Impact of COVID-19 on Supply Chains: A Hybrid Trade Credit Policy

: The COVID-19 pandemic has affected all sectors of the world’s economy and society. Firms need to have disaster recovery and business sustainability plans and to be able to generate proﬁts in order to develop. Trade credit may be a good way for ﬁrms to free up cash ﬂow and ﬁnance short-term growth. Extensions of payment will provide ﬁrms with low-cost loans under the COVID-19 credit guarantee scheme. Implementation of hybrid trade credit activities has been shown to improve the ﬁnancial crisis of many ﬁrms, and the effects are particularly evident within two-echelon supply chains. An economic order quantity (EOQ) model is derived under conditions of deteriorating items, an upstream full trade credit or cash discount, and downstream partial trade credit in a supply chain. A computer program is developed to provide a numerical solution and a numerical example is used to show the solution’s form and verify that the solution gives the minimum total cost per unit time. Author Contributions: and P.R.; methodology, software, validation, and investigation, resources, data writing—original


Introduction
The COVID-19 pandemic has had an unprecedented impact on health, economic, and financial systems around the world. From an economic and industry point of view, COVID-19 has brought uncertainties and disruptions to international businesses and supply chains. Thus, a supply chain may change the distribution network and route. Early theorization on the basic economic order quantity (EOQ) model that assumes instant payment, constant demand, and no shortages can be traced back to Harris [1]. Suppliers adopted a resolution for a hybrid payment strategy to sustain business during the COVID-19 crisis. COVID-19 could be the black swan event that finally forces many firms, and entire industries, to rethink and transform their global supply chain model. These shortages and supply-chain disruptions are significant and widespread. To protect their supply chain operations, firms may use digital supply networks, update inventory policies and planning parameters, and focus on cash flow. Some payment policies are commonly used among suppliers and retailers, such as prepayments, delays in payments, cash discounts, and the AC/DCF approach. A permissible delay in payments produces two benefits for the supplier: (1) it should attract new customers who consider it to be a type of price reduction; and (2) it should cause a reduction in the sales outstanding, since some established customers will pay more promptly in order to take advantage of permissible delays more frequently. Early theorization on the EOQ model can be traced back to Goyal [2] under the conditions of permissible delays in payments. Teng [3] amended Goyal's model [2] by considering the difference between the unit price and the unit cost and found that it makes economic sense for a well-established retailer to order a lower quantity and take the benefit of payment delays more frequently. Trade credit is used to motivate sales or decrease the on-hand inventory level to encourage customers. Numerous studies in the trade credit area can be found in the literature. Examples include Huang [4], Huang [5], Huang and Hsu [6], Hsieh et al. [7], Liao [8], Teng and Chang [9], Min et al. [10], Chen and Kang [11], Kreng and Tan [12], Lee and Rhee [13], Mathata [14], Soni and Patel [15], Ouyang et al. [16], Ouyang and Chang [17], Yang et al. [18], Chen et al. [19], Chen and Teng [20], Giri and Sharma [21], Lashgari et al. [22], and Sarkar et al. [23]. Furthermore, the classical EOQ model assumes that the purchasing cost is paid once an order is placed by a retailer. In the corporate world, companies often have to make advance payments to suppliers when their orders are large enough to be burdensome to the producer. An advance payment is a type of payment made ahead of its normal schedule; for instance, paying for a good or service before it is actually received. A prepayment is made when a selling firm receives payment from a buyer before the seller has shipped goods or provided services to the buyer. To produce a special product, the manufacturer may have to pay additional costs to set up a new process. This requires the manufacturer to obtain a fraction of the production or purchasing cost in advance. Various issues with advance payments are discussed in Maiti et al. [24], Gupta et al. [25], Thangam [26], Taleizadeh et al. [27], Zhang et al. [28], Tavakoli and Taleizadeh [29], Taleizadeh et al. [30], Shah et al. [31], Khan et al. [32], and Taleizadeh et al. [33]. Generally, in the real world, suppliers give different kinds of benefits to retailers due to advance payments. One of the popular benefits is an instant cash discount due to an advance payment. An example is a supplier who will provide a 2% discount on an invoice due in 30 days if the retailer pays within the first 10 days of receiving the invoice. Giving the buyer a small cash discount would benefit the seller as it would allow her to access the cash sooner. Khan et al. [34] proposed an inventory model for deteriorating items with a price-and stock-dependent demand rate under full/partial advance payment conditions. Shao and Meng [35] discussed the question of how to make decisions on whether the supplier's downstream enterprises should enjoy cash discounts. Several studies, including those of Huang and Chung [36], Ouyang et al. [37], Yang [38], Yang et al. [39], Feng et al. [40], Shah and Cárdenas-Barrón [41], Alshanbari et al. [42], Tripathi [43], and Mashud et al. [44], have provided extensive discussions on the applications of cash discounts. While trade credit is a powerful commercial tool for conquering new markets and building customer loyalty, it is well known that cash flow plays a pivotal role in determining firms' operation decisions. Zhou et al. [45] considered the structure of the retailer's optimal policies under different partial trade credit penalty rates. Laitinen [46] investigated the characteristics of the discounted cash flow (DCF) as a measure of a startup's financial success. Since then, several similar inventory EOQ models related to trade credit and discounted cash flow (DCF) have been proposed [47][48][49][50][51][52][53][54][55][56]. However, few studies have been done on the effect of COVID-19 on trade credit. Mashud et al. [44] showed the effect of advance and delayed payments on the retailer's total profit during the post-COVID-19 recovery period. De et al. [57] explored carbon emission issues with a production manufacturing system in the context of joint inventory control and sustainable trade credit financing for deteriorating items in a supplier-retailer-customer model in a volumetric fuzzy system. Demir and Javorcik [58] found that the impact of COVID-19 on trade finance matters included an increased risk of non-payment or non-delivery of pre-paid goods. Several studies (Agca et al. [59], Choi [60], Liu et al. [61], and Luo [62]) have suggested the effectiveness of COVID-19 in creating a trade credit policy. Some common practical issues are: (1) The prepayment policy. This issue is key to expressing the real credit trade problem.
These policies actually sustained business growth in a competitive market during the COVID-19 period; (2) The cash discount policy. The Government's SME Recovery Loan Scheme is designed to support economic recovery and to provide continued assistance; otherwise, the supplier offers the retailer a discounted rate on an invoice in exchange for an early payment discount.

Problem Description
The global production and supply chain system has been disrupted due to the COVID-19 pandemic. The COVID-19 pandemic has broken most of the transportation links and distribution mechanisms between suppliers, production facilities, and customers. Therefore, in response to the challenges resulting from the COVID-19 pandemic, firms are looking to implement some credit trade policies to fill financing gaps left by engaging in both shortterm (ST) and medium-and long-term (MLT) trade finance. While long-term partnerships are great for handling incremental changes during stable periods, disruptive environmental changes may require managers to consider disruptive changes to their businesses. In this paper, we specifically discuss these issues as hybrid credit trade problems during the COVID-19 period. In actuality, however, the COVID-19 pandemic has caused an unprecedented level of global disruption to economic systems and livelihoods. Zimon et al. [63] explored the trade credit management strategy in Polish group purchasing organizations during the COVID-19 pandemic. Table 1 presents a brief comparison of the results of the studies mentioned above. The following questions are often posed by suppliers and retailers as key points of interest: (1) When is the best time to start prepayment for export items in the post-COVID-19 period? (2) When is the best time to end prepayment for export items during the COVID-19 period? (3) What is the optimal discount rate for items? (4) What is the optimal selling price for items? (5) What is the optimal production rate for items? Table 1. Comparison of the financial policies in existing models with those in the proposed model.

Financial Policy
Other Consideration(s) EOQ/EPQ PP F/P CD DCF Goyal [2] EOQ F Trade credit financing Huang [4] EOQ F Different payment rule Huang [5] EPQ F Two levels of trade credit policies Huang and Hsu [6] EOQ P A powerful decision-making right Hsieh et al. [7] EOQ F √ Demand and deterioration fluctuate with time Liao [8] EOQ F Non-instantaneous and exponentially deteriorating items Teng and Chang [9] EPQ F Relaxes the assumption of N < M Min et al. [10] EOQ F Stock-dependent demand Chen and Kang [11] EOQ/EPQ F Imperfect items/Varying permissible delays in payments Kreng and Tan [12] EOQ F Order quantity Lee and Rhee [13] EOQ F Newsvendor framework Mathata [14] EOQ/EPQ P √ Exponentially deteriorating items Soni and Patel [15] EOQ F/P Defective items/Variable production Ouyang et al. [16] EOQ F AM-GM mean inequality Ouyang and Chang [17] EPQ F Imperfect production/AM-GM inequality Yang et al. [ the production run time. T the length of the replenishment cycle in years. TVC 1 (T) total cost per unit time (cash discount). TVC 2 (T) total cost per unit time (full delay in payments).

Assumptions
This paper is based on the following assumptions:

•
The rate of replenishment is considered to be infinite, while the lead time is zero; • The inventory system involves only one item; • An infinite planning horizon for the whole system is considered; • The items deteriorate at a constant rate θ, where θ > 0; • Before the COVID-19 pandemic, the logistic efficiency and the latest digital technologies (e-commerce technology) were regarded as critical elements in stabilizing demand. As the pandemic continued, it understandably became challenging to stabilize and recover the retailer's demand absolutely. The demand rate, D, is known and constant. • A discount is presented by the supplier (the manufacturer) to the retailer when the retailer agrees to delay a portion α of the prepayment for time period L. The discount rate (α) increases when TVC 1 (L − N) decreases during a lockdown period of the COVID-19 pandemic.

Model Formulation
This paper considers a two-echelon supply chain with an upstream supplier and a downstream retailer during the COVID-19 period. The structure is developed in a coordinated case. In the current COVID-19 pandemic situation, the supplier offers advance payments to the firm so that they will not cancel the order. The aim is to evaluate the effect of the cash discount and trade credit. In the replenishment period, [0, T], the retailer offers a trade credit policy to customers. In the Phase I trade credit period, [0, t 1 ], depletion of the inventory occurs due to the combined effects of production, demand, and deterioration on the replenishment cycle. Hence, the change in the inventory level can be illustrated by the following differential equation: with the boundary condition I(t 1 ) = 0. Solving Equation (1), one obtains Mathematics 2022, 10, 1209 6 of 22 In the Phase II trade credit period, [t 1 , T], the inventory level is decreased by the effects of demand and deterioration on the replenishment cycle. Hence, the change in the inventory level can be illustrated by the following differential equation with the boundary condition I(t 1 ) = P−D θ (1 − e −θt 1 ). Solving Equation (3) yields In considering the two-echelon supply chain issues, t 1 and T can be expressed as In this section, we construct an inventory model that consists of the following four elements:

•
The ordering cost (OC). The retailer's ordering cost per replenishment cycle is OC = A/T; • The holding cost (HC). The retailer's holding cost per replenishment cycle is

Taking a Cash Discount
Based on the lengths of N, L, and N + L, three cases are possible: (1) L ≤ T; We discuss each case in detail below.

Case 1 L ≤ T
Here, the retailer pays off all items at time 0. The interest charged per unit time is The retailer starts selling the items from time 0 but receives money at time N. Therefore, the interest earned per unit time is Consequently, the retailer's total cost, TVC 11 (T), per unit time for Case 1 is The graphical representation for Case 1 is shown in Figure 1. (1 ) The graphical representation for Case 1 is shown in Figure 1.

Case 2 L N T L   
In this case, the retailer receives the total revenue at time L and has to pay the supplier at T+N . Hence, the interest charged per unit time is 2 12 (1 ) and the interest earned per unit time is Thus, the retailer's total cost, 12 () TVC T , per unit time for Case 2 is (1 ) ( ) ( ) The graphical representation for Case 2 is shown in Figure 2.
In this case, the retailer receives the total revenue at time L and has to pay the supplier at T + N. Hence, the interest charged per unit time is and the interest earned per unit time is Thus, the retailer's total cost, TVC 12 (T), per unit time for Case 2 is The graphical representation for Case 2 is shown in Figure 2.

Case 3 T L N 
In this case, the retailer can sell the items and receives the total revenue at time L . The annual interest earned is From the above arguments, the retailer's annual total cost, 13 () TVC T , per unit time for Case 3 is

Case 3 T ≤ L − N
In this case, the retailer can sell the items and receives the total revenue at time L. The annual interest earned is Mathematics 2022, 10, 1209 8 of 22 From the above arguments, the retailer's annual total cost, TVC 13 (T), per unit time for Case 3 is Summarizing the above cases, the retailer's total cost, TVC 1i (T), is given by At T= L, we find TVC 11 (L) = TVC 12 (L); at T= L − N, TVC 12 (L − N) = TVC 13 (L − N). Hence, TVC 1i (T) is continuous and well-defined. TVC 11 (T), TVC 12 (T), TVC 13 (T), and TVC 1 (T) are all defined on T > 0. The graphical representation for Case 3 is shown in Figure 3.

Case 1 MT 
In this case, the retailer receives the total revenue at time M . The interest charged per unit time is The interest earned per unit time is From Equations (15) and (16), the annual total cost, 21 () TVC T , is given by The interest charged per unit time is The interest earned per unit time is The interest earned per unit time is From Equations (15) and (16), the annual total cost, TVC 21 (T), is given by The interest charged per unit time is Mathematics 2022, 10, 1209 The interest earned per unit time is From Equations (18) and (19), the annual total cost, TVC 22 (T), is given by From Equation (21), the annual total cost, TVC 23 (T), is given by Summarizing the above cases, the retailer's total cost, TVC 2i (T), is given by From the above argument, the annual total cost for the retailer can be expressed as:

Solution Procedures
The main purpose of this section is to develop a solution procedure to determine the optimal cycle time T * to minimize the annual total cost for each case.

Taking a Cash Discount
In an attempt to minimize the annual total cost for each case, we developed solution procedures consisting of two cases, with three propositions in each case.

Proposition 1.
For L ≤ T, if T * 11 ≥ L, then dTVC 11 (T)/dT is a strictly increasing function of T and there exists a unique real solution T * 11 ∈ [L, ∞) such that TVC 11 (T * 11 ) is the minimum.
Proof. By Theorem 3.2.10 in Cambini and Martein [64], let q(x) = f (x) g(x) . If f (x) is a differentiable and strictly increasing function in x, f (x) ≥ 0 and if g (x) is a differentiable and strictly decreasing function in x, g (x) ≥ 0. We have shown that q(x) is a concave function; therefore, there exists a unique value of x * that minimizes q(x * ). From Equation (6), we obtain TVC 11 and Then, substituting into Equation (25), we take the first-and second-order derivations of f (T) with respect to T and obtain and Therefore, TVC 11 (T) is convex in T. The minimum value of TVC 11 (T) will occur at the point T * that satisfies Next, the first-order derivatives of TVC 11 (T) with respect to T are Proposition 2. If L − N ≤ T ≤ L, then dTVC 12 (T)/dT is a strictly increasing function of T and there exists a unique real solution T * 12 ∈ [L − N, L] such that TVC 12 (T * 12 ) is the minimum.
Proof. We first take the first-order derivative of TVC 12 (T) with respect to T and obtain Since dTVC 12 (T)/dT is also strictly increasing in T, the minimum value of TVC 12 (T) will occur at the point T * that satisfies Proposition 3. If 0 ≤ T ≤ L − N, then dTVC 13 (T)/dT is a strictly increasing function of T and there exists a unique real solution T * 13 ∈ (0, L − N) such that TVC 13 (T * 13 ) is the minimum.
Proof. We first take the first-order derivative of TVC 13 (T) with respect to T and obtain Next, we let Since dTVC 13 (T)/dT is also strictly increasing in T, the minimum value of TVC 13 (T) will occur at the point T that satisfies Proof. From Proposition 2, we first take the first-order derivative of TVC 12 (T) with respect to T and obtain From Equation (28), since L ≥ N, we have ∆ 1 < ∆ 2 .
Proof. From (28), the first-order derivatives of TVC 11 (T) with respect to T are

Taking a Permissible Delay
In this situation, the supplier offers the retailer a trade credit. The solution procedures consist of two cases in which the business relationship is maintained during the COVID-19 period, with four propositions in each case. Next, we first take the first-order derivative of TVC 2i (T) with respect to T. Then, only one case of TVC 2i (T) has a solution to We then obtain the desired results.
respectively. Next, we let Proof. The proof is similar that of Lemma 1, we omit it here.

Application Example
The practicality of the proposed model was assessed using a case study involving SMEs in Taiwan. A numerical example of this case was used to verify our analytical results, and a sensitivity analysis was used to explore trends in the optimal policies in order to obtain managerial insights for the SMEs. The COVID-19 pandemic of 2019-2021 offers a unique setting in which to examine how the supply of trade credit is impacted during a crisis that emanates from the real sector, which is radically different to a crisis that emanates from financing difficulties, such as the global financial crisis (GFC) of 2008-2009. The parallel trends of average payables during the COVID-19 period and the GFC period based on the probabilty of default of a firm are shown in Figures 4 and 5. A high probability of default is defined as 1 for the creditrisk+ of firms whose probability of default is above the median. The figures display the parallel trend of average payables for the last two years for growing firms.
Step 3. Let 1 TT nn    and repeat Steps 1-2; Step 4. If Step 5. Let (T ) (T ) nn   ; therefore, * T is the optimal solution and the minimum total cost per unit time is * TVC ( ) j T .

Application Example
The practicality of the proposed model was assessed using a case study involving SMEs in Taiwan. A numerical example of this case was used to verify our analytical results, and a sensitivity analysis was used to explore trends in the optimal policies in order to obtain managerial insights for the SMEs. The COVID-19 pandemic of 2019-2021 offers a unique setting in which to examine how the supply of trade credit is impacted during a crisis that emanates from the real sector, which is radically different to a crisis that emanates from financing difficulties, such as the global financial crisis (GFC) of 2008-2009. The parallel trends of average payables during the COVID-19 period and the GFC period based on the probabilty of default of a firm are shown in Figures 4 and 5. A high probability of default is defined as 1 for the creditrisk+ of firms whose probability of default is above the median. The figures display the parallel trend of average payables for the last two years for growing firms.

Trade Credit and the COVID-19 Crisis
In this section, we describe a model currently in use by Small-and Medium-Sized Enterprises (SMEs) in Taiwan. The COVID-19 pandemic outbreak forced changes in trade credit management. Managers need to answer the following essential question: will the economic uncertainty affect the speed at which the firm adjusts to the target trade credit ratio? Online retailers have also endeavoured to increase the willingness of Step 4. If Step 5. Let ** ( ) ( 1) (T ) (T ) nn   ; therefore, * T is the optimal solution and the minimum total cost per unit time is * TVC ( ) j T .

Application Example
The practicality of the proposed model was assessed using a case study involving SMEs in Taiwan. A numerical example of this case was used to verify our analytical results, and a sensitivity analysis was used to explore trends in the optimal policies in order to obtain managerial insights for the SMEs. The COVID-19 pandemic of 2019-2021 offers a unique setting in which to examine how the supply of trade credit is impacted during a crisis that emanates from the real sector, which is radically different to a crisis that emanates from financing difficulties, such as the global financial crisis (GFC) of 2008-2009. The parallel trends of average payables during the COVID-19 period and the GFC period based on the probabilty of default of a firm are shown in Figures 4 and 5. A high probability of default is defined as 1 for the creditrisk+ of firms whose probability of default is above the median. The figures display the parallel trend of average payables for the last two years for growing firms.

Trade Credit and the COVID-19 Crisis
In this section, we describe a model currently in use by Small-and Medium-Sized Enterprises (SMEs) in Taiwan. The COVID-19 pandemic outbreak forced changes in trade credit management. Managers need to answer the following essential question: will the economic uncertainty affect the speed at which the firm adjusts to the target trade credit ratio? Online retailers have also endeavoured to increase the willingness of

Trade Credit and the COVID-19 Crisis
In this section, we describe a model currently in use by Small-and Medium-Sized Enterprises (SMEs) in Taiwan. The COVID-19 pandemic outbreak forced changes in trade credit management. Managers need to answer the following essential question: will the economic uncertainty affect the speed at which the firm adjusts to the target trade credit ratio? Online retailers have also endeavoured to increase the willingness of customers to place an order by addressing the risk-adjusted return on loans (direct fiscal transfers to borrowers to help reduce their credit risk; moratoriums on loan payments). The changes in the price of a product play a vital role in customers choosing the right kinds of products, and costs are sometimes affected by the fraction of the payment delayed. Another change in the strategy for managing receivables from customers is the discount rate policy. Sales were discontinued at any price, which was connected to the offering of additional discounts or extensions to trade credit. During the COVID-19 pandemic, retailers (suppliers) expected to quickly receive payment from customers (retailers). Government assistance for firms comes in the form of loan guarantees that increase firms' access to credit as a way of loosening liquidity constraints. On the demand side, trade credit represents the firm's access to capital, especially for SMEs. The hybrid (trade credit and discount rate) policy responses to COVID-19 may entice firms provided that the trade credit is lower in periods of lessrestrictive bank credit. However, given the high degree of integration of supply chains worldwide, multilateral collaboration and coordinated interventions among economies are imperative to ensure no disruptions in supply chains, help financially constrained businesses survive the pandemic, and minimize unfavorable consequences on industrial structures in the long term.
The most common terms for the use of trade credit require a retailer to make a payment within 7, 30, 60, 90, or 120 days. A percentage discount is applied if payment is made before the date agreed upon in the terms. The aim of these trade credit activities is to build long-term relationships with customers and suppliers. Figure 6 shows the trade finance in emerging markets during COVID-19. The retailer has offered a variety of trade credit agreements and the contract consists of six items: (1) a financing arrangement for the customer; (2) the customer repays the lender on the terms of the original payment (e.g., 60 days); (3) the lender pays the retailer upon approval of the invoice; (4) a financing arrangement for the manufacturer; (5) the manufacturer repays the lender on the terms of the original payment (e.g., 90 days); and (6) a commercial agreement. offering of additional discounts or extensions to trade credit. During the COVID-19 pandemic, retailers (suppliers) expected to quickly receive payment from customers (retailers). Government assistance for firms comes in the form of loan guarantees that increase firms' access to credit as a way of loosening liquidity constraints. On the demand side, trade credit represents the firm's access to capital, especially for SMEs. The hybrid (trade credit and discount rate) policy responses to COVID-19 may entice firms provided that the trade credit is lower in periods of less-restrictive bank credit. However, given the high degree of integration of supply chains worldwide, multilateral collaboration and coordinated interventions among economies are imperative to ensure no disruptions in supply chains, help financially constrained businesses survive the pandemic, and minimize unfavorable consequences on industrial structures in the long term.
The most common terms for the use of trade credit require a retailer to make a payment within 7, 30, 60, 90, or 120 days. A percentage discount is applied if payment is made before the date agreed upon in the terms. The aim of these trade credit activities is to build long-term relationships with customers and suppliers. Figure 6 shows the trade finance in emerging markets during COVID-19. The retailer has offered a variety of trade credit agreements and the contract consists of six items: (1) a financing arrangement for the customer; (2) the customer repays the lender on the terms of the original payment (e.g., 60 days); (3) the lender pays the retailer upon approval of the invoice; (4) a financing arrangement for the manufacturer; (5) the manufacturer repays the lender on the terms of the original payment (e.g., 90 days); and (6) a commercial agreement.

Numerical Example
Base settings were established for the model by conducting interviews and surveys with relevant staff in the firm. In the current COVID-19 pandemic situation, the supplier offers advance payments to the firm so that they will not cancel the order. Due to the shortages in demand, the supplier offers a discount rate that is dependent on the number of installments. The firm also offers delays in payments for customers who do not have transportation and goods available. The values presented here were altered to preserve the confidentiality of the commercial information.

Numerical Example
Base settings were established for the model by conducting interviews and surveys with relevant staff in the firm. In the current COVID-19 pandemic situation, the supplier offers advance payments to the firm so that they will not cancel the order. Due to the shortages in demand, the supplier offers a discount rate that is dependent on the number of installments. The firm also offers delays in payments for customers who do not have transportation and goods available. The values presented here were altered to preserve the confidentiality of the commercial information.

Sensitivity Analysis
The numerical example presented in Tables 2 and 3 were used to assess the effects of changes to system parameters (A, D, P, p, M, N, L, α, r, θ, c, and h) on the values T * , TVC 1 (T * 11 , TVC 1 (T * 12 , and TVC 1 (L − N). Each parameter was adjusted separately (i.e., the other parameters were left unchanged) by +50%, +25%, −25%, or −50%. Our analytical results in Table 4 permit the following interesting observations and managerial insights that could be used to guide decision-making:

•
The effect of decreasing the cost parameters (A, D, P, and N) would lead to a decrease in the total cost per unit time. In other words, if the costs could be reduced, then the enterprise would be able to earmark more money for the downstream trade credit period. This would also lead to a corresponding indirect increase in total profit per unit time due to decreased overall costs and/or increased sales; • The effect of decreasing the change to θ on the value of TVC 1 (T * 11 , TVC 1 (T * 12 , and TVC 1 (L − N) is minimal; that is, a decrease of 22.472%, 22.431% and 21.61%. This indicates that attempts to increase total profits per unit time should focus on lowering the deterioration of items; • In terms of holding cost parameters, increasing the values of the parameter h led to a corresponding decrease in T * . This is an indication that the length of replenishment cycle times could be shortened to prevent an increase in holding costs; • Decreasing the cost parameters (α, r) would lead to increase in the total cost per unit time. This indicates that if there were an increase in the cash discount rate, then the firm should use offers and discounts to drive customer loyalty and sales. Nonetheless, the amount spent on cash discounts could be increased to stimulate demand; • An increase in the defect parameter (I k or I e ) led to a corresponding increase in the total cost per unit time. This is an indication that the manufacturer can accumulate revenue by selling items and by earning interest and interest charges to reduce their finance risk. Table 2. Let us consider an inventory system with the following data for Example 1-3.  Table 3. The optimal results of T * and TVC * .

Example Conditional Expressions Results
T * TVC(T * )   Figure 7 compares the full delay in payments policy with the cash discount policy. It indicates that the cash discount policy in a general supply chain model in the COVID-19 situation is determined by each member's purchase quantity and price. amount and the due date through a loan service; for instance, coronavirus-related loan forgiveness options lawfully and duly declared during a COVID-19 pandemic national emergency.
(v) SMEs often have a limited number of suppliers. Firms are particularly vulnerable to the disruption of business networks and supply chains. Connections to larger operators (e.g., MNEs) and the outsourcing of business services are critical to their performance.

Conclusions
While the production of goods and services is either reduced or paused temporarily, retailers should continue to pay at-risk suppliers to ensure cash flow and supplier survival. In this paper, we provided a hybrid trade credit policy to stimulate supplierretailer business recovery during the COVID-19 period. Here, an alternative strategy to sustain business relationships through a hybrid payment system and discount facility considering the fraction of delayed payments was proposed. Two issues that need to be considered in this regard are: (1) due to the reduced default risk, the retailer should only provide a full trade credit policy to his/her customers with good credit; and (2) to reduce the risk of cash flow shortages and bad debt, the supplier should offer credit terms mixing a cash discount and trade credit to the retailer. Here, the supplier is likely to focus on maintaining business relationships through a hybrid payment system and discount rate policy. For example, the supplier may agree to a 2% discount off the retailer's purchasing price if payment is made within 120 days (during the COVID-19 period).

Managerial Insights
In real-world business, a firm's size will affect the trade credit supply and demand side. On the demand side, the frequency of use of external financing, the proportion of credit sales, and the day sales outstanding are conditioning factors of the volume of credit purchases (for trade credit demand). On the supply side, the trade credits are conditioned by cash flow generation and by the frequency of the use of loans. Next, we describe the impact of COVID-19 on business operations, the economy, and employment at the beginning of the crisis. To help firms affected by the COVID-19 pandemic to return to normal operations, banks have implemented major policies, including cutting policy rates (the discount rate on accommodations with collateral) and providing a special accommodation facility to support bank credit for SMEs. Herein, pricing is a crucial element of business, and costs are sometimes affected by the discount rate. Are companies able to pay their trade credits on time? Figure 8 indicates the percentage of trade credit balances being paid on time in each country. The percentage of on-time payments was 32%, 23%, and 16% (lower than February's values). In this paper, we explored some important managerial insights that could help managers make decisions during the post-COVID-19 recovery period: (i) The retailer should always examine the probability that a firm will default on its suppliers once a lockdown has been imposed, which varies depending on the degree of reliance on trade credit financing. A suggestion has been made for the retailer to be legally mandated to shut down during the first two months of the pandemic, which experienced by far the highest increase in defaults induced by trade credit payment obligations that had built up prior to the crisis. (ii) The supplier should offer early payment discounts in order to minimize late payments, increase customer loyalty, maximize profits, and improve supplier relationships. A suggestion has been made for the manager to be able to choose to implement a discount period with a fixed percentage of savings off of an item. (iii) As the discount is offered for the advance payment only, the retailer should often use this oppoortunity to intensify profits. A suggestion has been made for the manager to be able to choose the effective interest rate through the use of early payment discount terms. (iv) In the COVID-19 period, suppliers should offer retailers an estimate of the payment amount and the due date through a loan service; for instance, coronavirus-related loan forgiveness options lawfully and duly declared during a COVID-19 pandemic national emergency.
(v) SMEs often have a limited number of suppliers. Firms are particularly vulnerable to the disruption of business networks and supply chains. Connections to larger operators (e.g., MNEs) and the outsourcing of business services are critical to their performance.  Figure 7 compares the full delay in payments policy with the cash discount policy. It indicates that the cash discount policy in a general supply chain model in the COVID-19 situation is determined by each member's purchase quantity and price.

Managerial Insights
In real-world business, a firm's size will affect the trade credit supply and demand side. On the demand side, the frequency of use of external financing, the proportion of credit sales, and the day sales outstanding are conditioning factors of the volume of credit purchases (for trade credit demand). On the supply side, the trade credits are conditioned by cash flow generation and by the frequency of the use of loans. Next, we describe the impact of COVID-19 on business operations, the economy, and employment at the beginning of the crisis. To help firms affected by the COVID-19 pandemic to return to normal operations, banks have implemented major policies, including cutting policy rates (the discount rate on accommodations with collateral) and providing a special accommodation facility to support bank credit for SMEs. Herein, pricing is a crucial element of business, and costs are sometimes affected by the discount rate. Are companies able to pay their trade credits on time? Figure 8 indicates the percentage of trade credit balances being paid on time in each country. The percentage of on-time payments was 32%, 23%, and 16% (lower than February's values). In this paper, we explored some important managerial insights that could help managers make decisions during the post-COVID-19 recovery period: (i) The retailer should always examine the probability that a firm will default on its suppliers once a lockdown has been imposed, which varies depending on the degree of reliance on trade credit financing. A suggestion has been made for the retailer to be legally mandated to shut down during the first two months of the

Conclusions
While the production of goods and services is either reduced or paused temporarily, retailers should continue to pay at-risk suppliers to ensure cash flow and supplier survival. In this paper, we provided a hybrid trade credit policy to stimulate supplier-retailer business recovery during the COVID-19 period. Here, an alternative strategy to sustain business relationships through a hybrid payment system and discount facility considering the fraction of delayed payments was proposed. Two issues that need to be considered in this regard are: (1) due to the reduced default risk, the retailer should only provide a full trade credit policy to his/her customers with good credit; and (2) to reduce the risk of cash flow shortages and bad debt, the supplier should offer credit terms mixing a cash discount and trade credit to the retailer. Here, the supplier is likely to focus on maintaining business relationships through a hybrid payment system and discount rate policy. For example, the supplier may agree to a 2% discount off the retailer's purchasing price if payment is made within 120 days (during the COVID-19 period).
The results of this paper show that the retailer can optimize the replenishment cycle, discount rate, and time of prepayment for export items. Furthermore, we established retailer ordering policies that are given as solution procedures to determine the optimal solution under various conditions and provide a simple way to determine the optimal replenishment cycle time. The results of this paper clearly support the notion that an increase in the retailer's total cost will occur when discount rate, prepayment, and trade credit strategies are implemented wisely. The analytical formulations of the problem on the general framework described have been given. Despite the transition to cash sales in SMEs, sales with a large amount of trade credit were strongly limited, especially for new customers. In practice, suppliers allow customers a fixed period in which to settle the payment without penalty in order to increase sales and reduce on-hand inventory. The resulting nonlinear model was solved by the mathematical 12.0.0 software, and numerical examples were presented in order to illustrate the model. Demand patterns constitute an important topic to be explored in future research.