A holistic framework for short-term supply chain management integrating production and corporate financial planning

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Int. J. Production Economics 106 (2007) 288–306 www.elsevier.com/locate/ijpe

A holistic framework for short-term supply chain management integrating production and corporate financial planning Gonzalo Guille´n, Mariana Badell, Luis Puigjaner Chemical Engineering Department, Universitat Polite`cnica de Catalunya, ETSEIB, Diagonal 647, E-08028, Barcelona, Spain Received 7 September 2004; accepted 16 June 2006 Available online 7 September 2006

Abstract Traditional approaches for SCM usually focus on process operations and neglect the financial side of the problem. In this work we present a novel approach for holistically optimizing the combined effects of operations and finances in SCM. To achieve such integration between different business areas, it is derived an integrated model for SCM, which incorporates process operations as well as budgetary constraints. The novelty of this formulation lies not only in the insertion of financial aspects within a SC planning formulation, but also in the choice of a financial performance indicator, i.e. the change in equity, as the objective to be optimized in the integrated model. The main advantages of this mathematical formulation are highlighted through a case study, in which the results obtained by the integrated model are compared with those computed by the traditional sequential strategy, in which the operations are firstly computed and the finances are fitted afterwards. The obtained results show the importance of devising broader modeling systems for SCM leading to increased overall earnings and providing further insights on the interactions between operations and finances. r 2006 Elsevier B.V. All rights reserved. Keywords: Optimization; Supply chain management; Cash management; Finances

1. Introduction The concept of supply chain management (SCM), which appeared in the early 1990s, has recently raised a lot of interest since the opportunity of an integrated management of the supply chain (SC) can reduce the propagation of unexpected/undesirable events through the network and can influence decisively the profitability of all the members. SCM looks for the integration of a plant with its suppliers and its customers to be managed as a Corresponding author. Tel.: +34 93 401 6678; fax: +34 93 401 0979. E-mail address: [email protected] (L. Puigjaner).

whole, and the co-ordination of all the input/output flows (materials, information and finances) so that products are produced and distributed at the right quantities, to the right locations, and at the right time (Simchi-Levi et al., 2000). A large body of literature exists on SC analysis and optimization (Bok et al., 2000; Tsiakis et al., 2001; Cheng et al., 2003; Guille´n et al., 2005a, b, c, 2006). Traditional SC models focus solely on determining the profit or revenue-maximizing, or cost-minimizing production schedule in a SC that runs from suppliers to manufacturing plants to distribution facilities and finally to retail outlets. These models neglect the cash-flow consequences of the optimal production schedule, such us

0925-5273/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ijpe.2006.06.008

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opportunity costs associated with missed investment opportunities, interest on debt, etc. Until today, process operations and finances have been treated as separate problems and the modeling approaches supporting them have been traditionally implemented in independent environments. Although the need to account for financial aspects when constructing process operations models has been pointed out in the literature (Applequist et al., 2000; Shapiro, 2001; Shah, 2005), the integration of both areas has so far received little attention and is currently waiting for further study. However, the works of Romero et al. (2003) and Badell et al. (2004), which address the integration of financial aspects with short-term planning in the batch chemical process industry (CPI) are appreciated contributions to the field. At the design level, Yi and Reklaitis (2004) have also presented an integrated analysis of production and financing decisions regarding the optimal design of batchstorage networks. An integrated tool for SCM would allow managers to ‘‘play’’ with different planning alternatives taking into account all the available information and having a clear idea of the consequences of each alternative being tested. With this aid, it is possible to properly assess the impact of the process operations decisions on the financial area and to shift the slave/blind position of the business level towards a more prevalent role in SCM. This new philosophy will make managers gain a competitive advantage compared with those that check neither

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the feasibility nor the optimality of the process operations decisions from the financial viewpoint. The purpose of the present paper is to introduce budgetary considerations into a basic SC model and direct the management’s attention in the production-planning process to the more general objective of maximizing the firm’s net equity. The paper is organized as follows. First, a standard deterministic SC scheduling–planning model is presented. Then, budgeting models are reviewed, and a budgeting model suitable for SCM is described. Next, the integrated deterministic model, which merges SC operations and finances, is presented. Finally, a motivating example is introduced and the results computed by means of the integrated model are compared with those determined by the traditional sequential approach, in which the SC planning model is firstly computed and the finances are fitted afterwards. 2. Scheduling and planning The mathematical formulation presented in this work has been derived having in mind the structure of the four-echelon SC given in Fig. 1. However, the model could be extended to more complex SC structures. The aforementioned SC includes the following elements:



A set of external suppliers which provide raw materials, intermediate and final products to plants, warehouses and markets.

Fig. 1. Supply chain structure.

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A set of internal suppliers, which produce intermediate products from raw materials provided by external suppliers. A set of plants where final products are manufactured prior to being sent to warehouses. This work contemplates SCs with embedded multi-product batch chemical plants. It is considered that raw materials are transferred from stock to the process unit, and at the end of processing, products are directly transferred either to trucks to be transported to different customers or to stock. A set of warehouses where products are stored before being transported to final markets. A set of final markets where products are available to customers.

In this work, a time representation that allows the accommodation of uncertainties by running a deterministic formulation in the so-called rolling horizon mode (Reklaitis, 1982) has been adopted to address the integrated planning–scheduling of SCs with embedded batch chemical plants. That is, the operating horizon is divided into a certain number of periods, and the model with suitable demand forecasts is solved to yield scheduling/planning decisions for each period, and only those belonging to the first period are implemented. At the end of the first period, the state of the system, including inventory levels, is updated and the cycle is repeated with the horizon advanced by one period considering the demand forecast for the new period, which is now available. Therefore, the deterministic formulation next described comprises a set of planning periods, and only the first one includes the detailed

scheduling decisions with shorter time increments. Such detail period moves as the model is solved in time, thus the term rolling horizon. Moreover, the scheduling constraints provide an accurate estimation of the capacity limits of the plant for the first planning period, in which the decisions are implemented in real time. When such constraints are not added, the production rates computed by the planning formulation usually overestimate or underestimate the real plant capacity thus leading to either infeasible or suboptimal plans. In fact, historically, in complex batch chemical plants the planning business level overestimates the real plant capacity because the interactions among batches are not taken into account (Raaymakers et al., 1997). According to these authors, the performances of the plans computed at the business level and the ones really implemented in the plant may differ as much as 20–40%. The proposed model divides the planning and scheduling horizon H into a set of H1 periods where production is planned using both, known and estimated demands. The first period of the time horizon is divided into several H2 time intervals of lower length where production is scheduled (see Fig. 2). The model is to be rerun every period H1 as forecasts become real orders. Therefore, the results of the planning periods beyond the first current period H1 will never reach execution. However, they are important to be considered when solving the scheduling horizon, because one may consider the possibility of scheduling in the first planning period the production of materials needed in later periods and keep them as stock.

Fig. 2. Time representation.

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2.1. First stage: detailed scheduling Here, the detailed production schedules of the plants embedded in the SC and the transport decisions to be implemented through the nodes are computed. The first time period H1 is divided into t intervals of type H2 of lower length. Two type of constraints are considered within this first period of time, the mass balance equations and the scheduling constraints. Both sets of equations are next described. 2.1.1. Mass balance constraints These equations are necessary in order to ensure the mass balances in each of the sites embedded in the SC (internal suppliers IS, batch plants BP, warehouses WH and final markets MK). Therefore, for each time interval t the total amount of intermediate product p manufactured by an internal supplier i (QIS ipt ) plus the initial stock of p kept at i (INVIS ) must equal the amount of p ipt1 transported from i to plants j (Aijpt ) plus the final inventory (INVIS ipt ) kept at i, as stated by Eq. (1): X IS Aijpt þ INVIS 8i; p; t. (1) QIS ipt þ INVipt1 ¼ ipt j

Moreover, in every scheduling period t, the amount of raw material r transported from external suppliers e to internal suppliers i (ESIS eirt ) plus the initial inventory of r kept at i (INVIS irt1 ) must equal the amount of r consumed in the manufacture of the intermediate product p at i (QIS ipt multiplied by a mass conversion coefficient arp ), plus the final inventory of r at i (INVIS irt ), as it is expressed in constraint (2): X X IS IS ESIS QIS 8i; r; t. ipt  arp þ INVirt eirt þ INVirt1 ¼ e

p

(2) Eqs. (3) and (4) express the mass balances for the batch plants, and are similar to constraints (1) and (2). In this case, the plants can receive intermediate products either from an external or an internal supplier. In these equations, QoutBP jft represents the total amount of final product f manufactured at BP plant j during time interval t, INVBP jpt and INVjft the initial inventories of intermediate product p and final product f, respectively, kept at j, Bjkft the amount of f transported from batch plant j to warehouses k, ESBP ejpt the amount of intermediate product p transported from external suppliers e to plant j in time interval t, tij the duration of the

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journey between i and j and bfp a mass conversion coefficient. X BP QoutBP þ INV ¼ Bjkft þ INVBP 8j; f ; t jft jft1 jft k

(3) X

ESBP ejpt þ

e

¼

X

i X BP Qinjft f

Aijpttij þ INVBP jpt1

 bfp þ INVBP jpt

8j; p; t.

ð4Þ

Eq. (5) ensures the mass balance for the warehouses. Here, ESWH ekft is the amount of f provided by external suppliers e to warehouse k in time interval t, INVWH kft1 the initial inventory of f kept at warehouse k and C klft the amount of final product f sent from warehouses k to markets l. X X ESWH Bjkfttjk þ INVWH ekft þ kft1 e

¼

X

j

C klft þ INVWH kft

8k; f ; t.

ð5Þ

l

Constraint (6) represents the material balances for the markets. The markets behave as warehouses in which the depletion of materials is due to the sales of products. Therefore, for each time interval t, the amount of f purchased to external suppliers e (ESMK elft ) plus the amount of final product f coming from warehouses k (C klfttkl ) plus the initial inventory of f kept at l (INVMK lft1 ) must equal the amount of f sold at market l (Saleslft ) plus the final inventory of f at l (INVMK lft ). X X ESMK C klfttkl þ INVMK elft þ lft1 e

k

¼ Saleslft þ INVMK lft

8l; f ; t.

ð6Þ

Finally, the sales of final product p carried out in market k during time interval t (Saleslft ) are constrained to be lower or equal to the demand (7). We thus consider in this work that, unlike other works in the literature, part of the demand can actually be left unsatisfied due to capacity limitations. Saleslft pDemlft

8l; f ; t.

(7)

2.1.2. Scheduling constraints These constraints enable the computation of the initial and finishing times of all the tasks involved in the production of the batches manufactured at the plants and also ensure the feasibility of the

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corresponding schedules. The proposed formulation is derived based on a batch slot concept. With this formulation the time horizon is viewed as a sequence of batches, each of which is assigned to one particular product. The maximum number of batches that can be manufactured at each plant j can be either estimated based on capacity limitations or given by the decision-maker. Sequence decisions are linked to a binary variable X jl j f which represents the existence of a batch l j of final product f at plant j and takes the value of 1 in case l j belongs to f and 0 otherwise. 8 > < 1 if batch l j manufactured at plant j belongs to final product f ; X jl j f ¼ > : 0 otherwise X X jl j f p1 8j; l j , (8) f

X f

X jl j f p

X

X jl j þ1f

8l j oLj .

(9)

f

Thus, Eq. (8) states that a batch l j cannot belong to more than one product f, while constraint (9) is applied to ensure that non-produced batches are located at the beginning of the schedule. Although constraint (9) is not necessary, it helps computations. Indeed, by fixing the position of the nonproduced batches we get smaller branch-and-bound trees and shorter computational times. The specific position of these non-produced batches (at the beginning of the schedule) is absolutely arbitrary, and is chosen for simplicity. Concerning the production tasks performed at the plant and in order to reduce the complexity of the formulation, only the case of a zero wait policy (ZW) is here considered. Neither intermediate storage nor waiting times in the processing units are available. It is not the objective of this paper to discuss the consequences of the different transfer policies that can be found in a general batch plant. Under ZW policy, there can be no delay between the time a product batch finishes processing on stage o (TFjl j o ) and the time it commences processing on stage o þ 1 (TIjl j oþ1 ) as stated by constraint (10) TIjl j oþ1 ¼ TFjl j o

8j; l j ; ooO.

(10)

The finishing time of stage o at plant j involved in the production of batch l j (TFjl j o ) is computed from the initial time of o at j (TIjl j o ) and its operating time, which is given by the recipe of the product the batch belongs to (topjfo ), as it is expressed in

constraint (11). TFjl j o ¼ TIjl j o þ

X

topjfo  X jl j f

8j; l j ; o.

(11)

f

The ZW assumption resulting in Eqs. (10) and (11) can be easily modified in order to consider other transfer policies. As it is not the purpose of this paper to discuss the different equipment-task allocation possibilities that can be found in a batch plant, it has been also assumed that only one production line with one assigned equipment per stage is available. Therefore, stage o involved in the manufacture of batch l 0j at plant j must start after the end of the same stage o performed in any previous batch l j as expressed by Eq. (12). Let us mention at this point that the model presented here could be extended to consider other equipment-task allocations possibilities. However, this would lead to more complex formulations. 8j; o; l 0j 4l j .

TIjl 0 o XTFjl j o j

(12)

Finally, the initial and finishing times of any stage o of l j at plant j are constrained to be lower than the time horizon H provided l j is produced (constraints (13) and (14)). X TIjl j o pH  X jl j f 8j; l j ; o, (13) f

TFjl j o pH 

X

X jl j f

8j; l j ; o.

(14)

f

The total amount of product f manufactured at plant j during period t (QoutBP jft ) is calculated by adding all the batch sizes bsjf of the l j batches of f produced during period t as expressed by Eq. (15). X QoutBP bsjf  X jl j f  Y jl j t 8j; f ; t. (15) jft ¼ lj

In such equation, Y jl j t is a binary variable used to allocate batches to periods of time, and takes the value of 1 if the last stage of batch l j manufactured at plant j is finished within time interval t and 0 otherwise. If the limits of interval t 2 ½1; NT, where NT represent the total number of periods in which the scheduling horizon is divided, are denoted as T t1 and T t , the above definition can be represented by the following linear constraints: ( 1 if TFjl j O 2 ½T t1 ; T t ; Y jl j t ¼ 0 otherwise:

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X

Y jl j t ¼ 1 8j; l j ,

(16)

t

X t

TF0jl j Ot ¼ TFjl j O

8j; l j ,

Y jl j t  T t1 pTF0jl j Ot pY jl j t  T t

(17) 8j; l j ; t.

(18)

Constraint (16) ensures that each batch l j is finished within only one period of time, i.e. only one of the variables Y jl j t (say, for t ¼ t ) takes a value of 1, with all others being 0. Constraint (18) allocates each of the batches to its corresponding time interval using the defined binary variable Y jl j t . Such equation forces the auxiliary continuous variable TF0jl j Ot to 0 for all tat , while also bounding TF0jl j Ot in the range ½T t 1 ; T t . Finally, constraint (17) expresses the condition for which the summation of the auxiliary variable TF0jl j Ot over t must equal the time in which batch l j finishes its last stage O, what implies that TFjl j O ¼ TF0jl j Ot and, therefore, TFjl j O 2 ½T t 1 ; T t , as desired. Similar constraints can be derived in order to link the scheduling equations to the amount of f being manufactured at plant j during period t (QinBP jft ). In this case, a binary variable Y 0jl i t which takes the value of 1 if a batch l j is started within time interval t or 0 otherwise is defined. Therefore, constraint (19) ensures that each batch l j belongs to only one period of time, while Eqs. (20) and (21) are used to allocate l j to the correct interval period, using the auxiliary continuous variable TI0jl j Ot . X Y 0jl j t ¼ 1 8j; l j , (19) t

X t

TI0jl j Ot ¼ TFjl j O

8j; l j ,

Y 0jl j t  T t1 pTF0jl j Ot pY 0jl j t  T t

(20) 8j; l j ; t.

(21)

The total amount of product f being manufactured at plant j during period t (QinBP jft ) is finally determined by means of Eq. (22). X QinBP bsjf  X jl j f  Y 0jl j t 8j; f ; t. (22) jft ¼ lj

2.2. Second stage: production planning At the production stage, t0 periods are considered. Here, nor the exact number of batches produced neither their sequence in the manufacturing lines are calculated within every period, apart from the first

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one, but estimated by means of capacity factors. The corresponding equations (constraints (23)–(29)) are indeed equal to the ones used previously. In this case, the length of the intervals H1 for which they are defined is bigger than that of the scheduling periods H2. IS QIS H1ipt0 þ INVH1ipt0 1 X ¼ AH1ijpt0 þ INVIS H1ipt0

8i; p; t0 ,

ð23Þ

j

X

IS ESIS H1eirt0 þ INVH1irt0 1

e

¼

X

IS QIS H1ipt0  arp þ INVH1irt0 1

8i; r; t0 ,

ð24Þ

p BP QoutBP H1jft0 þ INVH1jft0 1 X ¼ BH1jkft0 þ INVBP H1jft0

8j; f ; t0 ,

ð25Þ

k

X

ESBP H1ejpt0 þ

e

¼

X

X

AH1ijpt0 t0 þ INVBP H1jpt0 1 ij

i

BP QinBP H1jft0  bfp þ INVH1jpt

8j; p; t0 ,

ð26Þ

f

X

ESWH H1ekft0 þ

e

¼

X

X

BH1jkft0 t0 þ INVWH H1kft0 1 jk

j

C H1klft0 þ INVWH H1kft0

8k; f ; t0 ,

ð27Þ

l

X e

ESMK H1elft0 þ

X

C H1klft0 t0 þ INVMK H1lft0 1 kl

k

¼ SalesH1lft0 þ INVMK H1lft0 SalesH1lft0 pDemH1lft0

8l; f ; t0 ,

8l; f ; t0 .

ð28Þ (29)

The link between the detailed scheduling variables applied to the periods H2 and those belonging to the planning intervals H1 is carried out by forcing the total amount of materials manufactured in all the t scheduling time intervals to equal the amount produced in the first planning period. Let us mention that the amount of materials manufactured, stored and transported through the different sites of the SC can be constrained to be lower than upper bounds, which should be given by the structure of the network. The objective function of the scheduling and planning model is to maximize the overall profit, ignoring the possible negative and positive effects on cash. Therefore, this performance is computed as the sum of cash inflows from sales of product minus

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the liabilities incurred in all the periods. Liabilities at a specific period are due to purchases of raw materials, execution of labor tasks, storage and transport activities, and purchases of part of the required product from an external supplier (outsourcing). 3. Cash management A number of budgeting models appeared in the literature of the late 1950s, when linear programming computation methods also emerged (Baumol, 1952; Robichek et al., 1965; Miller and Orr, 1966; Lerner and Stone, 1968; Orgler, 1969, 1970). In the work of Srinivasan (1986) a review of deterministic cash management models can be found. In our approach, the short-term management of cash associated with the SC operation is analyzed by merging a short-term budgeting formulation with the SC planning formulation previously presented. The connection between both models is thus carried out by taking into account the inflows and outflows of cash derived from the operation of the network. These flows are given by the dates and sizes of purchases of raw materials and utilities to suppliers (outflows of cash) and by the sales of final products to customers (inflows of cash). As a result of this connection between complementary formulations, an integrated model reflecting a holistic view of the business is constructed. This model allows the simultaneous computation of optimal decisions for both areas (i.e., process operations and finances). Payments to suppliers, taxes, short-term borrowing (credit line), pledging decisions and purchases/sales of marketable securities are thus scheduled together with the labor tasks carried out in the SC entities. The model includes the balance sheet categories (current and fixed assets and liabilities) required to compute the change in equity and a set of budgetary constraints representing balances of cash, debt, securities, taxes and so on. The model is next presented. 3.1. Budgeting model The budgeting variables and constraints of our model should be determined according to specific applicable rules (depreciation), legislation (taxes), etc. This may lead to different formulations depending on the case being analyzed. To overcome this problem, we have developed a set of general equations which intend to reflect a standard case.

Nevertheless, our mathematical formulation could be easily adapted to other particular cases. The budgeting constraints are defined for the same t0 planning periods applied in the planning formulation. These periods cover the whole time horizon, including the detailed scheduling intervals (see Fig. 2), and allow the integration of the budgetary constraints with the process operations equations. The cash balance for the H1 periods is given by constraint (30). Casht0 ¼ Casht0 1 þ ECasht0 þ NetCredit þ NetMS 0 t0 X X X t RM PR  Payet0 t00  Payt0 t00  PayTR t0 t00 e;t00

t00

 Divt0 þ Otherst0

t00 0

8t .

ð30Þ

In this equation, the cash for each period t0 (Casht0 ) is computed from the inflows and outflows of cash. Here, Casht0 is a function of the previous cash (Casht0 1 ), the exogenous cash (ECasht0 ), the amount borrowed or repaid to the credit line (NetCredit ), the sales and purchases of marketable t0 securities (NetMS t0 ), the payments on accounts payable incurred in any previous or actual period t00 PR TR (PayRM et0 t00 , Payt0 t00 and Payt0 t00 ), the dividends (Divt0 ) and other expected outflows or inflows of cash (Otherst0 ). Let us clarify at this point, that the exogenous cash concerns the cash coming from the sales of final products or fixed assets, from the pledging of accounts receivables, or from any other source of cash. The payments that the financial officer must face are due to the consumption of raw materials, labor and transport utilities, and also to the dividends (i.e., the amount of cash withdrawn from the company at a given instant of time and shared out among the shareholders of the firm). The different terms of the cash balance are next described in detail. X Pledt0 t00 pAInct0 8t0 . (31) t0 pt00 ot0 þtdel

A certain proportion of the accounts receivable may be pledged at the beginning of a period. Pledging is the transfer of a receivable from the previous creditor (assignor) to a new creditor (assignee). When a firm pledges its future receivables, it receives in the same period only a part, normally 80%, of their face value. Thus, it can be assumed that a certain proportion of the receivables outstanding at the beginning of a period is received during that period through pledge as stated by Eq. (31). In this

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equation, the variable Pledt0 t00 represents the amount pledged within time interval t00 on accounts receivable appearing in period t0 and maturing within period t0 þ tdel . We have assumed in this formulation that all the accounts receivable have the same maturing period. This consideration can be easily modified in order to reflect more complex situations. Pledging represents a very expensive way of funding that will only be used when no more credit can be obtained from the bank. X ECasht0 ¼ AInct0 tdel  Pledt0 tdel t00 X

þ t0 t

del

þ

8t0 .

ð32Þ

ot00 pt0

Casht0 XMinCash 8t0

(33)

Eq. (33) limits the cash in each period (Casht0 ) to be larger than a minimum value (MinCash), which has been previously negotiated with the bank. A short-term financing source is represented by an open line of credit constrained by MaxDebt. Under an agreement with the bank, loans can be obtained at the beginning of any period and are due after one week at a monthly interest rate (F) depending on the bank agreement. The bank usually requires a compensating balance, i.e. a percentage of the amount borrowed (normally a 20%). Therefore, the minimum cash (MinCash) has to be higher than the compensating balance imposed by the bank. Debtt0 ¼ Debtt0 1 þ Borrowt0  PayDebt t0 þ F  Debtt0 1 8t0 ,

ð34Þ

¼ Borrowt0  PayDebt NetCredit t0 t0

(35)

8t0 .

8 t0 ,

X

t00 4t0 Y MS t0 t00

 ð1 þ

t00 4t0 DMS t0 t00 Þ

t00 ot0



X

MS 0 Z MS t0 t00  ð1 þ E t0 t00 Þ 8t

ð37Þ

t00 ot0

The exogenous cash is then computed by means of Eq. (32), as the sum of the accounts receivable incurred in period t0  tdel and expected to be collected in period t0 , plus the cash obtained through the pledging of the accounts receivable incurred in periods from t0  tdel þ 1 to t0 . The accounts receivable to be collected in period t0 are computed as the difference between the whole amount of accounts incurred in period t0  tdel minus the amount of these accounts pledged in periods t0  tdel to t0  1. In this equation, f represents the face value of the receivables being pledged, normally 80%:

Debtt0 pMaxDebt

Eqs. (34)–(35) make a balance on the credit line considering for each period the updated debt (Debtt0 ) from the previous periods and the balance between borrows and repayments (NetCredit ). t0 Eq. (36) defines the maximum allowable debt (MaxDebt) that the bank has agreed with the firm. X X MS NetMS Y MS ZMS t0 ¼ S t0  t00 t0 þ t00 t0

t0 tdel pt00 ot0

Pledt00 t0  f

295

(36)

Eq. (37) makes a balance of marketable securities. All marketable securities can be sold prior to maturity at a discount or loss for the firm. Revenues and costs associated with the transactions in marketable securities are given by technical coeffiMS MS cients DMS t0 t00 and E t0 t00 , respectively. Y t00 t0 is the cash 0 invested at period t on securities maturing at period t00 . Z MS t00 t0 is the cash inflow obtained through the security sold at period t0 maturing at period t00 . Therefore, the net cash-flow due to the transactions of securities is computed from the initial portfolio of marketable securities held by the firm at the beginning of the first period (SMS t0 ), which includes several sets of securities with known face values in monetary units (m.u.), the cash invested in t0 on marketable securities maturing in periods beyond t0 , the marketable securities sold prior to maturity in period t0 and the securities purchased and sold in periods previous to t0 and maturing in t0 . X MS MS Z MS t0 t00  ð1 þ E t0 t00 ÞpS t0 t00 ot0

þ

X

MS Y MS t0 t00  ð1 þ Dt0 t00 Þ

8t0 .

ð38Þ

t00 ot0

Eqs. (38) is applied to constraint the total amount of marketable securities sold prior to maturity to be lower than the available ones (those belonging to the initial portfolio plus the ones purchased in previous periods). With regard to the accounts payable (raw materials, production and transport purchases) it is assumed that the financial officer, at his option, may stretch or delay payments on such accounts. Discounts for prompt payment can be obtained if purchases are paid in time and cannot be taken if the payments are stretched. X RM RM PayRM 8e; t0 , (39) et0 t00  Coef et0 t00 pPurchet0 t00 Xt0

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296

X

PR PR PayPR t0 t00  Coef t0 t00 pPurcht0

8t0 ,

(40)

TR TR PayTR t0 t00  Coef t0 t00 pPurcht0

8t0 .

(41)

t00 Xt0

X t00 Xt0

Since it is not reasonable to require that total accounts payable be zero at the end of the planning period, the payment constraints are formulated as inequalities as stated by Eqs. (39)–(41), where PR technical coefficients (Coef RM and et0 t00 ,Coef t0 t00 TR Coef t0 t00 ), which multiply the payments executed in periods t00 on accounts payable incurred in t0 , are introduced in the formulation to take into account the terms of the raw materials, production and transport credits, i.e. 2%—one week, net-28 days. With regard to the dividends, these are withdrawn from the system in form of enterprise earnings, which might by employed as shareholders’ dividends or reinvested. It is assumed that the exact amount of cash to be withdrawn from the budget is known beforehand as it has been previously negotiated with the shareholders of the company.

market prices that these products would reach in the market if they were sold at the end of the time horizon. On the other hand, FA refers to illiquid assets such as plants or equipments. X ARect0 DCA ¼ CashT 0 þ T 0 t0 otdel

X



Pledt0 t00

t0 ;t00 jT 0 t0 otdel ^t00 4T 0 tdel

X

þ

IS INVIS H1irt0  PriceirT 0

i;r

þ

X

IS INVIS H1ipt0  PriceipT 0

i;p

þ

X

BP INVBP H1jpT 0  PricejpT 0

j;p

þ

X

BP INVBP H1j;f ;T 0  PricejfT 0

j;f

þ

X

WH INVWH H1kfT 0  PricekfT 0

k;f

X

þ

! MK INVMK H1lfT 0  PricelfT 0

l;f

3.2. Objective function

 Casht0  ARect0 0

The more common objectives used by the process systems engineering (PSE) community over the last decades have been makespan, cost, profit and due date fulfillment. However, the financial community has been for years making decisions taking into account other indicators such as market to book value, liquidity ratios, capital structure ratios, return on equity, sales margin, turnover ratios and stock security ratios, among others. Nevertheless, the direct enhancement of the shareholder’s value (SHV) in the firm seems to be today’s priority. This can be improved by maximizing the change in equity of the company (DEquity). The change in equity can be computed as the net different between the change in assets, which includes both, the current (CA) and the fixed assets (FA), and the change in liabilities, which includes the current liabilities (CL) and the long-term debt (L), as it is stated in Eq. (42) (Shapiro, 2001). DE ¼ DCA þ DFA  DCL  DL.

(42)

DCA refers to liquid assets. In our model, this term has been computed from the accounts receivable, the available cash and the inventories at the end of the time horizon (T 0 ) and at time zero (t00 ), as it is expressed in Eq. (43). In this constraint, the prices of the materials kept as inventories represent the

X



0

IS INVIS H1irt0  Priceirt0

þ

X

IS INVIS H1ipt0  Priceipt0 0

i;p

þ

X

þ

0

þ

WH INVWH H1kft0  Pricekft0

k;f

þ

l;f

0

0

X

0

BP INVBP H1jft0  Pricejft0

j;f

X

0

BP INVBP H1jpt0  Pricejpt0

j;p

X

0

0

i;r

0

0



PriceMK lft00

! INVMK H1lft00

.

ð43Þ

DCL refers to short-term liabilities. This terms includes the accounts payable, which are due to either the remaining debt or to the consumption of raw materials, labor and transport utilities, as it is stated in Eq. (44). DebtT 0 þ

DCL ¼

X e;t0

þ

X t0

PurchTR t0

PurchRM et0 þ

!

X t0

PurchPR t0

ARTICLE IN PRESS G. Guille´n et al. / Int. J. Production Economics 106 (2007) 288–306

X



RM PayRM et0 t00  Coef et0 t00

e;t0 ;t00

X

þ

PR PayPR t0 t00  Coef t0 t00

t0 ;t00

þ

X

!

PayTR t0 t00



Coef TR t0 t00

þ Debtt0

0

t0 ;t00

ð44Þ

costs associated with having money invested in inventory instead of investing it somewhere else. Finally, constraint (48) computes the amount of money spent in transport utilities from the flows of materials among the SC entities. X IS PurchRM ESIS H1eirt0  CostESeirt0 et0 ¼ i;r;t0

X

þ þ Nowadays, financial and planning/scheduling decisions are computed in isolated environments. Therefore, in real industrial scenarios, SC process operations are firstly decided and finances are fitted afterwards. Due to the lack of concrete links between process operations and finances, the SC scheduling and planning decisions are typically computed by optimizing some performance indicator, like makespan, cost, profit, or revenues from sales. A typical SC planning model (M1) that accounts for the maximization of the profit could be expressed as follows: MODEL M1: Profit

subject to

Eqs: ð1Þ2ð29Þ;



X

WH ESWH H1ekft0  CostESekft0

k;f ;t0

X

þ

MK ESMK H1elft0  CostESelft0

8e; t0 ,

l;f ;t0

ð46Þ PurchPR t0 ¼

X

IS QIS H1ipt0  CostQip

i;p;t0

þ

X

BP QBP H1jft0  CostQjf

j;f ;t0

þ

X

IS INVIS H1irt0  CostINVir

i;r;t0

þ

X

IS INVIS H1ipt0  CostINVip

i;p;t0

þ

X

BP INVBP H1jpt0  CostINVjp

j;p;t0

þ

where the profit is computed as the difference between the inflows of cash, which are due to the sales of products, minus the outflows, which are associated with the purchases of raw materials, and the consumption of labor and transport utilities, as it is stated in Eq. (45) X X Profit ¼ SalesH1lft0  Pricelft0  PurchRM et0 l;f ;t0

BP ESBP H1e;j;p;t0  CostESejpt0

j;p;t

X

4. Traditional approach

maximise

297

e;t0 TR ðPurchPR t0 þ Purcht0 Þ  FCost. ð45Þ

BP INVBP H1jft0  CostINVjf

j;f ;t0

þ

X

WH INVWH H1kft0  CostINVkf

k;f ;t0

þ

X

MK INVMK H1lft0  CostINVlf

8t0 ,

l;f ;t0

ð47Þ PurchTR t0 ¼

X

AH1ijpt0  CostAijp

i;j;p

t0

To determine the outflows of cash required to compute the profit, Eqs. (46)–(48) are applied. Specifically, constraint (46) computes the total consumption of raw materials from the amount of raw materials required in each of the plants embedded in the network. Eq. (47) computes the labor tasks cost from the production rates at the plants and taking also into account the inventory levels at the warehouses. Here, the inventory cost coefficients (CostINV) include the handling and storage costs associated with keeping the inventory at every distribution node. These coefficients could be incremented in order to include also the financial

X

þ

X

BH1jkft0  CostBjkf

j;k;f

þ

X

C H1klft0  CostCklf

8t0 .

ð48Þ

k;l;f

Once the process operations are fixed, the budget is adjusted. A typical short-term budgeting model (M2) which maximizes the corporate equity and considers the cash flows associated with the SC operations is given by: MODEL M2: maximise

DE

subject to Eqs. ð30Þ2ð44Þ.

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298

5. Integrated model

6. Case study

To achieve the integration, the production liabilities and exogenous cash at every week-period are calculated as a function of the process operations variables. Production liabilities are thus computed by means of Eqs. (46)–(48). In Eq. (47), only the handling and storage costs associated with the inventories kept at the SC entities must be considered, as their financial cost is evaluated through the budgeting constraints. The value of the accounts receivable incurred in the t0 planning periods is determined from the sales of products, as it is stated by Eq. (49). Here, the maturing period (tdel ) of such accounts, which should be determined from the sales conditions negotiated with the customers, represents the probable or estimated delay between the purchase incidence and the corresponding payment. X ARect0 ¼ SalesH1lft0  Pricelft0 8t0 . (49)

A hypothetical case study has been studied to illustrate the capabilities of the proposed model. The problem is that of finding the optimal planning decisions, in terms of economic performance (DE), to be implemented in an existing SC. The network comprises a set of disperse facilities, which are established in different European countries. The information available concerns the structure of the SC, the demand, and the set of prices and costs. Twelve planning periods with a length of 1 week each are considered. The first planning period t0 1 is also divided into five detailed periods t of 24 h each. The structure of the case study is summarized in Fig. 3. The SC under study manufactures three different products (P1, P2 and P3), which are delivered to six final markets. The plants embedded in the SC, which are assumed to be multi-product batch chemical plants, are located in Barcelona (B) and Bratislava (Br). These plants consume 1 kg of intermediate product IP1 per kg of final product P1, 1 kg of IP2 per kg of P3 and finally 0.9 kg of IP1 and 0.1 of IP2 per kg of P2. IP1 can be either manufactured by a continuous plant owned by the firm, which behaves as an internal supplier, or provided by an external supplier. The internal supplier, which is located in B, consumes 1.5 kg of raw material RM1 per kg of IP1. RM1 is provided by the external supplier with a cost equal to 10 m.u./ kg. The labor cost associated with the internal supplier is equal to 30 m.u./kg. The external supplier can also provide plants and final markets with intermediate and final products. The prices of IP1 and IP2 offered by the external supplier are equal to

l;f

These equations allow the integration of the scheduling/planning variables into the budgeting model. The overall model can be therefore expressed as follows: INTEGRATED MODEL: maximise

DE

subject to

Eqs: ð1Þ2ð44Þ ð46Þ2ð49Þ.

The integrated model applies a mixed-integer-linearprogramming (MILP) formulation, which can be solved by standard branch-and-bound techniques.

Fig. 3. Case study.

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70 and 1275 m.u./kg for the plant located in B, and 55 and 1,250 m.u./kg for the one placed in Br. With regard to the final products offered by the external supplier, it is supposed that only P2 is available at a price equal to 168 m.u./kg for all the markets. Final products are stored in three different warehouses located in B, Br and Dover (D) prior to be sent to the final markets which are placed in Valencia (V), B, Br, Bristol (Bs), Manchester (M) and London (L). The capacities of the multiproduct batch plants are equal to 5,000 (B) and 7,500 (Br) kg of product per week respectively. Equal capacity coefficients are assumed for all the products. On the other hand, the capacity of the warehouses and the transport links connecting the SC entities is assumed to be unlimited. The transport costs associated with the network are given in Tables 1–3, while the inventory costs are shown in Tables 4–7. The initial inventories at the different nodes of the network are supposed to be equal to 0 and it is also assumed that the

299

Table 4 Inventory cost of raw materials r and intermediate products p in IS continuous plants i (CostINVIS ir and CostINVip m.u./kg week) Continuous plant location

B

Raw material

Intermediate product

RM1

IP1

0.1

0.7

Table 5 Inventory cost of intermediate products p and final products f in BP batch plants j (CostINVBP fp and CostINVjp m.u./kg week) Batch plant location

B Br

Intermediate product Final product IP1

IP2

P1

P2

P3

0.7 0.6

12.8 12.5

14.0 13.3

1.7 1.6

1.0 0.9

Table 1 Transport cost between continuous plants i and batch plants j for all intermediate products p (CostAijp , m.u./kg)

Table 6 Inventory cost of final products f in warehouses k (CostINVWH kf m.u./kg week)

Continuous plant location

Warehouse location

Batch plant location

B

B

Br

0.0

18.8

B Br D

Table 2 Transport cost between batch plants j and warehouses k for all final products f (CostBjkf m.u./kg) Batch plant location

Warehouse location

B Br

Br

D

0.0 18.3

18.3 0.0

12.9 13.1

Table 3 Transport cost between warehouses k and final markets l for all final products f (CostCklf m.u./kg) Warehouse location

B Br D

P1

P2

P3

14.0 13.3 16.8

1.7 1.6 2.0

1.0 0.9 1.1

Table 7 m.u./ Inventory cost of final products f in markets l (CostINVMK lf kg week) Final market location

B

Final product

V B Br Bs M L

Final product P1

P2

P3

14.0 14.0 13.3 16.8 16.8 16.8

1.7 1.7 1.6 2.0 2.0 2.0

1.0 1.0 0.9 1.1 1.1 1.1

Final market location V

B

Br

Bs

M

L

3.4 16.0 21.7

0.0 12.9 18.3

18.3 13.1 0.0

13.2 3.2 17.0

15.8 4.6 18.4

14.0 1.2 15.0

transport of materials among the SC nodes is carried out with an average speed of 60 km/h. With regard to the batch plants, their structure, which is depicted in Fig. 4, have been taken from the case studied introduced by Robinson and Loonkar

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300

CENTRIFUGE

PUMP 1

REACTOR

PUMP 2

TANK

HEAT EXCHANGER

PUMP 3

DRIER Fig. 4. Robinson and Loonkar case study (1972).

Table 8 Processing times of final products f in plants j in stages o (topjfo hr)

Table 9 Production cost of final products f in batch plants j (CostQIS ip m.u./kg)

Product

Batch plant location

P1 P2 P3

Stage o1

o2

o3

o4

o5

o6

o7

o8

2.1 2.3 2.0

4.5 9.0 3.0

4.2 4.5 3.8

4.2 4.5 3.8

1.5 0.0 3.0

4.8 0.0 4.2

4.8 4.5 4.2

7.5 12.0 7.5

(1972). The batch sizes associated with the products manufactured at B and Br are equal to 500 and 750 kg, respectively. The associated processing times, which are assumed to be equal in both plants, are given in Table 8. The labor costs are also shown in Table 9. The prices of the final products, which are supposed to remain constant in all the time periods, are shown together with the demand in Tables 10–12. Concerning the financial matters, it is assumed that the firm has an initial portfolio of marketable securities investments at the beginning of the time horizon (see Table 13). The initial cash is equal to the minimum cash (50,000,000 mu). Under an agreement with a bank, the firm has an open line of credit at a 10% annual interest with a maximum debt allowed of 7,500,000 mu. The initial debt is equal to zero and the final prices of the materials kept as inventories at the end of the time horizon are a 40% of their market prices. Sales executed in any period are paid with a delay equal to 4 weeks and receivables on sales are pledged at a 80% of their face value. Liabilities incurred with the external supplier and with the supplier that provides the plants with

Final product

B Br

P1

P2

P3

45 40

30 25

25 20

Table 10 Demand of final products f in markets l (DemH1lft0 kg) Period Valencia

t0 1 t0 2 t0 3 t0 4 t0 5 t0 6 t0 7 t0 8 t0 9 t0 10 t0 11 t0 12

Barcelona P2

Bratislava

P1

P2

P3

P1

P3

P1

P2

P3

227.0 153.0 148.0 155.0 1.5 1.5 1.5 1.5 157.0 151.0 148.0 147.0

225.0 154.0 155.0 151.0 291.0 296.0 310.0 306.0 145.0 146.0 149.0 156.0

150.0 97.0 103.0 105.0 189.0 196.0 187.0 207.0 102.0 101.0 101.0 99.0

754.0 1.5 734.0 3.0 1.1 754.0 520.0 1.0 487.0 2.0 780.0 511.0 494.0 1.0 495.0 1.9 763.0 498.0 515.0 967.0 512.0 2.0 724.0 501.0 4.8 1.8 983.0 19.6 1.5 1.0 5.0 1.9 1.0 19.7 1.5 1.0 5.2 1.9 1.0 20.0 1.4 1.0 5.0 2.0 1.0 19.6 1.4 988.0 501.0 1.0 491.0 2.0 742.0 515.0 518.0 953.0 499.0 2.0 757.0 522.0 486.0 1.0 507.0 2.1 737.0 485.0 488.0 1.0 490.0 2.1 718.0 517.0

production utilities have to be repaid within 4 weeks according to the terms of the credit negotiated with them (2%—7 days, net-28 days for the raw materials supplier and net-28 days for the second one). The payments associated with the transport services cannot be stretched and must be satisfied within the same period of time in which the transport task takes place. Concerning the technical

ARTICLE IN PRESS G. Guille´n et al. / Int. J. Production Economics 106 (2007) 288–306

coefficients associated with transactions of marketable securities, we assume a 2.8% annual interest for purchases and a 3.5% for sales.

Table 11 Demand of final products f in markets l (DemH1lft0 kg) Period

0

t1 t0 2 t0 3 t0 4 t0 5 t0 6 t0 7 t0 8 t0 9 t0 10 t0 11 t0 12

Bristol

Manchester

London

P1

P2

P3

P1

P2

P3

P1

P2

P3

226.0 150.0 152.0 150.0 1.6 1.5 1.5 1.5 154.0 151.0 147.0 147.0

221.0 151.0 152.0 146.0 302.0 305.0 325.0 286.0 150.0 156.0 151.0 154.0

443.0 296.0 300.0 302.0 622.0 590.0 585.0 585.0 310.0 294.0 299.0 307.0

294.0 203.0 205.0 201.0 2.1 2.0 2.0 2.0 196.0 195.0 202.0 199.0

295.0 198.0 197.0 188.0 425.0 421.0 406.0 385.0 197.0 205.0 196.0 201.0

148.0 102.0 98.0 99.0 192.0 186.0 208.0 191.0 102.0 103.0 102.0 98.0

1.5 1.1 1.0 1.0 9.9 10.2 10.5 10.2 996.0 989.0 1.0 971.0

1.5 1.0 960.0 1.0 2.2 1.9 2.1 2.1 1.0 1.0 1.0 1.0

2.2 1.4 1.5 1.5 3.0 3.0 2.9 3.0 1.5 1.5 1.5 1.6

Table 12 Prices of final products f in markets l for the whole time horizon (PriceMK lft0 m:u:) Final market location

Final product

V B Br Bs M L

P1

P2

P3

1,400 1,400 1,330 1,680 1,680 1,680

170 170 162 204 204 204

95 95 90 114 114 114

Table 13 Initial portfolio of marketable securities 103 (SMS t0 m:u:) t0 1

t0 2

t0 3

t0 4

t0 5

t0 6

t0 7

t0 8

t0 9

t0 10

t0 11

t0 12

150

150

70

50

40

75

60

100

100

25

60

80

301

We also assume that the dividends of the firm are withdrawn at the end of the time horizon (period 12). In each period of time, 1,000,000 m.u. are also withdrawn from the company’s budget in order to cover payrolls, wages and rents. There are also inflows of cash of 4,000,000 in time periods 1 and 3, and of 500,000 m.u. in periods 2 and 4. These flows are due to the collection of accounts receivable on sales of products executed in periods earlier than 1. Finally, in period 3, an investment of 1,000,000 m.u. in fixed assets is carried out, while in period 8, 500,000 m.u. are credited in the company’s account due to the sales of fixed assets. No changes in the long term-debt are considered. The implementation in GAMS (Brooke et al., 1998) of the planning model consists of 6116 single equations, 4252 continuous variables, and 860 discrete variables. It takes 54 CPU seconds to reach a solution with a 0% integrality gap on a AMD Athlon 3000 computer using the MIP solver of CPLEX (7.0). Once the scheduling–planning model is solved, the budgeting model is optimized. This model has 456 single equations and 664 continuous variables. The model is solved in 0.03 CPU seconds. On the other hand, the integrated model leads to 6571 single equations, 4915 continuous variables, and 860 discrete variables and 116 CPU seconds to reach a solution with a 0% integrality gap on the same computer. Results obtained by means of both approaches are summarized in Table 14. Let us note that the change in equity achieved by the company improves substantially (61% of improvement) when the integrated approach is applied (9,621,028 m.u. for the sequential approach and 15,697,124 m.u. for the integrated one). Fig. 5 shows how the integrated solution incurs in less debt than the sequential one and also avoids having to pledge receivables (financial transaction of high cost for the firm). The sequential approach is pledging around 33,931,590 m.u., and this means a cost of around 8,482,897 m.u. for the firm.

Table 14 Results

Sequential Integrated

DCA ðm:u:Þ

DFA ðm:u:Þ

DCL ðm:u:Þ

DL ðm:u:Þ

DE ðm:u:Þ

17,140,346 16,239,736

500,000 500,000

8,019,318 1,042,611

0 0

9,621,028 15,697,124

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302

8000000 Sequential Integrated

7000000

Debt (m.u.)

6000000 5000000 4000000 3000000 2000000 1000000 0 1

2

3

4

5

6

7

8

9

10

11

12

Period (week) 18000000 Se quential Integrated

16000000 Pledging (m.u.)

14000000 12000000 10000000 8000000 6000000 4000000 2000000 0 1

2

3

4

5

6

7

8

9

10

11

12

Period (weeks) Fig. 5. Debt and pledging.

The case study presented in this work is a very specific situation where there is one product (P1) with a very high profit margin in comparison with the others. Such product exhibits a high market price and consumes an expensive raw material. Given this data, the planning–scheduling model decides to fulfill the demand of P1 as much as possible. Figs. 6 and 7 show that the sequential approach is producing and storing a high amount of expensive product at early periods with low demand (t0 1 to t0 4) in order to sale it in later periods when the demand increases (t0 5–t0 8). To carry out the SC planning decisions, the budgeting model is forced to pledge receivables mainly in periods t0 5–t0 8, when the raw materials purchased in the first four periods must be paid. On the other hand, the integrated approach leads to lower production rates of P1. This policy avoids having to pledge receivables and also leads to less debt, which finally results in a higher change in equity.

7. Conclusions This paper has addressed the importance of integrating planning and budgeting models in SCM. To achieve the integration, a standard SC planning formulation has been extended through the insertion of budgeting constraints that explore the financial area of the SC. The change in equity, which is related to the shareholders’ value (SHV) of the firm, has been chosen as the objective to be optimized in the integrated SC planning/budgeting model. The advantages of our approach have been highlighted through a case study, in which the results obtained by the integrated model have been compared with those determined by the sequential strategy, in which operations are firstly decided and finances are fitted afterwards. Results indicate that the sequential approach leads to poorer solutions, in terms of change in equity, than the integrated

ARTICLE IN PRESS Total production (kg) Sequential

G. Guille´n et al. / Int. J. Production Economics 106 (2007) 288–306

303

14000 12000

P3 P2

10000

P1

8000 6000 4000 2000 0 1

2

3

4

5

6

7

8

9

10

11

12

Total production (kg) Integrated

Period (weeks) 14000 P3 P2 P1

12000 10000 8000 6000 4000 2000 0 1

2

3

4

5

7 6 8 Period (weeks)

9

10

11

12

Fig. 6. Total production.

formulation. This illustrates the inadequacy of treating process operations and finances in isolated environments and pursuing as objective myopic performance indicators such as profit or cost. The implications for production scheduling, for the firm’s cash flow, and for stockholder equity that incorporating financial considerations into a SC analysis can have, may well differ from firm to firm, depending upon the specifics of the situation. We believe that the PSE community must enlarge the scope of the currently narrow approaches for SCM and extend the underlying concepts and ideas to offer a wider perspective of the whole business at all the decision-support levels (operational, tactical and strategic). It is a fact that the tight profit margins under which the chemical industry will operate in the future will make managers pay more and more attention to the financial area. Thus, the approach of this work will become more relevant in the course of time, not only in the academic world but also in the industrial community.

Notation AH1ijpt0 AInct0 BH1jkft0 Borrowt0 bsjf C H1klft0

Casht0 Coef PR t0 t00 Coef RM et0 t00 Coef TR t0 t00 CostAijp

amount of p transported from internal supplier i to plants j in period t0 accounts incurred in period t0 amount of final product f sent from plants j to warehouse k in period t0 total amount of money borrowed to the credit line in period t0 batch size of final product f at plant j amount of final product f sent from warehouse k to final markets l in period t0 cash in period t0 technical coefficient technical coefficient technical coefficient transport cost of intermediate product p between internal supplier i and plant j

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304

Total inventory (kg) Sequential

40000 P3

35000

P2 30000

P1

25000 20000 15000 10000 5000 0

1

2

3

4

5

6

7

8

9

10

11

12

Period (weeks)

Total inventory (kg) Integrated

40000 P3

35000

P2 30000

P1

25000 20000 15000 10000 5000 0 1

2

3

4

5

6

7

8

9

10

11

12

Period (weeks) Fig. 7. Total inventory.

CostBjkf CostCklf

CostESBP ejpt0 CostESIS eirt0 CostESMK elft0 CostESWH ekft0 CostINVBP jp

transport cost of final product f between plant j and warehouse k transport cost of final product f between warehouse k and final market l cost of intermediate product p provided by external supplier e to plant j in period t0 cost of raw material r provided by external supplier e to internal supplier i in period t0 cost of final product f provided by external supplier e to final market l in period t0 cost of final product f provided by external supplier e to warehouse k in period t0 inventory cost of intermediate product p in plant j

CostINVBP jf CostINVIS ip CostINVIS ir CostINVWH kf CostINVMK lf CostQBP jf CostQIS ip DCA DCL DMS t0 t00 Debtt0

inventory cost of final product f in plant j inventory cost of intermediate product p in internal supplier i inventory cost of raw material r in internal supplier i inventory cost of final product f in warehouse k inventory cost of final product f in final market l production cost of final product f in plant i production cost of intermediate product p in interval supplier i change in current assets change in current liabilities technical coefficients debt in period t0

ARTICLE IN PRESS G. Guille´n et al. / Int. J. Production Economics 106 (2007) 288–306

DemH1lft0 Divt0 E MS t0 t00 ESBP H1ejpt0 ESIS H1eirt0

ESMK H1elft0 ESWH H1ekft0 ECasht0 DE FCost DFA H INVBP H1jft0 INVBP H1jpt0 INVIS H1ipt0 INVIS H1irt0 INVMK H1lft0 INVWH H1kft0 DL MaxDebt MinCash NetCredit t0 NetMS t0 Otherst0 PayDebt t0 PayPR t0 t00 PayRM et0 t00

demand of final product f in final market l in period t0 dividends in period t0 technical coefficients amount of intermediate product p transported from external supplier e to plant j in period t0 amount of raw material r transported from external suppliers e to internal supplier i in period t0 amount of final product f provided by external supplier e to final market k in period t0 amount of final product f provided by external supplier e to warehouse k in period t0 exogenous cash in period t0 change in equity fixed cost change in fixed assets time horizon inventory of final product f kept at plant j in period t0 inventory of intermediate product p kept at plant j in period t0 inventory of intermediate product p kept at internal supplier i in period t0 inventory of raw material r kept at internal supplier i in period t0 inventory of final product f in final mar-ket l in period t0 inventory of final product f kept at warehouse k in period t0 change in long-term debt maximum debt minimum cash total amount of money borrowed or repaid to the credit line in period t0 total amount of money received or paid in securities transactions in period t0 other expected outflows or inflows of cash in period t0 total amount of money repaid to the credit line in period t0 payments of production utilities consumed in period t00 in period t0 payments of raw materials purchased in period t00 to external supplier e in period t0

PayTR t0 t00 Pledt0 t00

PriceBP jft0 PriceBP jpt0 PriceIS ipt0 PriceIS irt0 PriceMK lft0 PriceWH kft0 Profit PurchPR t0 PurchRM et0 PurchTR t0 QIS H1ipt QinBP H1jft0 QoutBP H1jft0 Otherst0 SalesH1lft0 S MS t0 TFjl j o TF0jl j Ot TIjl j o TI0jl j Ot topjfo X jl j f

305

payments of transport services consumed in period t00 in period t0 amount pledged within time interval t00 on accounts receivable appearing in period t0 price of final product f stored in plant j in period t0 price of intermediate product p stored in plant j in period t0 price of intermediate product p stored in internal supplier i in period t0 price of raw material r stored in internal supplier i in period t0 price of final product f stored in final market l in period t0 price of final product f stored in warehouse k in period t0 profit purchases of production utilities in period t0 purchases of raw materials to external supplier e in period t0 purchases of transport services in period t0 total amount of intermediate product p manufactured by internal supplier i in period t amount of final product f manufactured at plant j in period t0 total amount of final product f manufactured at plant j in period t0 others inflows or outflows of cash in period t0 sales of final product f in final market l in period t0 initial amount of marketable securities maturing in period t0 finishing processing time of batch l j on stage o at plant j auxiliary variable initial processing time of batch l j on stage o at plant j auxiliary variable processing time of stage o of final product f at plant j binary variable (1 if batch l j at plant j belongs to intermediate product f and 0 otherwise)

ARTICLE IN PRESS G. Guille´n et al. / Int. J. Production Economics 106 (2007) 288–306

306

Y jl j t Y 0jl j t Y MS t00 t0 Z MS t00 t0

binary variable (1 if batch l j is finished within time interval t at plant j and 0 otherwise) binary variable (1 if batch l j is started within time interval t at plant j and 0 otherwise) cash invested at period t0 maturing at period t00 security sold at period t0 maturing at periodt00

Greek letters arp

bfp

f

mass conversion coefficient of raw material r and intermediate product p mass conversion coefficient of intermediate product p and final product f pledging factor

Acknowledgments Financial support received from the Spanish ‘‘Ministerio de Educacio´n y Ciencia’’ (FPU programs), GICASA-D (I0353), OCCASION (DPI2002-00856) and PRISM (MRTN-CT-2004512233) projects is gratefully acknowledged. References Applequist, G.E., Pekny, J.F., Reklaitis, G.V., 2000. Risk and uncertainty in managing manufacturing supply chains. Computers and Chemical Engineering 24, 47–50. Badell, M., Romero, J., Puigjaner, L., 2004. Planning, scheduling and budgeting value-added chains. Computers and Chemical Engineering 28, 45–61. Baumol, W.J., 1952. The transactions demand for cash: An inventory theoretic approach. Quantitative Journal of Economy 66 (4), 545. Bok, J.W., Grossmann, I.E., Park, S., 2000. Supply chain optimization in continuous flexible process networks. Industrial and Engineering Chemistry Research 39, 1279–1290. Brooke, A., Kendrik, D., Meeraus, A., Raman, R., Rosenthal, R.E., 1998. GAMS—A User’s Guide. GAMS Development Corporation, Washington, DC. Cheng, L., Subrahmanian, E., Westerberg, A.W., 2003. Design and planning under uncertainty: issues on problem formula-

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