400g OPTIMAL DESIGN OF BATCH-STORAGE NETWORK WITH FINANCIAL TRANSACTIONS AND CASH FLOWS

This paper presents an integrated analysis of production and financing decisions. We construct a model in which a cash storage unit is installed to manage the cash flows associated with production activities such as raw material procurement, process operating setup, inventory holding costs and finished product sales. Temporary financial investments are allowed to increase profit. The production plant is modeled by the BatchStorage Network model with Recycle Streams developed by Yi and Reklaitis (2003). The objective function of the optimization is minimizing the opportunity costs of annualized capital investment and cash/material inventory minus the benefit to stockholders. The major constraints of the optimization are that the material and cash storage units must not be depleted. A production and inventory analysis formulation, the periodic square wave (PSW) model, provides useful expressions for the upper/lower bounds and average levels of the cash and material inventory holdups. The expressions for the Kuhn-Tucker conditions of the optimization problem are reduced to a subproblem and analytical lot sizing equations. This subproblem is then decomposed into two separable concave minimization network flow problems whose solutions yield the average material and cash flow rates through the networks. The production and financial transaction lot sizes and startup times can be determined by analytical expressions after the average flow rates are already known. We show that, when financial factors are taken into consideration, the optimal production lot and storage sizes are smaller than is the case when such factors are not considered. An illustrative example is presented to demonstrate the potential of this approach. . Introduction Most production planning and scheduling models developed to date in process system engineering endeavor to identify a plan or schedule that minimize the overall cost while satisfying production capacity and demand constraints. A key assumption of these models is that an unlimited amount of cash is available. In practice, however, cash is usually the scarcest resource and cash availability is an important factor influencing the feasibility of a production plan or schedule. It is commonplace for a planned production to be unrealizable for a period of time due to a lack of cash to cover the production costs, resulting in other resources being under-utilized during that period. Then, when the cash does become available, overproduction must be conducted to fill backorders. These inefficiencies can cause substantial loss of profit. In fact, every aspect of production involves financial transactions and cash flows. Manufacturers purchase raw materials for production purposes, creating accounts payable owed to suppliers. The actual disbursement of cash occurs when the payment medium used to pay for the purchase, such as a check, is redeemed through the bank system. Raw materials are converted into finished products by consuming operational utilities that incur costs associated with their purchase or production. The finished product inventory is converted into accounts receivable as customers make purchases on credit. Receivables are then collected from customers remitting payment to the company. Cash is received when the payment medium, such as a check, is redeemed through the bank system. In the mean time, the company must pay taxes, salaries, and disburse loans. To prevent temporary cash shortages in some circumstances, new loans must be arranged. If there is excess cash, temporary investment in marketable securities should be considered to increase income. If operating cash flows are not well managed, seemingly profitable firms may experience financial strains that could potentially lead to bankruptcy. For example, if too many resources are tied up in inventory or accounts receivable, then even a profitable company may not be able to pay its bills. Therefore, it is essential to consider cash flow when making production planning and scheduling decisions. A successful firm manages its operations so as to optimize both profit and cash flow. Yi and Reklaitis (2000) developed a novel production and inventory analysis method called the periodic square wave (PSW) method and used it to determine the optimal design of a parallel batch-storage system. They subsequently extended the PSW formalism to model the more complicated plant structure of a sequential multistage batch-storage network (Yi and Reklaitis, 2002). In another study (Yi and Reklaitis, 2003), the same authors suggested a non-sequential network structure that can deal with recycled material flows in a plant site. In the present study, we extend the batch-storage network model suggested by Yi and Reklaitis (2003) to include both the cash storage and the financial transactions required to support the production activities. In the proposed model, all production activities are accompanied by financial transactions in which the appropriate amount of cash is withdrawn from the cash storage to pay for the costs. Cash is inputted to the storage after delivery of the finished product to consumers. The cash inventory should be managed so as to ensure that it is not depleted. The objective function of the optimization is minimizing the opportunity costs of annualized capital investment and cash/material inventory minus the benefit to stockholders. Definition of Parameters and Variables We use the plant structure introduced by Yi and Reklaitis (2003). Suppose that there exists a cash storage unit that, through financial transactions, operates the chemical plant composed of batch process setIand material storage unit set J, as depicted in Figure 1. Let set N with subscript n represent the set of temporary financial investments in marketable securities and set O with subscript o represent the set of stockholders. Corporation income tax is usually proportional to net profit and is thus considered as a payment to a fictitious stockholder without loss of generality. Sales tax, which is usually proportional to sales revenue, is collected from customers when finished products are delivered to them and is paid to the IRS (Internal Revenue Service) yearly. In chemical companies, total labor cost is usually proportional to total sales revenue. We ignore the cash flow of labor costs in the present study because it is treated in the same way as sales tax. Note that the setup cost usually includes the operating labor cost. Figure 1. Cash Storage and Financial Transactions The incoming cash flows into the cash storage unit are: CF1) Collection of account receivable after collection drifting time j m t ∆ from shipping of the finished product to consumer m. (Sales tax is included.) CF2) Return of temporary financial investment n at interest rate n κ ($/$/year) after investment period n t ∆ . The outgoing cash flows from the cash storage unit are: Revenue Sales Purchase Material Raw Storage Cash rs Stockholde to Dividend Cost Setup Purchase Material Raw Cost Setup Process Investment Investment of Return n E ) 1 ( n n n t E ∆ +κ