For answering the above questions, this study develops a mathematical model considering both supply and demand disruptions and optimizes the revised production plan in the recovery window. Using a numerical example, this study demonstrates how the model is capable of optimizing the recovery plan for better tackling the disruption. We simultaneously consider both demand-side disruptions, i.e. sudden demand spikes and supply-side disruptions, i.e. shortage of material supply, of manufacturing companies. Given that manufacturers of a high-demand item are currently facing both supply shortage and demand boost (Ivanov, 2020a; Lee et al., 2020), it is essential, as well as practical, to consider both the disruptions. In line with the nature of the problem, we also consider the combination of two strategies, increasing production capacity and enhancing raw material supply using emergency sourcing and strong collaboration. Using dual strategies in the presence of dual disruptions makes the model robust and practical (Lücker et al., 2019). The main contributions of this study can be summarized as follows.

1. Developing a mathematical model for production recovery considering the impacts of a pandemic such as COVID-19.

2. Considering dual disruptions such as increasing demand and shortage of raw material supply in the recovery model.

3. Analyzing the properties of the model and discussing managerial implications.

The remainder of this paper is organized as follows. Section 2 provides the disruption literature with a focus on major outbreaks and recovery modeling. Section 3 describes the problem and presents the model. The results of the model are analyzed using a numerical example in Section 4 and discussed in Section 5. Managerial implications for the practitioners and contributions of the study's findings are discussed in Section 6. This paper is concluded by summarizing the main insights and outlining the agenda for future research in Section 7.

## 2. Literature review

### 2.1 Disruptions and major outbreaks

It has been reported that the recovery plan for supply chain disruptions varies based on the severity of supply chain disruptions. For example, the recovery plan of less severe and more severe supply chain disruptions is different (Pavlov et al., 2019). At the same time, firms need to make a different and more robust plan for an extraordinary supply chain disruption like COVID-19 (Ivanov, 2020a; Ivanov and Dolgui, 2020b). While firms have experience more than 1,400 epidemic outbreaks in last ten years, each of which significantly affected operations and productivity of impacted supply chain of commercial products (Blos and Wee, 2020), till to date the research on epidemic outbreaks mostly focused on humanitarian logistics (Ivanov, 2020a). A systematic literature review on the epidemic outbreaks (Dasaklis et al., 2012) reports that research in this area mostly consider humanitarian logistics to develop several models and strategies to (1) decide the location and number of centers to distribute relief; (2) assign the centers to serve populations within a geographical boundary; (3) select of optimal transportation modes for distributing aid; (4) decide optimal inventory level for commodities and supplies and (5) formulate replenishment strategies. On the other hand, it is surprising to note that research on commercial products considering epidemic or pandemic outbreaks is scarce.

Even the studies that examine commercial products, mostly investigate the impact of the epidemic outbreaks rather than designing recovery models or strategies for different types of products to respond to the outbreak for quick recovery. For example, the economic burden raised from the 2014 Ebola outbreak, which ranges between $2.8 and$32.6bn in loss of gross domestic product (GDP) was modeled and reported in Huber et al. (2018). Similarly, studies indicate the effect of the 2003 SARS outbreak on different contexts such as on the Toronto Pearson International Airport (Johanis, 2007) and the economy of Taiwan, China and Hongkong (Chou et al., 2004). In their study Chou et al. (2004) predict a loss of GDP of Taiwan, China and Hongkong for 0.67, 0.20 and 1.56%, respectively. Using a simulation study, a recent article (Ivanov, 2020a) also predicts the impacts of COVID-19, the findings of which conclude that the closing and opening of the facilities at various nodes might become one of the most influential factors that decide the impact on the operations. Another study also suggests that the short-term impacts of COVID-19 are already more than all previous outbreaks, including SARS and Ebola, the medium to long-term impact is also predicted as very severe. Still, it is uncertain how severe it would be (Laing, 2020). Recently, Choi (2020) builds an analytical model, explicitly focusing on the distribution side of the supply chain, to show how logistics and technologies together can ensure “bring-service-near-home” mobile operations from the “static service operations“.

### 2.2 Disruptions and recovery modeling

In the recent decade, many studies have been carried out on building production recovery models by considering several recovery strategies for managing disruptions. Two main reasons are repetitively mentioned why researchers predominantly focused on formulating recovery models and strategies, rather than mitigating the probability of occurrence, for disruption management. First, disruptions refer to the catastrophic events that are generally hard to predict and control; hence, impossible to eliminate from the operations (Chen et al., 2015; Ivanov et al., 2017). Appropriate recovery strategies are more suitable for tackling these unknown risk events and for making the supply chain resilient (Peck, 2005) and viable (Ivanov, 2020b). Second, firms that failed to implement appropriate recovery strategies failed soon after the disruptions (Cerullo and Cerullo, 2004; Peck, 2005; Chen et al., 2015; Bao et al., 2019). For example, 80% of the companies experienced by disruptions failed within two years due to poor disruption recovery strategies (Cerullo and Cerullo, 2004).

In building production recovery models, disruptions in all major parts of supply chains, such as the upstream supply side, internal production side, and downstream distribution and demand management side, have been considered. Among them, supply disruptions, such as disruptions in supplier facility centers due to fire and machine or system failures and in the sourcing city/country due to natural disasters, political and financial instability, have received the most attention (Shao, 2012; Shao and Dong, 2012; Pal et al., 2014; Silbermayr and Minner, 2014; Paul et al., 2016; Darom et al., 2018; Paul and Shams, 2018; Safaeian et al., 2019). Disruptions in the own production facilities, such as machine breakdown, technology obsolescence or breakdown, fire, utility failure and system damage, have also received considerable focus in building production recovery models (Hishamuddin et al., 2012; Paul et al., 2014a, b; Paul et al., 2015a, b; Ivanov, 2019). Studies also considered demand-side disruptions, such as sudden fall of customers' demand, immediate product obsolesce, in designing the recovery strategies (Asian and Nie, 2014; Paul et al., 2014a, b; Ali and Nakade, 2017). In addition to these three major types of disruptions in a supply chain, studies have also developed production recovery model for managing transportation and scheduling disruptions (Hishamuddin et al., 2013; Fathollahi-Fard et al., 2019b; Paul et al., 2019a). Some researchers have also considered more than one disruptions as multiple disruptions may happen simultaneously (Ali and Nakade, 2017), or one disruption may affect numerous operational functions due to the ripple effect of supply chain disruptions (Ivanov et al., 2013; Ivanov et al., 2014). For example, studies build production recovery model in the presence of dual disruptions, such as supply and transportation disruptions (Hishamuddin et al., 2015b), supply and demand disruptions (Ivanov et al., 2014; Sawik, 2019) and three disruptions, such as supply, demand and production disruptions (Paul et al., 2019b).

In these studies, researchers proposed several disruption recovery strategies. Among them, backorder (Hishamuddin et al., 2013, 2015a; b), buffer inventory or safety stock (Darom et al., 2018; Paul and Shams, 2018; Lücker et al., 2019), alternative sourcing and backup suppliers (Hou et al., 2010; Paul et al., 2017; Pavlov et al., 2019), leveraging collaboration and relationship with supply chain partners (Chowdhury et al., 2016; DuHadway et al., 2017) appropriate compensation policy (Shao and Dong, 2012), spare/reserve capacity (Hishamuddin et al., 2013; Paul et al., 2014), capacity increase or expansion (Ivanov et al., 2016), flexibility (Glenn Richey et al., 2009), restructuring of the supply chain such as production-distribution replanning and redesign (Ivanov et al., 2013; Ivanov et al., 2014; Ivanov et al., 2016) are mostly used. Some studies also proposed a combination of more than one of these strategies (Shao and Dong, 2012; Hishamuddin et al., 2013; Ivanov et al., 2016; Lücker et al., 2019). Depending on the particular scenario and condition, one strategy may be preferred than others. For example, while backup sourcing is a preferred strategy at the beginning of a supply disruption, appropriate policy for compensating customers is more effective as time elapses (Shao and Dong, 2012). Therefore, careful selection of appropriate strategies by considering various factors such as severity, duration and area affected is essential.

### 2.3 Knowledge gap

While existing studies made substantial contributions in the literature in managing less severe to more severe disruptions specific to a particular manufacturing company or supply chain (Pavlov et al., 2019), none of these studies considered extraordinary outbreaks such as epidemic or pandemic disruptions, as explained in the previous section. As a result, these production recovery models are not readily applicable to manage a pandemic disruption like COVID-19. Moreover, some of the recovery strategies considered in these studies are not applicable in a pandemic situation for high-demand items. For example, these studies mostly used backorders to develop recovery models. However, backorders are not useful for recovering from a pandemic for high-demand essential items given that quick responding to this demand is required for survival (Dasaklis et al., 2012). Besides, during a pandemic situation, firms simultaneously need to enhance the supply of raw materials and production capacity to respond to the increased demand quickly. A combination of these two strategies was not considered in any of the previous mathematical modelings. By considering both strategies, this study demonstrates how a mixture of strategies can be used during a pandemic situation to formulate a production recovery plan for high-demand items that face both demand and supply disruptions.

## 3. Problem description and model formulation

In this paper, we consider a batch production system, which produces a single product with lot size  Q. In the ideal manufacturing plan, we assume that the annual production rate (P) is higher than the annual demand (D). During the COVID-19, the demand of the product increases substantially due to the necessity of specific products such as toilet paper and hand sanitizer, and the raw material supply of such products also reduces considerably as many suppliers unable to supply. Due to having these dual disruptions, it is crucial to design the proper recovery strategies and optimize the production plan accordingly. To develop the recovery model, we consider the following strategies to minimize the impact of the dual disruptions.

Increase in production capacity: During a pandemic, manufacturers of high-demand items can take several actions to increase the production capacity; hence to mitigate the increased demand of a product (Iswara, 2020). For example, a manufacturer can increase the number of shifts, buy additional machinery, utilize the idle time and hire human resources to increase the production capacity. There is an additional cost for increasing production capacity. We consider the cost for increasing capacity in the recovery model.

Emergency sourcing and collaboration: During a pandemic, there is a significant shortage of raw material supply from current suppliers, the manufacturer can do emergency sourcing (Huang et al., 2018) from alternative, backup or new suppliers and leverage collaboration with upstream supply chain partners (Lavastre et al., 2012) to increase the raw material supply. In this strategy, the raw material price would be higher than the normal situation. We consider this emergency sourcing cost in the recovery model.

In the recovery model, the main objective is to meet the increased demand and to maximize the total profit in the recovery window. We consider a lost sales cost in the objective function for any unmet demand, which will ensure meeting most of the increased demand. To fulfill the objective, we develop a constrained mathematical model, which determines the optimal production plan in the recovery window with maximization of the total profit.

In the following subsections, we discuss the mathematical models for the ideal production system and the recovery plan.

### 3.1 Model for the ideal production system

We consider following notations for the ideal production system.

• D→Annual demand in the ideal plan

• P→Annual production rate the ideal plan (P>D)

• A→Set-up cost

• H→Holding cost per unit per year

• Q→Lot size in the ideal plan

• Tc→Cycle time = QD

• Ts→Set-up time

• Td→Idle time = QDQPTs

• R→Raw material required per cycle = Q

We consider an economic production quantity model for the ideal plan. We determine the total annual cost and the optimal lot size of production as follows.

Annualholdingcost=Q2HDP

Annualset-upcost=DQA

Totalannualcost=Q2HDP+DQA

Tominimizethetotalannualcost,ddQ( Q2HDP+DQA)=0

After simplifying, the lot size in the ideal production system is calculated as shown in Eqn (1).

(1)Q=2APH

### 3.2 Model for the recovery plan

We consider following additional notations for the recovery model.

1. N→Number of cycles in the recovery window

2. ni→Times of demand increase in cycle i in the recovery window

3. mi→Times of capacity increase in cycle i in the recovery window

4. di→Demand in cycle i in the recovery window = ni×D×QD=niQ

5. pi→Capacity in cycle i in the recovery window = miP×(QP+Td)

6. ai→The fraction of raw material sourced using emergency sourcing and collaboration in cycle i

7. bi→The fraction of raw material sourced from current suppliers in cycle i

8. bi→Available raw material in cycle i in the recovery window = aiR+biR

9. cp→Production cost per unit

10. cc→Capacity increase cost

11. ce→Emergency sourcing cost per unit of raw material

12. cs→Current sourcing cost per unit of raw material

13. L→Lost sales cost per unit

14. Sp→Selling price per unit

15. Xi→Production quantity in cycle i in the recovery window

In the recovery plan, we have added several COVID-19-related parameters such as the average cost of increasing production capacity, which includes costs for extra shifts, overtime, hiring staff members and buying machinery. Another parameter, emergency sourcing cost per unit of raw material, is used to determine the cost for sourcing materials from emerging sources. Lost sales cost, another important parameter in the recovery plan, which considers a penalty cost for any unmet demand, hence the recovery plan will try to reduce the unmet demand to maximize the profit in the recovery plan. These COVID-19-related parameters make the recovery model unique.

In the recovery plan, we have developed mathematical equations for different costs, such as cost to capacity increase, sourcing, lost sales, holding and set-up within the recovery window. Production cost is determined by multiplying per unit production cost by total production quantity (Eqn 2) (Hishamuddin et al., 2014). Capacity increase cost is determined by multiplying the amount of capacity increase by capacity increase cost per shift (Eqn 3). Lost sales cost (Eqn 4) is determined by multiplying per unit lost sales cost by total unmet demand (Paul et al., 2015b). Holding cost is calculated as multiplying holding cost per unit per year, average inventory quantity and time required to keep the inventory (equation 6) (Paul et al., 2014). Set-up cost is calculated by multiplying the cost per set-up with the number of set-ups in the recovery window (Eqn 7).

We have also determined the selling price in the recovery window by multiplying per unit selling price with total production quantities in the recovery window (Eqn 8). Finally, the total profit is determined by subtracting the total cost from the total selling price in the recovery window.

(2)Productioncost=Cpi=1NXi
(3)Capacityincreasecost=Cci=1Nmi
(4)Sourcingcost=Ce(i=1NXibiR)+Csi=1NbiR
(5)Lostsalescost=L(i=1Ndii=1NXi)
(6)Holdingcost=H2P(i=1NXi2)
(7)Set-upcost=AN
(8)Sellingprice=Sp×i=1NXi

The objective function is the maximization of the profit in the recovery window. The total profit (TP) is calculated as presented in Eqn (9).

Max(TP)=Totalsellingpricetotalcost
(9)Max(TP)=Spi=1NXiCpi=1NXiCci=1NmiCe(i=1NXibiR)Csi=1NbiRH2P(i=1NXi2)ANL(i=1Ndii=1NXi)

Subject to the constraints presented in Eqns (10)–(13).

(10)i=1NXii=1Ndi
(11)Xiri;i
(12)Xipi;i
(13)Xi0;i

Eqn (10) represents the constraint for demand, such as total production quantities must be less than or equal to the total demand. The production quantity is restricted by the raw material supply, which is presented in Eqn (11). Eqn (12) provides the constraint for production capacity, in which production quantity is also restricted by production capacity. Finally, the non-negativity constraint is shown in Eqn (13).

### 3.3 Analyzing properties of the recovery model

In this section, we have developed some propositions to describe the properties of the mathematical model developed in Section 3.2.

P1.

If Xi = X (equal batch sizes in the recovery window), the profit will be reduced as this will consider the minimum capability of production in the recovery window. Hence, equal batch sizes in the recovery window should not be imposed in the recovery window.

P2.

If  CcorCe is significantly high (which is most unlikely), and if this negatively impacts the profit lower than the no-action situation, then it is suggested not to implement the strategies.

P3.

if i=1Ndi>i=1Ni=1Nmin(ri,pi), then the lost sales cost will be present in the recovery plan. In this situation, the production quantity (Xi) will be limited by raw material availability or increased production capacity, which will ultimately lead to unmet demand. Hence, there will be lost sales in the recovery plan.

P4.

If min(ri,pi)di, then Xi=di. In this situation, the raw material availability or increased production capacity is more than the increased demand, and the production process will be capable of recovering fully. Therefore, Xi will be equal to the increased demand, di.

P5.

If i=1Nmin(ri,pi)<i=1Ndi, then Xi=min(ri,pi). In this situation, the total increased demand is more than the capability in the production, which is i=1Nmin(ri,pi), and the production process will not be capable of recovering fully as Xi will be limited by min(ri,pi). Hence, Xi will be equal to min (ri, pi).

### 3.4 Solution approach

There are different mathematical models in operation research, ranging from deterministic single-objective models to multi-objective stochastic models (Fathollahi-Fard et al., 2019a; Fathollahi-Fard et al., 2020). The selection of a mathematical model depends on the type of research. As the mathematical model of this study belongs to constrained and nonlinear programming, we have applied a Generalized Reduced Gradient (GRG) nonlinear approach to solving the model. GRG nonlinear approach is capable of handling the constrained and nonlinear programming model (Eiselt and Sandblom, 2019). The steps of the solution approach are as follows.

• Step 1: Input parameters for the ideal plan.

• Step 2: Determine the lot size in the ideal plan using Eqn (1).

• Step 3: Input cost and selling price parameters for the recovery plan.

• Step 4: Input  ni, mi, ai, bi for the recovery plan.

• Step 5: Solve the model, presented in Section 3.2, using a GRG non-linear optimization approach.

• Step 6: Record the results.

## 4. Result analysis

We analyze the results using a numerical example with hypothetical data for both the ideal production system and the recovery plan. We also compare the results between our model and if the manufacturer does not take any step for recovery, known as no-action situation.

### 4.1 Results for the ideal production system

We assume the following data to determine the ideal plan.

1. D = 8,000 per year

2. P = 10,000 per year

3. A = $50 per set-up 4. H =$2/unit/year

5. Ts = 0.005

Lot size, in the ideal plan, is calculated using Eqn (1) as follows.

1. Q = 707 units

We have also calculated cycle time and idle time in a cycle as follows.

1. Cycle time, Tc = 0.088388

2. Idle time in a cycle, Td = 0.012678

As we assume, one unit of finished product requires one unit of raw material, and we calculate raw material requirement per cycle as follows.

1. R = 707 units

### 4.2 Results for the recovery plan

To analyze the results for the recovery plan, we assume the following hypothetical data.

1. Cp→$3 per unit 2. Cc→$2000

3. Ce→$0.5 per unit 4. Cs→$0.2 per unit

5. L→$8 per unit 6. Sp→$15 per unit

7. N→5

The parameters for increased demand, capacity and raw materials are presented in Table 1.

After solving the model presented in Section 3.2, using GRG nonlinear optimization approach, we determine the revised production plan in the recovery window as follows.

• X1 = 1,251 units

• X2 = 1,061 units

• X3 = 849 units

• X4 = 1,202 units

• X5 = 849 units

We also calculated different costs and the selling price as follows.

• Total production cost = $15631.87 • Capacity increase cost =$20,000

• Sourcing cost = $2159.83 • Lost sales cost =$23368.84

• Holding cost = $2715.06 • Set-up cost =$250

• Selling price = $78159.35 • The value of the objective function (total profit) is optimized as follows. • Total profit =$14033.75

For this numerical example, we have observed that the unmet demand is 2,921 units, which constitute the lost sales cost of $23,368.84. We have also compared the results if the manufacturer does not take any action (no-action situation)for the recovery. In this case, the production plan would be as follows. • X1 = 707 units • X2 = 354 units • X3 = 141 units • X4 = 141 units • X5 = 141 units The different costs, selling price and total profit would be as follows. Production cost$454.77
Capacity increase cost0
Sourcing cost$296.98 Lost sales cost$53174.43
Holding cost$68.5 Set-up cost$250
Selling price$22273.86 Total profit−$35970.8 (loss)

In this no-action situation, the lost sales cost is significantly high compared to the recovery model, as the manufacture was not able to meet the demand, which was lost. The total unmet demand is 6,647 units, which constitute the total lost sales cost of $53174.43. If the manufacturer does not take any steps for the recovery plan, the total profit would substantially reduce to –$35970.8, which is a loss. By applying the recovery strategies and our model, the improvement in total profit is significant.

## 5. Discussion on findings

The findings from our developed model and results are discussed in this section.

Impact of recovery strategies: Both of the proposed strategies have a positive effect on the recovery plan. However, they should be implemented together. An increase in production capacity will ensure the increment in production quantity to meet the increasing demand. Emergency sourcing and collaboration will help to increase the supply of raw materials, which is another requisite for producing additional amounts.

Impact of lost sales cost: if any manufacturer fails to meet the demand, there will be a cost for this. The cost of this unmet demand is high if the manufacture does not have any recovery strategy. Our proposed model will help to reduce these lost sales cost significantly by lowering the unmet demand during the recovery process. However, the total profit in the recovery window will decrease with the increment of lost sales cost (L), as shown in Figure 1.

Changes in the total profit: From the results of our proposed model, we can see significant improvement in profit, compared to the no-action taken. The total profit mainly depends on the capability of meeting increased demand. However, other costs, such as cost of increasing capacity, cost for emergency sourcing and lost sales cost, play an essential role in the total profit function. Figures 2 and 3 show the impacts of capacity increase cost and sourcing cost, respectively, on the total profit. Other cost parameters, such as holding cost and set-up, have little impact on the total profit. The impact of holding cost on the total profit in the recovery window is presented in Figure 4. Total profit in the recovery plan decreases with the rise of capacity increase cost, sourcing cost and holding cost. However, it was observed that if capacity increase cost is more than a certain level (e.g., it was \$5,000 in our numerical example – see Figure 2), then the total profit reduces below the no-action taken situation. Therefore, manufacturers should be careful with the trade-off of capacity increase cost with the overall profit while making the decision.

Impact of  ni, mi, ai, and bi: total profit in the recovery window also depends on the changed scenarios such as the value of  ni, mi, ai, and bi. Table 2 shows the comparison of results for different values of ni, mi, ai and bi. In this analysis, we have changed the value of one parameter and fixed the values of others. It is observed that our model performs better than the no-action situation in all scenarios.

## 6. Managerial implications and theoretical contributions

The model and strategies, developed in this paper, can be applied in determining a recovery plan for a high-demand and essential product, such as toilet paper and hand sanitizer, during a pandemic like COVID-19. The COVID-19 outbreak creates dual disruptions such as a sudden increase in demand substantially and a decrease in raw material supply in supply chains of a high-demand item (Ivanov, 2020b; Koonin, 2020). In addition, there is a limitation of production capacity. We have considered all of these impacts of COVID-19 on the supply chain of a high-demand item in the developed model, which make the model realistic, robust and practical. Managers can use the concept and model to generate a revised production plan. Hence, it can be said that this study contributes to the practice by providing an implementable production recovery model to manage the impacts of a pandemic like COVID-19 on global supply chains. In this research, the model is found effective in improving the total profit in the recovery window. Moreover, proper implementation of the model can help managers of the supply chains of a high-demand item to remain viable during the recovery process, as suggested in Ivanov (2020b).

In this paper, we have considered two recovery strategies (increase in production capacity and increase in raw material supply) to develop the recovery model. Managers can take several actions to implement these strategies, such as an increase in production shifts, use of spare capacity, buying new machinery and hiring human resources to increase production capacity and emergency sourcing from available suppliers and collaborations with supply chain partners to increase the raw material supply. As the results suggest, practitioners need to improve both strategies simultaneously as those are the constraints in the decision-making model. If a manager implements one strategy out of the proposed two, the recovery plan may not be useful (Shao and Dong, 2012). For example, in a situation when managers only increase the raw materials supply without enhancing production capacity, then the additional materials will only create buffer materials and increase the operating cost for the companies (Wilson, 2007). Hence, to get the maximum benefits from the model, decision-makers are suggested to implement both strategies and determine the recovery plan using the proposed model as soon as possible they experienced the impact of a pandemic.

As an option to increase production capacity, managers can increase the number of production hours by introducing the second or even third shift each day or simply increasing the current production hours. For example, Kimberly-Clark, the leading toilet paper producer in Australia, runs 24 h at its South Australian factory to respond to the increased demand (Bagshaw and Powell, 2020). As we consider, ideally, the production capacity is greater than the demand rate; hence there is some spare capacity in the system, which managers can utilize to increase the capacity. However, these require additional workforce and extra maintenance of machinery. It is also possible to buy additional machinery to use other production facilities to increase production capacity. Managers should also try using emergency sourcing options to increase the raw material supply. This emergency sourcing includes utilization of supply capacities of current suppliers, alternative and backup suppliers, and sourcing from new suppliers. Moreover, collaboration and information sharing with supply chain partners such as other distributors and suppliers could help to find new sourcing options and ultimately help to increase the raw material supply (Cheong and Song, 2013).

In this model, we have considered lost sales costs, which determines the cost of the unmet demand during the recovery. The cost of this lost sales is an important parameter, and managers should be careful to determine the accurate data for lost sales costs. Lost sales cost per unit should not be greater than the per unit selling price because this is the cost of not meeting demand, which cannot be greater than the selling price. Finally, to recover for a high-demand item during a pandemic, it is vital to implement the recovery strategies quickly (Chen et al., 2015; Ivanov, 2020a), although, in real-life cases, it is a challenging task to implement them in a speedy manner. As such, we urge managers to be proactive in looking for actions for implementing the two strategies proposed in this study.

Moreover, managers can take advantage of digital technologies as these technologies can play a significant role in implementing the strategies and recovery plan suggested in this study. For example, this study suggests better supply chain collaboration, which requires on-time sharing of accurate information between buyers and suppliers (Chowdhury et al., 2019), to improve raw material supply. In this regard, data analytics and blockchain can be employed to improve the supply chain visibility (Ivanov and Dolgui, 2020a), thereby, enhancing collaborations with supply chain partners. Moreover, blockchain systems can assist in keeping the data needed for recoveries such as information and data for production capacity, human resources requirements, and information of supplier capacities, and emergency suppliers. Hence, managers can use the data and information to undertake actions for implementing the developed recovery model. Another digital technology, additive manufacturing, can also help to implement the proposed recovery strategies quickly by utilizing its reserved inventory and capacity and by identifying and maintaining contingent suppliers for emergency sourcing (Ivanov et al., 2019). A recent empirical study (Das et al., 2019) has also supported the application of digital technologies, such as Industry 4.0, blockchain, Internet of things (IoT) and additive manufacturing, for improving the recovery capabilities in the recovery window. Therebefore, we suggest that managers use digital technologies to ensure the successful implementation of the recommended strategies.

The main contribution of this study lies in the development of a production recovery model for the high-demand items during a major pandemic outbreak. A recent study (Ivanov, 2020a) focusing on COVID-19 clearly states that the current body of literature using major epidemic or pandemic outbreaks mainly focused on humanitarian logistics but ignored commercial companies. On the other hand, the current COVID-19 pandemic outbreak is a unique disruption and an extraordinary situation, which is different from any other previous disruptions (Ivanov and Dolgui, 2020b). As such, developing a production recovery model focusing on this extraordinary outbreak for the high-demand commercial products can enhance the current knowledge. Moreover, this study demonstrates how mathematical modeling can be used to develop a recovery plan by accommodating several actions such as increasing the number of production shifts, buying or hiring machinery, hiring human resources, emergency sourcing and collaboration with supply chain partners. These actions ultimately help to achieve two broad strategies, i.e. an increase in production capacity and an increase in raw material supply, in the presence of both demand-side and supply-side disruptions during a pandemic. Such a robust model is a unique contribution of this study as using mathematical modeling; none of the previous research on disruption management has considered these two strategies and two large-scale disruptions simultaneously. In addition, the outcome of this study, a robust and practical recovery model, can substantially assist practitioners of commercial high-demand products in designing a production recovery plan for a quick recovery during a pandemic situation.

## 7. Conclusions

COVID-19 is an exceptional and extraordinary event that impacts the supply chain globally. The challenge for the manufacturers of high-demand and the essential product has twofold: (1) the demand of the product increases substantially and suddenly, (2) the supply of the raw material decreases without notice. These dual disruptions make the production planning complex, and without proper action, the business could be unable to ramp up the production and could lose the demand. This research tackles both of these disruptions and develops a recovery model to revise the production plan, for a certain time in the future – known as the recovery window, to maximize the total profit. In this mathematical recovery model, we consider an increase in production capacity and emergency sourcing and collaboration as recovery strategies. Our research finds that there are significant improvements in the total profit if manufacturers can implement both recovery strategies simultaneously. This research supplements the inadequate studies on developing mathematical models and strategies for production recovery, considering the impact of an epidemic or pandemic situation.

As COVID-19 is a new experience for supply chain decision-makers, they would face numerous challenges to decide on recovery planning. The model, developed in this paper, could be a base paper for decision-makers to make a recovery decision. Moreover, this paper provides a mathematical model and numerical results, which could be useful to understand the impact of the COVID-19 and formulate recovery strategies.

The developed recovery model, in this research, is only applicable for revising the production plan. While this study substantially contributes to the literature on the production recovery plan for high-demand commercial products during a major outbreak such as an epidemic or a pandemic, in the future, the concept can be further extended to develop a recovery plan in a complex and global supply chain network considering the impact of a global pandemic like COVID-19. This extension will help to formulate the strategies to revise the supply, manufacturing and distribution plans simultaneously in the supply chain. In this paper, we use hypothetical data to analyze the recovery plan. Future studies may consider collecting real data from specific supply chains, such as supply chains of food and medicine products, to develop and analyze the recovery model. Such an extension could potentially allow the researchers to consider product-specific parameters in the model formulation. Furthermore, a future study could investigate the recovery models for low-demand items such as garments or athletic products during a pandemic as the current model only considers the high-demand items. Besides, full empirical studies, such as in-depth case studies or a large-scale survey, can be conducted to provide an in-depth understanding of how the proposed strategies help recover or to validate the proposed strategies and their impact on the profit.

## Figures

#### Figure 1

Impact of lost sales cost on the total profit during recovery

#### Figure 2

Impact of capacity increase cost on the total profit during recovery

#### Figure 3

Impact of emergency sourcing cost on the total profit during recovery

#### Figure 4

Impact of holding cost on the total profit during recovery

## Table 1

Hypothetical data for increased demand, capacity and raw material supply

ParameterCycle
12345
ni232.51.52.5
mi1.5222.52
ai1111.51
bi10.50.20.20.2
di1,4142,1211,7681,0611,768
ri1,4141,0618491,202849
pi1,2511,6681,6682,0851,668

## Table 2

Impact ofni, mi, ai and bi

Fixed valuesniTotal profit (our model)Total profit (no-action)
mi = 2
ai = 1
bi = 0.5
1.538455.25−7737.05
224313.25−21879
2.510171.25−36021
3−3970.75−50163
3.5−18112.70−64305
4−32254.70−78447
Fixed valuesmiTotal profit (our model)Total profit (no-action)
ni = 2
ai = 1
bi = 0.5
1.529313.25−21879
224313.25−21879
2.519313.25−21879
314313.25−21879
Fixed valuesaiTotal profit (our model)Total profit (no-action)
ni = 2
mi = 2
bi = 0.5
0.5−8,595.40−21879
124313.25−21879
1.556596.92−21879
256596.92−21879
Fixed valuesbiTotal profit (our model)Total profit (no-action)
ni = 2
mi = 2
ai = 1
0.24324.86−42827.4
0.417675.46−28856.8
0.630926.05−14906.3
0.844076.65−975.68
157127.2512934.9

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## Corresponding author

Sanjoy Kumar Paul can be contacted at: sanjoy.paul@uts.edu.au