Modelling Financial Flow of the Supply Chain

Modelling Financial Flow of the Supply Chain M.H Jahangiri 1, F.Cecelja 2 1 Department of Chemical and Process Engineering, University of Surrey, UK 2 Department of Chemical and Process Engineering, University of Surrey, UK Abstract - Many works have been done on the product flow ofthe supply chain whereas there is a little research works on the financial aspect of the supply chain. Moreover, bullwhip effect like lead time is usually considered on the product flow of the supply chain and no literatures review this effect on the cash flows. In this paper, the flow of cash in a supply chain is considered from the manufacturer point of view who receives money from its customers and makes payment to the suppliers.astochastic model to maximise firm s profit and to find the best strategy of paying payment is developed.furthermore,weinvestigatethe effect of late payment onthe firm s profit withinthe supply chain.finally, the effect oflogistic bullwhip on the cash flow and firm s profit is investigated. Keywords: Cashinflow,Cash outflow, Bullwhip effect, Lead time, Supply chain management INTRODUCTION Supply chainconsists of coordination and corporationamong business partners to deliver a product or information from the point of raw material to the final customers [9].Two flows is usually defined on the supply chain: the product flow flowing downstream toward customers and cash flow flowing upstream towards the raw material suppliers[9]. However, one of the main differences between the cash flow and product flow may happen during the normal operation wherethe product flow operates normally within the supply chain whilethe cash flow may not. Moreover, keeping product in stock imposes holding cost to the firm and decreases profit while keeping cash may increase profit by earning interest [4]. Obviously, it is critical to manage both flows on the supply chain simultaneously to have a smooth supply chain and to increase supply chain profitability [7]. Many studies have been done on the product flowand transportation whereas very little attention given to the cash flow on the supply chain[6]. Cash flow on the supply chain can be classified into two types, cash inflow and cash outflow. Cash inflow, receivables,is the amount of cash that each firm receives while cash outflow, payables, is the amount of cash thateach firm should pay [4]. Basically, each firm is desirous to receive its receivables earlier to manage its payments to maximize the profit however, the time of receivables is uncertain. Therefore, the firm tries to understand the exact time and amount of received money. On the other hand, firm s cash outflow can be paid before due date with the normal value or after due date with the penalty value. The time of payment not only affects the firm s profit but also will be propagated through the whole supply chain partners. Morover,unforeseen events called bullwhip effect such as lead time and demand variation not only affect logistic supply chain but also cash flow supply chain. Therefore, this study tries to develop a mathematical model for cash inflow and outflow of the firm to maximise the profit by optimising the time of payment. Finally, the effect of lead time as a logistic bullwhip effect is investigated on the cash flow of the supply chain. CASH FLOW ON THE SUPPLY CHAIN Based on the available literatures, researches have been done on the design and optimization of the product flow on the supply chain whereas cash flow has not yet attracted the attention of researchers even though it is very important and has a great resemblance to the material flow [1], [2], [4], [6]. However, recently, more and more researchers and economists are emphasizing the importance of managing the financial supply chain, the counterpart of the physical supply chain [4], [5], [6], [7].Gupta and Dutta (2011) measured cash outflow from the viewpoint of a wholesaler who receives finished products from several manufacturers and then distribute these products to several retailers. Theyestablished an integer-programming model to minimize the net present value of the payment and to schedule the time of payment.based on their model, the amount paid for invoice may take one of the following three values: Where is the set of all invoices, denotes the amount paid for invoice at time, is the face value ofthe invoice, is the discount rate of the invoice applied if the invoice paid before, is the penalty rate for invoice applied if the payment for invoice is not made within a due date, is the time the invoice was generated by upstream partner, is due date for invoice,t is the time that invoice is paid. On (1), the first statement,, illustrates the amount of invoice in discount rate if it is paid on or before,the second statement,, shows the normal value of the invoice when it is paid after but before due date and the third statement,,demonstrates that the penalty value of invoice when it is paid after due date.the present value of denoted by is where is the daily interest rate. The wholesaler s objective function is to minimize the total 978-1-4799-6410-9/14/$31.00 2014 IEEE 1071

present value of the cash outflow made against all invoices, thus Where is considered as the number of future days representing the planning horizon, is a decision variable that equals to1 if the invoice k is paid on day t otherwise it is 0. The constraint 3 shows that each invoice needs to be paid only once during the planning time horizon while constraint 4 used to show that the invoice cannot be paid before it is generated. SUPPLY CHAIN INTEGRATED MODEL In this section, for the sake of simplicity one simple combinationof three-tier supply chain is chosen.this supply chain consists of supplier, manufacturer and customer. From the manufacturer points of view, two kinds of cash flow are defined, the cash inflow comes from customer and cash outflow goes to the supplier. Therefore, manufacturer defines the time horizon that covers all cash flows. Fig. 1 illustrates this time horizon for the manufacturer within the supply chain. As can be seen from the fig. 1, the cash flow process starts at time where the supplier s invoices are issued and finish at T where all invoices must be paid. Moreover, and are the due date of supplier s and manufacturer s invoices respectively,also is the time that manufacturer s invoices are generated. Cash inflow may not completely overlap with cash outflow in some periods therefore, it is vital for the firm to know the amount of available money in the firm on each day of time horizon to manage cash outflow andto cover all expenses. In order to understand the time of receiving cash inflow, different scenarios are generated. On the following section the formula for calculating cash inflow and outflow is represented. A. Cashinflow The cash inflow of the manufacturer presented on (5) consists of FVL, the face value of the short-term loan, as an external source of fund which is known and constant and, the money received from customer for delivered product. Figure 1Time horizon for firm cash flow on(6) is the summation of the money receives from customers whether on the normal value or penalty value. Moreover, the present value of normal rate and penalty rate is represented on (7) and (8) respectively. Normal payable Cashoutflow Penalty payable A decision variable on (6)is defined to show that the invoice is received on normal or penaltyvalue. In fact, if the invoice receives before due date, is equal to 1 otherwise it is zero.all parameters of the model are given in table 1. On the other hand, as mentioned earlier the firm shouldknow the amount of money available in the firm on each day within the time horizon to manage their payables. Equation (9) is used to calculate the amount of available cash on the firm on day. Normal receivable Cashinflow Penalty receivable On (9), is the total amount of available money on the firm on the day, is a variable shows that whether the invoiceon the day is received or not? B. Cashoutflow Cash outflow as shown on (10)is the summation of production cost, debt paymentand the material cost that should be paid for bought materials. 1072

The present value of the production cost denoted by consists of as the constant overhead cost and as the production cost per product unit. Regards to the material costs denoted by out2, firm has two options to pay the invoices in order to maximize the profit, pay with delay on penalty value with a possibility to invest the money in hand to earn interest or pay on due date on normal value and hence to avoid penalties [8]. The first statement on the right hand side of(12)representsthe normal value of material cost when it is paid before due date and the second statement illustrates the penalty value. Moreover, the decision variable b is defined to show whether the invoice is paid on normal value or on penalty value. For the parameters see table 1. Finally,PL on (10)is the loan repayment when the firm use external source of fund. Based on the HSBC business banking, the business short term loan can be repaid by the agreement between 12 months and 10 years. Therefore, the short term loan repayment cash of the firm is calculated by the following formula. Where is the monthly interest rate, is the face value of loan, is the number of month that loan should be paid based on the agreement. However, in order to manage the cash outflow, the firm requiresto have enough cash in hand on the time of payment therefore, the amount of available cash on the time of each payment is calculated below. As can be seen, is the amount of cash available on the time of paying invoice, is a decision variable shows that the invoice is received on the time of paying invoice or not. Finally, it is obvious that the main goal of each firm on the supply chain is to maximize the profit by optimizing the time of payment;therefore the firm should consider cash inflow and outflow simultaneously. Equation (15) is used as an objective function of the manufacturer. I Q i c i M i p i b i s i d i r J Q j bp j s j pr j d j t'' T Table 1 Parameters of the model Set of Supplier invoices Quantity of material for invoice i Price of material for invoice i Added value for invoice i Daily penalty rate for invoice i Due date of invoice i Generating time of invoice i Time of receiving invoice i Daily interest rate Set of Manufacturer invoices Quantity of product for invoice j Due date of invoice j Generating time of invoice j Daily penalty rate of invoice j Time of paying invoice j Due date for overhead cost End of Time Horizon Subject to: The first constraint illustrates that the amount of available cash on the firm should be more than the amount ofinvoice. The second and third constraintsshow that all invoices must be paid within the time horizon T and finally the fourth constraint is used to define that all decision variables are accept value between 0 and 1. BULLWHIP EFFECT ON THE FINANCIAL SUPPLY CHAIN In this section, the effect of logistic bullwhip effect, lead time, is investigated on the cash flow of the supply chain. Lead time is defined as the length of time between the times when an order for an item is placed and when it is actually available for satisfying customer demands [9]. However, on the simple supply chain with three-tiers the lead time can be created by the supplier and manufacturer. In order to understand the effect of logistic bullwhip on the cash flow different scenarios are defined from the manufacturer point of view. The chart on fig. 2 illustrates all possible scenarios that lead time may affect firm s cash flow where parameter is the expected time of delivery of product from supplier to the manufacturer, Rd is real time of delivery from supplier to the manufacturer, d' is delivery time from manufacturer to the customer, TT is the expected time of delivery product from supplier to the customer and is real time of delivery product from supplier to the customer. 1073

First of all, if positive lead time of manufacturer or supplier leads late delivery of product to the customer then the firm might face customer dissatisfaction therefore, manufacturer is forced to apply customer discount in order to avoid customer dissatisfaction (e.g. 1% for each day delay) therefore, positive lead time may affect manufacturer cash outflow.present value of the customer discount denoted by CD is represented on (18). On(18), k is the set of product, c is the cost of product, M is the added value for product k, Q is the quantity of sold product and T is the end of time horizon. Moreover, positivesupplier lead time not only affects cash outflow but also cash inflow of the manufacturer. In fact, manufacturer forcessupplier to pay penalties for each day delay (e.g. 1% for each day late delivery)thus it affects cash inflow of the manufacturer. Present value of supplier penalty is represented on (19). Negative supplier or manufacturer lead time may affect manufacturer cash outflow by imposing storage cost. In fact, manufacturer cannot deliver product before delivery time therefore the product should store until the time of deliverycomes to. The storage cost, ST, is shown on the (20). On the (20), b is the overhead cost for storage dd is the keeping cost per unit of product per day. Therefore, lead time also affect cash inflow and outflow of the firm on the supply chain by adding additional cost to the firm. Finally, In order to unify the equations for the profit, the decision variable and are defined to consider the effects of lead time on the cash flow and on the profit equation. Therefore:, RESULTS AND ANALYSIS In order to solve and test the model with typical data different scenarios are defined for a manufacturer company like smartphone producer with different suppliers and customers then, the model is solved in GAMS modelling tool.finally some graphsare plotted for further verification. The table 2 illustrates the range of values for parameters of the input and output of the manufacturer.the table also shows that manufacturer has two suppliers, S1 and S2 with different share 80 and 20 percentagerespectively and also two customers, C1 and C2. With the help of generating best case and worst case scenarios and customer payment history, the manufacturer knows the exact amount of cash available on the firm on each specific dayduringthe timehorizon. The Min trend on fig. 3 illustrates that on the best scenarios, the first and second receivables receive on day 10 th and 13 th respectively while this numbers on the maxtrend or worse case are 21 th and 26 th. As can be seen from fig3, there is no cash on the firm before the day 10 th therefore the firm can schedule its payment. Amountofcash( ) 15000 10000 5000 0 1 5 9 1317212529 min max Dayonthetimehorizon Figure 3 Time and amount of cash on each day Table 2 Values for model parameters Input Q i c i b i p i M i share C1 80 60 15 0.000192 40 80 C2 20 60 15 0.000192 40 20 Output Q j c j bp j pr j Share S1 60 60 10 0.000192 60 S2 40 60 10 0.000192 40 Figure 2 Supply chain lead time 1074

The effect of supplier lead time on the manufacturer s profit is quite related to the supplier share. Fig 4 shows the relationship between supplier lead time and profit based on the different supplier share. On the other hand, the manufacturer s profit drop sharply when supplier lead time is positive therefore, the manufacturer should set more penalties for the suppliers with fewer shares. On the other hand, fig. 5 helps manufacturer who faces supplier lead time to choose the best strategy for its own lead to increase the profit. As can be seen, when the manufacturer faced with the supplier with -1 day lead time then manufacturer with 1 day lead time can reach the maximum profit. In fact, manufacturer can adjust its own lead time based on the supplier lead time in order to maximize the profit. CONCLUSION The aim of this research is to consider the effect of cash flow management/optimisation on firm s profitability and further on its supply chain. Then the effect of lead time as a logistic bullwhip effect on the cash flow is investigated. In this work, the main focus so far was to quantify receivables as cash inflow that come from upstream partners and then to find out the best strategies for making payments in a way that maximise the firm s profit. Therefore, a mathematical model to maximise the firm s profit and schedule the payment is developed. Profit( ) Profit( ) 1900 1650 1400 1150 900 650 400 1200 1000 800 600 400 200 5 0 5 Supplierleadtime(day) Figure 4 Supplier lead time and Manufacture profit 0 4 3 2 1 0 1 20% 30% 40% 50% 60% 70% 80% Ls=1 Ls=0 Ls=1 Ls=2 Ls=3 all possible cases of receiving cash for the firm but also determines the amount of available cash on each day within time horizon. The results show that, the optimum time of payment is a relative function of company s weighted average cost of capital to the amount of penalty on each payment, thus sometimes it is optimum to pay the penalty and use the money internally. Finally, the effect of lead time as a logistic bullwhip effect on the cash flow is modelled. As mentioned earlier, lead time affect cash flow of the supply chain by adding additional costs such as supplier penalty, storage cost and customer discount to the firm. REFERENCES 1. CHEN, I. J. & PAULRAJ, A. 2004. Understanding supply chain management: critical research and a theoretical framework. International Journal of Production Research, 42, 131-163. 2. CHILDERHOUSE, P. & TOWILL, D. R. 2003. Simplified material flow holds the key to supply chain integration. Omega, 31, 17-27. 3. COOPER, M. C., LAMBERT, D. M. & PAGH, J. D. 1997. Supply chain management: more than a new name for logistics. International Journal of Logistics Management, The, 8, 1-14. 4. GUPTA, S. & DUTTA, K. 2011. Modeling of financial supply chain. European journal of operational research, 211, 47-56. 5. HE, M., REN, C., SHAO, B., WANG, Q. & DONG, J. Year. Financial supply chain management. In: Service Operations and Logistics and Informatics (SOLI), 2010 IEEE International Conference on, 2010. IEEE, 70-75. 6. PFOHL, H.-C. & GOMM, M. 2009. Supply chain finance: optimizing financial flows in supply chains. Logistics research, 1, 149-161. 7. PREVE, L. & SARRIA-ALLENDE, V. 2010. Working capital management, Oxford University Press, USA. 8. SHAO, J.-P., DONG, S.-H., MA, T.-Y. & WANG, D. Year. Research review on bullwhip effect controlling methods in a supply chain under uncertainty environments. In: Industrial Electronics and Applications, 2008. ICIEA 2008. 3rd IEEE Conference on, 2008. IEEE, 1803-1808 9. LI-NA, Y. & QI, X. Year. Coordinating a supply chain with material flow and capital flow integrated. In: Logistics Systems and Intelligent Management, 2010 International Conference on, 2010. IEEE, 1271-1274. Manufacturer leadtime(day) Figure5 Relationship between supplier and manufacturer lead time The time of receivables is not under control of the firm hence, different scenarios to find a feasible region for cash inflow are defined. This method of finding not only covers 1075