2nd INTERNATIONAL CONFERENCE ON SUPPLY CHAINS
A mathematical programming approach to supply chain network design with financial considerations
Pantelis Longinidis1andMichael C. Georgiadis2
Department of Engineering Informatics & Telecommunications, University of Western Macedonia, Kozani, Greece
,
Abstract
A successful operation of a supply chain network (SCN) requires a healthy financial operation that supports and assists production and distribution operations. Financial performance and credit solvency are two dimensions that characterize the status of the financial operation. This paper introduces a mathematical model that integrates financial performance and credit solvency modelling with supply chain network design (SCND) decisions under economic uncertainty. The developed multi-objective Mixed-integer Non Linear Programming (moMINLP) model enchases financial performance through economic value added (EVA™) and credit solvency through a valid credit scoring model (Altman’s Z-Score). The applicability of the model is illustrated by using a real case study. The model could be used as an effective strategic decision tool by supply chain managers, supporting their decisions with figures and indexes convenient for financial managers.
Keywords:supply chain network design, financial performance, credit solvency, economic value added (EVA™), Altman’s Z-Score, weighted average cost of capital (WACC).
1. Introduction
SCN management has become for modern companies a strategic prioritythat initially ensures sustainability and then profitability, growth and competitiveness (Chen et al., 2004; Li et al., 2006; Tan et al., 1999; Tracey et al., 2005). Academia has developed several optimization models aiming to support SCN decision making (DM). A relatively large number of these models deal with the design of SCNs, a process of determining the infrastructure (e.g. plants, warehouses, distribution centers, transportation modes and lanes, production processes, etc.) that will be used to satisfy customer demands. These models are strategic in scope, use a time horizon of months or years, and typically assume little or no uncertainty with the data (Harrison, 2001).
A variety of recent SCND models exist in the optimization literature ranging from single objective deterministic modelsto multiple objective stochastic models(see (Klibi et al., 2010; Melo et al., 2009)and references therein). However, the vast majority of these models ignores corporate financial decisions (Comelli et al., 2008; Gupta and Dutta, 2011; Klibi et al., 2010; Shapiro, 2004).Integration of financial decisions in optimization models allows for the systematic assessment of the impact of production decisions in the financial operation and further selects their ideal combination thus providing a competitive advantage in the company (Guillén et al., 2006; Laínez et al., 2009). Neglecting financial issues may have undesirable negative impacts for a firm, as it may lead to suboptimal or even infeasible overall plans for the whole SCN (Puigjaner and Guillén-Gosálbez, 2008a).
With the absence of financing, expansion in new emerging markets is hard to accomplish whereas investment in new production processes, new production equipment, new innovative products, is restricted and thus the sustainability and growth of the SCN is jeopardized. Financial performance and credit solvency are two semantic pillars that have a discernible contribution on the SCN’s ability to attract and earn the necessary funds.Although considered together, financial performance and credit solvency are not necessary moving to the same direction as each one has a different fundamental objective. The former focuses on increasing the wealth (profits, net present value of stocks, shareholder value, etc.) while the latter on minimizing the default possibilities.
This paper aims to enrich the SCND literature by presenting a robust SCN design model capable of capturing the trade-offs between financial performance and credit solvency under economic uncertainty. By providing a set of Pareto optimal SCN configurations, the model will assist managers in strategic DM.
The rest of the paper is structured as follows. Section 2 reviews prior studies in the field while Section 3 presents the SCN design problem and its mathematical formulation. The applicability of the proposed model is illustrated, through a case study, in Section 4 followed by concluding remarks, managerial implications and further research directions.
2. Prior Research
Although many researchers have highlighted the importance of financial considerations in SCN modelling (Hammami et al., 2008; Melo et al., 2009; Papageorgiou, 2009; Shapiro, 2004) very few research contributions can be found in the literature. SCN models dealing with financial issues might be divided into: (a) those where financial issues are known parameters used in constraints and in the objective function and (b) those where financial issues are endogenous variables modelling a financial operation and being optimized.
Regarding the former literature stream, Canel and Khumawala (1997) provided an efficient branch and bound procedure for solving the uncapacitated multi-period international facilities location problem. Financial incentives, exchange rates, taxes and tariffs were the financial parameters incorporated in their 0-1 mixed integer problem that aimed to determine: (1) in which countries to locate manufacturing facilities; (2) quantities to be produced at these facilities; and (3) the quantities to be shipped from manufacturing facilities to the customers. A budget constrained dynamic, multiple objective, MILP model was proposed by Melachrinoudis and Min (2000). The model aimed to determine the optimal timing of relocation and phase-out in a multiple planning horizon. In a similar vein, Wang et al. (2003) introduced a budget constrained location problem in which the opening of new facilities and closing of existing facilities was considered simultaneously. The objective was to minimize the total weighted travel distance for customers and due to the model’s NP-hardness the authors developed three heuristic algorithms to solve the problem. Avittathur et al. (2005) presented a model for determining the optimal locations of distribution centers based on trade-offs between central sales tax structure and logistics efficiency in the Indian context. The model was initially formulated as a MINLP problem and then it was approximated to a MIP problem. Simulation experiments showed that the central sales tax rate is an important driver of the optimal number of distribution centers required. Melo et al. (2006) presented a dynamic multi-commodity capacitated facility location model. The model was formulated as a MILP problem that consider simultaneously many practical aspects of SCND such as external supply of materials, inventory opportunities for goods, distribution of commodities, storage limitations and availability of capital investments which was the financial aspect incorporated in the model. In each time period, there was a limited amount of capital for capacity transfers, for shutting down existing facilities and/or for setting up new facilities. This amount was given by a budget initially available as a parameter. Tsiakis and Papageorgiou (2008) presented a deterministic MILP model for the optimal configuration of a production and distribution network. The objective was to minimize the total cost across the network and financial constraints for exchange rates and duties were incorporated in the model. Hammami et al. (2009) proposed a SCND model that integrated all the relevant components that characterize the delocalization problems, as identified in Hammami et al. (2008). The model was multi-product, multi-plant, and multi-echelon and was formulated as a MILP. Financial aspects in this model were transfer pricing, allocation of suppliers’ costs and transportation cost allocation. Sodhi and Tang (2009) presented a stochastic linear programming SC planning model similar to the asset-liability management model. Cash flow management and borrowing constraints were the financial aspects of the model which aimed at maximizing the expected present value of the net cash in a given planning horizon.
Concerning the latter literature stream, Romero et al. (2003) build a deterministic multi-period mathematical model for the batch chemical process industry that combined scheduling and planning with cash flow and budget management. Yi and Reklaitis (2004) presented a two level parametric optimization model at plant level for the optimal design of batch storage networks that integrated production decisions with financial transactions through cash flow assignment in each production activity. In the same vein, Badell et al. (2004) proposed an unequal multi-period deterministic MILP model for the batch process industries that integrated advanced planning and scheduling at plant level with cash flow and budgeting. Guillén et al. (2006; 2007) introduced a deterministic MILP model, for a multi-product, multi-echelon chemical SC, which optimized planning/scheduling and cash flow/budgeting decisions simultaneously. The model was multi-period and its objective function was the change in company’s equity, a novel feature against previous models. Laínez et al. (2007) proposed a deterministic MILP model for the optimal design of a chemical SC based on holistic models that covered both the process operations and the finances of the company and aimed at maximizing the corporate value of the firm. Puigjaner and Guillén (2008b) developed a holistic agent-based system that was able to use a number of different tools such as if-then analysis rules and mathematical programming algorithms in order to capture all processes in a batch chemical SC. A budgeting model was among these features and its connection to the agent-based system was made through payments of raw materials, production and transport utilities, and the sale of products. Longinidis and Georgiadis (2011) presented a SCND model under demand uncertainty that incorporated financial statement analysis and aimed to optimized the SCN’s added value to shareholders. The problem was formulated as a MILP and its applicability was tested via a case study. Nickel et al. (Nickel et al., 2012) considered a multi-period multi-commodity stochastic SCND problem with financial decisions and risk management. The proposed MILP model aimed at maximizing the total financial benefit of the SCN and incorporated uncertainty in demand and interest rates.
3. Problem Definition and Mathematical Formulation
3.1 Problem Statement
A company wide, multi-product, multi-period, SCN with four-echelons is considered, as shown in Fig. 1. Plants are in fixed locations and can produce any product included in company’s portfolio while their production capacity and availability of production resources is subject to certain constraints. A number of customer zones existed in fixed locations and with forecasted product demand patterns that should be satisfied by establishing a network of warehouses and distribution centers. Potential warehouses and distribution centers have specified maximum material handling capacities. Warehouses can be supplied from more than one production plant and can supply more than one distribution centre. In the same manner, each customer zone can be supplied from more than one distribution centre. Inventories can be kept in plants, warehouses and distribution centers based on the customer service level policy.
Figure 1. The supply chain network considered in this study
The design and operation of the SCN yields earnings and costs. Earnings are created by sales of products to customer zones whereas costs by establishment of warehouses and distribution centers, production and transportation of materials, handling of materials at warehouses and distribution centers. Both earnings and costs have a direct effect on company’s financial performance and credit solvency and are presented in its income statement and balance sheet.
These two financial statements interact via the transfer of retained earnings form the income statement to the right side of the balance sheet. But in order to satisfy the basic equation of the balance sheet (left side equals right) an analogous increase should take place in its left side. One part increases cash and the remaining increases receivable accounts, where this analogy is determined by both market conditions and company’s credit policy. Fig. 2 presents a typical pair of these statements along with their interaction illustration.
Figure 2.A typical income statement and balance sheet
The SCN decisions to be determined by the proposed model are:
a. The number, location and capacity of warehouses and distribution centers to be set up
b. The transportation links that need to be established in the network
c. The flows of materials in the network
d. The production rates at plants
e. The inventory levels at each plant, warehouse and distribution centre
f. The level of leverage
g. The level of equity
h. The level of fixed assets
i. The level of current assets
such as the average expected financial performance and credit solvency metrics are optimized, under all economic scenarios, over the planning horizon.
3.1.1 Economic Uncertainty
Economic uncertainty is modelled by employing the notion of economic cycle. Economic cycle is divided into three stages, namely, boom, stagnation, and recession, each of which has several macroeconomic, financial, and market conditions whose deviation express to a large extend the economic uncertainty. In our model seven parameters are uncertain reflecting the uncertain economic environment including product demand, short-term and long-term interest rates, risk-free rate of interest, expected return of the market, underwriting cost, and market liquidity.
During a boom period households and firms have an increased purchasing power and their consumption is increasing resulting in excessive demand for products and services. Short-term and long-term interest rates are decreasing as they incorporate less risk of borrowers’ default. Risk-free rate of interest, which is usually the interest rate of a Treasury bill, is decreasing as the intensive economic activity yields more taxes for the state and thus the risk of default is decreasing. Expected return of the market, which is usually the return of the most representative stock market index, is increasing as investors oversee that this pick in economic activity will provide them more dividends and capital gains. Underwriting cost, which is the cost of issuing new equity in capital markets and raising capital for investment purposes, is decreasing as the underwriters’ risk of holding the unsold underlying securities is low and the competition in the underwriting industry is immense in a capital market with fierce investing interest. Market liquidity, which is the cash, instead of checks, notes and credits, used to pay expenses, is increasing as financial institutions are less hesitant to provide money to both households and firms. On the other hand, during a recession period all the aforementioned parameters are moving to the contrary direction. In a stagnation period the deviations in these parameters is minor and the governing rule is that the past shapes the future.
Economic uncertainty is incorporated through a scenario approach that contains both “wait-and-see” and “here-and-now” decisions. The latter decisions are implemented at the initial stage of the planning period and are those concerning the structure of the SCN (see decisions (a)–(b) in Section 3.1). The former decisions are implemented when additional uncertainty information becomes available at some future time and are those concerning operation of the SCN (see decisions (c)–(i) in Section 3.1). In such problems the postulated scenarios are typically of the form shown in Fig. 3. Here the information pertaining to economic uncertainty in a given period becomes available at the end of the preceding period resulting in each scenario branch breaking into multiple branches at these points. In many cases there is little or no economic uncertainty regarding the very first period resulting in a single scenario branch over this period as shown in Fig. 3.
Figure 3. Scenarios for problems involving both “here-and-now” and “wait-and-see” decisions
All aforementioned parameters are assumed to vary as piecewise constant functions of time over a number of time periods of given duration. The uncertainty in these parameters is taken into account by postulating a number of scenarios s (), each with a potentially different set of piecewise constant parameter values. The proposed model handles any one of these scenarios by multiplying each scenario with its probability to occur () where the probability of all economic scenarios will add up to one ().
3.1.2 Economic Value Added (EVA™)
Economic value added (Stewart, 1994) is a well-known and widely used index that provides investors an impartial assessment, because it overcomes the pessimistic interpretations of net income reported in the income statement, of how well the company performed (Brealey et al., 2004; Ross et al., 2006). Its calculation is given in Eq. (I), where (NOPAT) is the Net Operating Profits after Taxes reported in the income statement and (WACC) is the Weighted Average Cost of Capital, a figure expressing, in general, the real costs associated with the main sources of capital employed by the company (Ogier et al., 2004).
(I)
Since its introduction, EVA™ has received great popularity among financial practitioners and analysts and moreover various companies’ surveys reported great improvements by its implementation (Kleiman, 1999; Lovata and Costigan, 2002; Young, 1997). Because of its widespread application and significant financial impact, EVA™ has recently stimulated the interest of academics specializing in SCN modelling. Although the lion share of SCN design and operation/planning models featuring a cost minimization objective (Melo et al., 2009; Mula et al., 2010), it is argued that sustainable value creation should gradually substitute cost and profit objective functions (Hofmann and Locker, 2009; Klibi et al., 2010).