11
This article was downloaded by: [University of New Mexico] On: 23 November 2014, At: 17:05 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK Journal of the Chinese Institute of Industrial Engineers Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/tjci20 COLLABORATIVE MARKETING AND PRODUCTION PLANNING WITH IFS AND SFI PRODUCTION STYLES IN AN ERP SYSTEM Liang-Tu Chen a & Jen-Ming Chen b a Department of Commerce Automation and Management , National Pingtung Institute of Commerce , 51 Minsheng E. Road, Pingtung City, Pingtung County 900, R.O.C. b Institute of Industrial Management National Central University Published online: 09 Feb 2010. To cite this article: Liang-Tu Chen & Jen-Ming Chen (2008) COLLABORATIVE MARKETING AND PRODUCTION PLANNING WITH IFS AND SFI PRODUCTION STYLES IN AN ERP SYSTEM, Journal of the Chinese Institute of Industrial Engineers, 25:4, 337-346, DOI: 10.1080/10170660809509097 To link to this article: http://dx.doi.org/10.1080/10170660809509097 PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http:// www.tandfonline.com/page/terms-and-conditions

COLLABORATIVE MARKETING AND PRODUCTION PLANNING WITH IFS AND SFI PRODUCTION STYLES IN AN ERP SYSTEM

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  • This article was downloaded by: [University of New Mexico]On: 23 November 2014, At: 17:05Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: MortimerHouse, 37-41 Mortimer Street, London W1T 3JH, UK

    Journal of the Chinese Institute of IndustrialEngineersPublication details, including instructions for authors and subscription information:http://www.tandfonline.com/loi/tjci20

    COLLABORATIVE MARKETING AND PRODUCTIONPLANNING WITH IFS AND SFI PRODUCTION STYLES INAN ERP SYSTEMLiang-Tu Chen a & Jen-Ming Chen ba Department of Commerce Automation and Management , National Pingtung Institute ofCommerce , 51 Minsheng E. Road, Pingtung City, Pingtung County 900, R.O.C.b Institute of Industrial Management National Central UniversityPublished online: 09 Feb 2010.

    To cite this article: Liang-Tu Chen & Jen-Ming Chen (2008) COLLABORATIVE MARKETING AND PRODUCTION PLANNINGWITH IFS AND SFI PRODUCTION STYLES IN AN ERP SYSTEM, Journal of the Chinese Institute of Industrial Engineers, 25:4,337-346, DOI: 10.1080/10170660809509097

    To link to this article: http://dx.doi.org/10.1080/10170660809509097

    PLEASE SCROLL DOWN FOR ARTICLE

    Taylor & Francis makes every effort to ensure the accuracy of all the information (the Content) containedin the publications on our platform. However, Taylor & Francis, our agents, and our licensors make norepresentations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose ofthe Content. Any opinions and views expressed in this publication are the opinions and views of the authors,and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be reliedupon and should be independently verified with primary sources of information. Taylor and Francis shallnot be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and otherliabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to orarising out of the use of the Content.

    This article may be used for research, teaching, and private study purposes. Any substantial or systematicreproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in anyform to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions

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  • Journal of the Chinese Institute of Industrial Engineers, Vol. 25, No. 4, pp. 337-346 (2008) 337

    COLLABORATIVE MARKETING AND PRODUCTION PLANNING WITH IFS AND SFI PRODUCTION STYLES IN

    AN ERP SYSTEM

    Liang-Tu Chen* Department of Commerce Automation and Management

    National Pingtung Institute of Commerce 51 Minsheng E. Road, Pingtung City, Pingtung County 900, R.O.C.

    Jen-Ming Chen Institute of Industrial Management

    National Central University

    ABSTRACT

    The latest manufacturing technologies, such as enterprise resource planning (ERP) system, enhance cross-functional interaction between manufacturing and marketing, but many pro-duction decision-making processes do not take marketings dynamic nature into account. It is due in large part to the inherent weaknesses of ERP system such as the fixed and static parameter settings and uncapacitated assumption. To remedy these drawbacks, we propose two decision models that solve optimally the production lot-size/scheduling problem taking into account the dynamic aspects of customers demand as well as the restriction of finite capacity in a plant. More specifically, we consider a single product that is subject to con-tinuous decay, faces a time-varying and price-dependent demand, and time-varying variable production cost and production rate, with the objective of maximizing the profit stream over multi-period planning horizon. The problem is formulated as a dynamic programming model and solved by numerical search techniques. The main purpose behind this study is to propose a conceptual framework of a robust decision support system that can be served as an add-on optimizer like an advanced planning system in an ERP system. Special emphasis is placed on the comparative study between the proposed optimization models that are based on the inventory followed by shortages (IFS) and shortages followed by inventory (SFI) styles. Numerical result shows that the SFI style outperforms the IFS style in maxi-mizing the total profit and minimizing inventory investment. Further, the percentage of profit difference between the two styles increases significantly in price-elasticity coefficient of the demand function as well as the production unit cost. Keywords: Collaborative Planning, Pricing, Production, Dynamic Programming, ERP,

    Deteriorating Item

    1. INTRODUCTION**

    The need for cross-functional coordination

    between marketing and production planning has re-ceived a great deal of attentions for many decades. Shapiro [16] identified eight key areas of necessary cooperation but potential conflict between the two adversary functions. These conflicts, however, can be managed and further eliminated through properly designed mechanisms such as organizational design, communication, reward systems, and models [1, 6, 10]. The benefits of inter-functional cooperation in-clude substantial profit increments, higher customer * Corresponding author: [email protected]

    satisfactions, better organizational atmosphere, and other tangible and intangible rewards.

    This paper investigates the interplay between marketing and production decision-making within a company organization. Specifically, we deal with the problem of joint decisions on pricing and production schedule for deteriorating items by a monopolistic producer who maximizes the total expected profit over a finite planning horizon. In the decentralized decision process, the marketing department sets the price by maximizing its gross profit function disre-garding the production cost, the market responds with a specific demand, and the production department makes the lot-sizing and scheduling decision with the objective of minimizing the total production cost

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  • 338 Journal of the Chinese Institute of Industrial Engineers, Vol. 25, No. 4 (2008)

    while satisfying the demand. As contrast to the de-centralized process, the coordinated policy makes the pricing and production decisions at a time. It is well documented [7, 8, 11, 14] that the cooperative ap-proach is superior to the decentralized approach in many dimensions such as minimizing cost or maxi-mizing profit. Successful use of cooperative approach to integrate distinct functions has been reported by several firms including 3M, Wright Line, and Na-tional Starch & Chemical [6].

    Nahmias [13] classified the deteriorating in-ventory problems into two broad categories: fixed lifetime and random lifetime. In this paper, a random lifetime model is considered. Most of the existing random lifetime models consider a constant deterio-ration rate over time (exponential decay) such as the pioneer research by Ghare and Schrader [9] who ex-tended the classical EOQ model by considering the combined effect of demand usage and linear decay. Other EOQ-based inventory models for deteriorating items include Chang and Wu [2], Chen and Lin [3], Lee and Ma [12], Wee et al. [17], Wu [18], and Yang and Wee [19, 20], who extended past research by considering a constant demand rate or time-varying demand function with or without shortages allowed. However, the anterior literature does not incorporate pricing decision. Instead, we consider a single prod-uct that is subject to continuous decay, a multivariate demand function of price and time, and the selling price, production cost, and production rate are al-lowed to vary along time, and shortages allowed and completely backlogged in a periodic review inventory style in which the selling price is allowed to adjust arbitrarily, upward or downward, in response to the shift of customer valuation and/or change in market demand over product lifecycle. The objective of this paper is to present a dynamic version of the pric-ing-production decision model under multi-period setting so that the total profit is maximized.

    The proposed tactical-level decision models solve the production lot-size/scheduling problem tak-ing into account the dynamic nature of customers demand which is partially controllable through pric-ing schemes. As analogous to the sales and operations planning, the proposed scheme can be used as an add-on optimizer of the advanced planning system within a generic ERP framework, which integrates and coordinates distinct functions within a firm. In this paper, we use calculus-based formulation cou-pled with dynamic programming techniques to solve the cross-functional decision problem. Particular at-tention is placed on the comparative study between the proposed optimization models that are based on various production styles, i.e., the inventory followed by shortages (IFS) and shortages followed by inven-tory (SFI) styles.

    The remainder of this paper is organized as follows. Section 2 describes problem scenario, basic

    settings, and notations. A conceptual framework of decision support system is developed in section 3. Section 4 conducts an in-depth comparative study between the solutions generated by the two produc-tion styles, and investigates the impacts of the trend of market magnitude and price-sensitivity of demand on the dynamic behavior of price trajectory. Con-cluding remarks and suggestions for future research are given in section 5.

    2. NOTATIONS AND

    ASSUMPTIONS

    In this section, we describe the underlying problem and settings, including necessary notations and assumptions. To facilitate further discussions, the following notations are defined and will be used throughout the paper.

    =),( tpD The price-dependent and time-varying

    demand function. =H The planning horizon. =p The selling price. =Q The lot-size. =T The production scheduling. =1iz The sequence of times, i = 1, 2,, n. ))(( t = The deteriorating coefficient of the item

    over product lifetime )(t . ),( tpI = The inventory level at time t when the sell-

    ing price is p. =maxI The maximal inventory level. =)(t The production rate at time t. =)(t The variable production cost per unit of

    item at time t. =K The fixed production setup cost per run. =h The holding cost per unit of time and unit

    of item. =s The shortage cost per unit of time and unit

    of item. =b The price-sensitivity coefficient of de-

    mand. =c The production unit cost. = The deteriorating rate. = The coefficient of changing pattern, direc-

    tion, and magnitude of the price-sensitivity of demand over the planning horizon.

    =3 The coefficient of trend of market magni-tude.

    =dQ The deteriorating quantity (i.e., dQ =DQ ).

    =SL The service level (i.e., product availabil-ity).

    = The periodic profit. = The accumulated profit.

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  • Chen and Chen: Collaborative Marketing and Production Planning with IFS And SFI Production 339 Styles in an ERP System

    We consider a manufacture firm who produces

    and sells a single product that is subject to continuous decay over lifetime, faces a price-dependent and time-varying demand function, and has the objective of determining price and production lot-size/sched-uling so as to maximize the total profit stream over multi-period planning horizon. The reason of using time-varying demand under multi-period setting is twofold: to reflect sales fluctuation over time and to reflect sales trend in different phases of product life cycle in the market. We assume the production rate is finite and shortages are allowed and completely backordered. To remain focus, we assume no inven-tory is held at the beginning and at the end of the time horizon. If the initial inventory level is positive in the style, no action will be taken until the depletion of inventory. In addition, we assume the deterioration of units occurs only when the item is effectively in stock, and there is no repair or replacement of dete-riorated units during the planning period. To incor-porate the multi-period setting in a typical MRP II/ERP environment, we assume the inventory and selling price are reviewed periodically at time t, t = 0, 1, 2,, H. At the beginning of each period, a joint decision is made regarding the lot-size and schedule of a new production run (if any) and its associated selling price. The problem is equivalent to determin-ing the optimal sequence of times, at which a new cycle starts, the selling price is reset, and the produc-tion scheduling and lot-size are specified simultane-ously so that the total profit stream over [0, H] is maximized. It is worthy noting that nH, 0z = 0,

    nz = H, 1iz is integer and 1iz [0, H), and n is the total number of productions to be scheduled over the horizon.

    The demand function considered in this paper satisfies the following mild and realistic assumptions (see Rajan et al. [15] for further discussions): (i) 0),( tpD and is continuous for 0p , 0t , (ii) ),( tpD decreases in p, (iii) +tpD for ),0[ maxpp , 0t . The assumptions are asser-tions that demand is nonnegative, changes continu-ously with price and time, decreases as price in-creases, and is finite. The function is a generalized form of Rajan et al. who assumed ),( tpD is nonin-creasing in p and t, separately. Their specific demand function captures the property of diminishing effect toward the end of product lifetime in single period setting; ours can reflect sales trend, upward or downward, over multi-period horizon.

    A typical behavior of the production schedule, i.e., inventory followed by shortages (IFS) coupled with time-decreasing demand is illustrated in figure 1. Each cycle, say [ 1iz , iz ], of the produc-tion/inventory style starts with the production run lasting over period [ 1iz , 1T ], followed by the con-

    sumption period over [ 1T , 2T ] due to demand re-quirements and deterioration loss, after which the style starts with the shortage period over [ 2T , 3T ], at which the production resumes over [ 3T , iz ] to meet the backlogged and demand requirements. To com-pare the effect on employing different modeling ap-proaches, we also use another production style, i.e., shortages followed by inventory (SFI). Figure 2 graphically shows the variable production schedule with time-decreasing demand. Each cycle, say [ 1iz , iz ], of the production/inventory style starts with shortages lasting over period [ 1iz , 1T ], after which the style starts the production run over period [ 1T , 3T ] to meet the backlogged and demand re-quirements during the cycle.

    1iz iz0

    H1T Time

    lev

    el

    Inv

    en

    tory

    3T

    2T

    Figure 1. IFS style for deteriorating items with

    time-decreasing demand

    1iziz

    0H

    1T

    Time

    level

    Inven

    tory

    3T2T

    Figure 2. SFI style for deteriorating items with

    time-decreasing demand 3. THE DECISION SUPPORT

    SYSTEM

    The main purpose behind this study is to pro-pose a conceptual framework of a robust decision support system that can be served as an add-on opti-mizer like an advanced planning system in an ERP system by accessing and using data and analytic

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  • 340 Journal of the Chinese Institute of Industrial Engineers, Vol. 25, No. 4 (2008)

    models. The four-layered framework given in figure 3 represents one of the emerging extensions of ERP systems, focusing on operations research methods with an aim at cross-functional cooperation and tac-tical-level planning.

    The first layer of the framework is the data needed by the decision system, including the charac-teristic of the product such as deterioration property, the demand type and sales trend, cost structure, ca-pacity of production line, and inventory level. The proposed decision support system or the optimizer is outlined in the second layer which consists of three

    stages under the SFI production style and IFS pro-duction style, respectively: problem formulation, al-gorithmic development, and program development (We give a detailed mathematical formulation of the optimizer in the Appendices A and B). The third layer reports the output of the decision system in-cluding the joint decisions on production schedul-ing/lot-size and pricing. Performance evaluation is given in the fourth layer, based on which the deci-sion-maker can assess both operational and financial indicators such as the sales volume, service level in-ventory level, cost, revenue, and net profit.

    Figure 3. Four-layered decision support system for integrating marketing and production planning

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  • Chen and Chen: Collaborative Marketing and Production Planning with IFS And SFI Production 341 Styles in an ERP System

    4. IMPLEMENTATION AND

    SENSITIVITY ANALYSIS The dynamic solution procedure for both poli-

    cies was implemented on a personal computer with Pentium CPU at 1.8 GHz under Windows XP operat-ing system using Mathematica version 4.1. In our experiments, we first verified numerically the con-cavity of the models, and then determined the optimal price *p or **p and associated lot-size

    ),( *2* TpQ or ),( **2

    ** TpQ , and the production

    schedule * 1iz or **1iz , i = 1, 2,, n. For the iterative

    procedure, the process continued until the absolute value of relative error between consecutive iterates was less than or equal to 410 . The process took about 2-7 iterations to converge in all experiments being studied. The computer time required for the dynamic programming was, on the average, less than 7 seconds.

    Several experiments were conducted to attend qualitative insights into the structures of the proposed policies and their sensitivity with respect to major parameters. We focused in particular on investigating the solution property as well as the benefit of the SFI production style compared to the IFS production style in settings with time-decreasing demand. Further, we explored the impacts of price-sensitivity coefficient of demand, production unit cost, shortages cost, holding cost, set-up cost, and deteriorating rate on the profits generated by the two styles, and investigated the impacts of the trend of market magnitude and price-sensitivity of demand on the dynamic behavior of price trajectory generated by the SFI production style.

    4.1 An illustrative example

    An illustrative example is based on the set-tings: number of periods 12=H , cost parameters

    120=K , 5.0=h , 6=s , and variable production cost tt ecet 02,010)( 1 == , i.e., 10=c and

    02.01 = , production rate tfet 2)( =

    te 02.0150 = , deteriorating rate 08.0))(( == t ,

    and demand function pebeatpD tt 43 00),( =

    tt epeba 334 )( )(00 = 100()( 3)(00 ==

    tt epeba tt epe 02.00 )5 . The scenario simulates the diminish-

    ing effect of demand function toward the end of product lifecycle. The solutions generated by the two IFS and SFI production styles are summarized in table I which represents the output in the third layer of the decision system. The selling price p and pro-duction scheduling ( 1T , 2T , and 3T ) generated by

    the decision system is reported in table 1a and the market demand D and lot-size Q over the planning horizon is reported in table 1b.

    Table 1a. Numerical results of optimal pricing (p)

    and production scheduling ( 1T , 2T , and 3T ) Period 1 2 3 4 5 6 7 8 9 10 11 12

    p 15.48 15.48 15.48 15.16 15.16 15.16 14.86 14.86 14.86 14.70 14.70 14.70

    1T 0.38 3.41 6.44 9.57

    2T 2.36 5.38 8.40 IFS

    styl

    e

    3T 2.90 5.90 8.90

    p 15.48 15.48 15.48 15.15 15.15 15.15 14.85 14.85 14.85 14.57 14.57 14.57

    1T 0.54 3.51 6.49 9.47

    2T 0.63 3.61 6.59 9.57SFI s

    tyle

    3T 1.01 4.02 7.03 10.04

    Table 1b. Numerical results of optimal demand (D)

    and lot-size (Q) Period 1 2 3 4 5 6 7 8 9 10 11 12

    D 22.37 21.93 21.49 22.57 22.12 21.69 22.58 22.14 21.70 21.92 21.49 21.06

    IFS

    styl

    e

    Q 56.39 13.74 57.37 13.40 57.86 12.97 71.14

    D 22.39 21.95 21.52 22.57 22.12 21.69 22.60 22.15 21.71 22.46 22.01 21.58

    SFI s

    tyle

    Q 70.18 70.81 70.86 70.43

    Several key performance measures as outlined

    in the fourth layer of the decision system are given in table 2, including the second order sufficient condi-tions and Hessian matrix, deteriorating quantity, maximal inventory level, service level, periodic profit, and accumulated profit. In the example, both policies generated identical production cycles ( 9,6,3,01 =iz ) and the same number of produc-tions n = 4. It is worth mentioning that the deterio-rating quantity is the production lot-size minus the quantity demanded in the market. Comparing the solutions generated by the two styles, the SFI produc-tion style generates lower price and more net profit (758.02 vs. 734.13). Intuitively, the lower price yields more quantity demanded in the market as well as larger production lot-size. It is worth mentioning that production lot-size of the IFS production style is lar-ger than that of the SFI policy over the last cycle (71.14 vs. 70.43), because the former has no shortage and more amount of deteriorating units. In addition, the SFI production style produces smaller value of

    maxI (47.01 vs. 57.24) which implies less storage ca-pacity required and, as a result, less investment needed in warehousing and material handling system.

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  • 342 Journal of the Chinese Institute of Industrial Engineers, Vol. 25, No. 4 (2008)

    4.2 Comparative study

    Using the settings in the example above, we compare the net profits generated by the two produc-tion styles with respect to major parameters, such as the price-sensitivity coefficient of demand b, produc-tion unit cost c, shortages cost s, holding cost h, set-up cost K, and deteriorating rate . As shown in figure 4, the SFI production style outperforms the IFS production style significantly in the total net profit as b and c increase, while it is insignificant to the larger value of s, h, K, and .

    Table 2. Sufficiency conditions and key performance

    measures

    [ ii zz ,1 ] [0,3] [3,6] [6,9] [9,12]

    22

    p -27.22 -25.70 -24.25 -22.48

    22

    2

    T -136.54 -134.90 -132.33 -124.66

    Hessian Matrix 3716.92 3466.28 3209.15 2697.80

    dQ 70.13 70.77 70.83 71.14

    maxI 47.18 47.33 47.11 57.24

    SL 0.80 0.81 0.82 1.00 157.69 180.79 200.44 195.22

    IFS

    styl

    e

    734.13

    22

    p -27.24 -25.71 -24.26 -22.90

    22

    2

    T -142.89 -141.22 -138.57 -135.18

    Hessian Matrix 3891.64 3630.18 3361.80 3094.85

    dQ 70.18 70.81 70.86 70.43

    maxI 46.85 47.01 46.79 46.27

    SL 0.80 0.80 0.81 0.82 158.37 181.42 201.01 217.21

    SFI s

    tyle

    758.02

    20151050-5-10-15-20

    Percentage changes from basic setting

    0

    2

    4

    6

    8

    10

    12

    14

    16

    18

    20

    22

    24

    26

    Per

    cent

    age

    diffe

    renc

    e in

    pro

    fit o

    f SFI

    and

    IFS

    sys

    tem

    s

    b c s h K

    Figure 4. Impact of price-sensitivity coefficient of demand (b), production unit cost (c), shortages cost

    (s), holding cost (h), set-up cost (K), and deteriorating rate () on profit improvements: SFI vs. IFS

    4.3 Dynamic behavior of price trajectory This study is to investigate the impact of key

    factors such as 3 and on the dynamic behav-ior of price trajectory generated by SFI production styles. For better observation, a longer planning ho-rizon H = 24 was applied. Figure 5 graphically shows the price trajectories under various settings of market magnitude and price-sensitivity. In the cases of con-stant price-sensitivity, the price changes larger for increasing and higher values of 3 (= + 0.03). In the cases of time-varying price-sensitivity ( 0), the price is larger adjusted significantly for the in-creasing price-sensitivity along time, and insignifi-cantly for the time-decreasing sensitivity.

    0 2 4 6 8 10 12 14 16 18 20 22 24

    Period

    12.0

    12.3

    12.6

    12.9

    13.2

    13.5

    13.8

    14.1

    14.4

    14.7

    15.0

    15.3

    15.6

    15.9

    Pric

    e

    3= 0.01, = 0 3= 0.03, = 0 3= +0.01, = 0 3= +0.03, = 0 3= 0, = 0.005 3= 0, = +0.005 3= 0.005, = +0.005 3= +0.005, = 0.005

    Figure 5. Price trajectories in SFI production styles over the planning horizon

    5. CONCLUSIONS

    This paper has proposed two production styles, SFI and IFS, that determine the optimal price and production lot-size/scheduling for a deteriorating item over finite planning horizon. We have presented the necessary and sufficient conditions to the maxi-mization problem, formulated the problem as a dy-namic programming model, and provided the solution procedure. An extensive numerical study has been conducted to attend qualitative insights into the structures of the proposed styles and their sensitivity with respect to major parameters such as price-sensitivity coefficient, unit production cost, shortages cost, holding cost, set-up cost, and deterio-rating rate. The numerical results have shown that the solution generated by the SFI production style out-performs that by the IFS in maximizing the net profit and other quantifiable measures such as minimizing inventory investment and storage capacity. Further, we have shown that the percentage of profit differ-ence between the two styles increases significantly in price-elasticity coefficient of the demand function as well as the production unit cost, and the price

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  • Chen and Chen: Collaborative Marketing and Production Planning with IFS And SFI Production 343 Styles in an ERP System

    changes larger for increasing and higher values of trend of market magnitude under constant price-sensitivity and the price is larger adjusted sig-nificantly for the increasing price-sensitivity along time.

    The proposed models are based on a periodic review policy which makes it applicable in many manufacturing planning and control practices. They can be used as an add-on optimizer like the advanced planning system in an ERP system. The main restric-tion for the practical implementation of the model is subject to its dynamic pricing mechanism which may be unacceptable by the contract-based customers. Further, a single product assumption may make the research impractical and restrict its potential applica-bility. However, as with most management science applications, the proposed scheme is purely theoreti-cal. In our study, the product was assumed to be sin-gle, the pricing policy was periodic, and the proposed scheme can only apply to designated scenario. These assumptions and restrictive conditions may limit its applicability, yet does not degrade its merit. Our ex-ploratory research has demonstrated technical feasi-bility of the proposed scheme. A natural extension of this research is to consider more complicated and practical demand and deterioration functions in the model, such as the stochastic demand and the fuzzy-modeling deterioration. Another direction of this research is to develop a prototype of an advanced planning system with an ERP system that integrates the management science techniques into commercial software for collaborative and robust planning.

    APPENDIX A: THE MODEL OF IFS PRODUCTION STYLE

    In the IFS style, a production/inventory cycle can be divided into four periods (see figure 1). The variation of the inventory level ),( tpI with respect to time t can be described by the following style of equations:

    ),( tpI =

    t

    z

    vdv

    i

    u

    t dueupDu1

    )())(()),()((

    ,

    for 11 Ttzi ; (1) =

    2 )())((),(

    T

    t

    vdvdueupD

    u

    t

    ,

    for 21 TtT ; (2) =

    2

    ),(T

    t

    duupD ,

    for 32 TtT ; (3) =

    t

    zi

    duupDu )),()(( ,

    for iztT 3 . (4)Derivations of equations (1-4) are analogous to

    Chen and Chen [5]. Accordingly, the production lot-size can be obtained by integrating the production rates over [ 1iz , iz ]:

    ),( 2TpQ =

    1

    1

    )(T

    zi

    dtt + iz

    T

    dtt3

    )( ,

    for ii ztz 1 . (5)

    In what follows, the two-variable maximization problem over cycle ],[ 1 ii zz is formulated and solved optimally. Determination of the optimal start-ing time of the cycle, 1iz , i = 1, 2,, n, for the multi-period problem is then solved by using dy-namic programming.

    For an arbitrary cycle ],[ 1 ii zz , the total profit

    is the net value of the total revenue )(1

    piz

    and the

    total cost ( )2,1 Tpiz in the IFS style as expressed below:

    ),( 21 Tpiz =

    i

    i

    z

    z

    dttppD1

    ),(

    2

    1 1

    ),()())((

    T

    z

    t

    T

    vdv

    i

    t

    u dttpDdueh

    iz

    T

    dttpDtTs2

    ),()( 3

    dtttTCtT

    z i

    1

    1

    )()),()(( 11

    iz

    T

    dtttTCt3

    )()),()(( 32 K

    for ii ztz 1 . (6) Derivations of equation (6) are analogous to

    Chen and Chen [5]. Model (6) is a function of the selling price p and the time-variable 2T . For a given cycle over ],[ 1 ii zz , the optimal production lot-size and selling price in the cycle can be determined si-multaneously by solving the first order differential equation of model (6) with respect to p and T2 sepa-rately and setting the results equal to zero. The con-cavity property of the profit model can be proved by verifying Hessian matrix. We will take a numerical approach to ensure the concavity of the problem to be studied in the examples.

    The optimal production schedule and associ-ated price trajectory and lot-sizes over the planning

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  • 344 Journal of the Chinese Institute of Industrial Engineers, Vol. 25, No. 4 (2008)

    horizon can be determined by solving the dynamic programming model:

    { }HzzTp iizzz iii

  • Chen and Chen: Collaborative Marketing and Production Planning with IFS And SFI Production 345 Styles in an ERP System

    6. Crittenden, V. L., Close the marketing/manufacturing

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    ABOUT THE AUTHORS

    Liang-Tu Chen is an assistant professor in the De-partment of Commerce Automation and Management at the National Pingtung Institute of Commerce (Taiwan). He received a B.S. in Industrial Manage-ment from the National Taiwan University of Science and Technology in 1991, an MS in Industrial Engi-neering and Management from the National Chiao Tung University (Taiwan) in 1996, and a Ph.D. in Industrial Management from the National Central University (Taiwan) in 2005. His research interests include supply chain management, enterprise re-source planning, channel coordination, pricing, and yield management. Dr. Chen is the recipient of the Dragon Dissertation Award from the Acer Foundation (Taiwan) in 2004. Jen-Ming Chen is a professor in the Institute of In-dustrial Management at the National Central Univer-sity (Taiwan). He received a B.S. in Industrial Man-agement Science from the National Cheng Kung University (Taiwan) in 1983, an M.S. in Industrial Engineering from the University of Arizona in 1988, and a Ph.D. in Industrial Engineering from the Penn-sylvania State University in 1992. His research inter-ests include inventory and supply chain management, channel coordination, and pricing and yield manage-ment. Dr. Chen is the recipient of the George B. Dantzig Dissertation Award from the Informs and the recipient of the IIE Doctorial Dissertation Award, both in 1994. (Received November 2007; revised January 2008; accepted March 2008)

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    *

    900 51

    (SFI)(IFS)

    SFIIFS

    (*: [email protected])

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