An integrated approach to product design and process selection

An integrated approach to product design and process selection

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UNIVERSITY OF ILLINOIS LIBRARY AT URbANACHAMPAIGN BOOKSTACKS CENTRAL CIRCULATION BOOKSTACKS The person charging this material is re for disciplinary action and moy result the Unlwenlty _„„,_ /ENTER 3338400 A PR 6 1999 When renewing by phone, write new due date below previous due date Digitized by the Internet Archive in 2011 with funding from University of Illinois UrbanaChampaign http://wwwarchiveorg/details/integratedapproa92178chha Faculty Working Paper 920178 330 B385 bTX An Integrated Approach to Product Design and Process Selection Ditip Chhajed Narayan Raman Department of Business Administration Department of Business Administration University of Illinois University of Illinois Bureau of Economic and Business Research College of Commerce and Business Administration University of Illinois at UrbanaChampaign BEBR FACULTY WORKING PAPER MO 920178 College of Commerce and Business Administration University of Illinois at ClrbanaChampaign November 1992 An Integrated Approach to Product Design and Process Selection Dilip Chhajed Narayan Raman Department of Business Administration An Integrated Approach to Product Design and Process Selection Dilip Chhajed Narayan Raman Department of Business Administration University of Illinois at UrbanaChampaign Champaign, Illinois 61820 November 1992 ABSTRACT The conventional approach to new product design involves a sequential flow of decisions At the first step, the marketing function determines the product profile by specifying the required product attributes based upon consumer research Manufacturing is then expected to determine the appropriate processes capable of delivering these attributes efficiently In practice, such a sequential approach leads to substantial delays in product introduction and frequent product redesigns long after it has been introduced Increasing competitive pressure necessitates an alternative, integrated approach in which the product design and the process selection decisions are made simultaneously This study models such an integrated approach for the objective of maximizing the producer's incremental profit as an integer program Process selection is merged with product design by explicitly considering the alternative processes available, and the associated fixed and variable costs, for providing an attribute at a given level The overall decision involves simultaneously determining the levels at which each attribute will be present in the new product as well as the processes used for providing these attribute levels In addition, we treat product price as an extrinsic decision variable In view of the problem complexity, we propose a heuristic solution method that decomposes the overall problem into the product design and the process selection subproblems; the solution algorithm essentially iterates between these two subproblems Computational studies indicate that the suggested algorithm performs effectively with respect to the optimal solution Furthermore, the relative effectiveness of the integrated approach is seen to depend strongly on process related problem parameters In particular, the integrated approach is increasingly superior as the producer faces more intensive competition, greater product complexity, and high fixed and variable process costs 1 INTRODUCTION Manufacturing and service firms need to introduce new products frequently in order to remain competitive Product design involves the consideration of the needs and preferences of individual market segments, products offered by the competition, as well as the company's own existing products in view of the possible cannibalization The marginal profitability of the new product clearly depends upon the fixed and variable production costs in addition to the incremental net revenue generated Thus, the process selection decision plays an important role in determining the overall success of the new product The traditional approach to product design and process selection, also known as "over the wall approach" and " relay race", involves a sequential flow of decisions Marketing function determines the "product profile" by specifying the required product attributes Subsequently, the production function determines the processes capable of delivering these attributes While such a delineation of decisions appears to be logical conceptually, in practice it leads to substantial delays in product introduction, bureaucracy, high cost, and frequent product redesigns long after it has been introduced Increasing competitive pressure has necessitated a significant reduction in the lead time required for introducing new products This trend has generated increasing interest in an integrated approach in which both product and process are designed concurrently Such an integrated approach has been operationalized in a variety of ways such as simultaneous engineering (Evans 1988), concurrent engineering (Brazier and Leonard 1990), quality function deployment, house of quality (Hauser and Clausing 1988) In particular, the house of quality provides a good framework for an objective analysis as well as a tool for integrating the product design process However, decisions on many design alternatives are still made without considering the entire system While there is substantive empirical evidence suggesting the potential of the integrated approach, the literature on modeling this problem is relatively sparse The bulk of the existing literature on product design focuses exclusively on consumer preferences Two approaches to this problem have been proposed Multidimensional Scaling (MDS) and Con joint Analysis In the MDS approach, each customer's ideal product is represented as a point in a continuous multiattribute space whose dimensions are differentially weighted across customers The relative preference of any customer for a given product is inversely related to the "distance" of the product from the customer's ideal point in this space Product selection is either deter ministic, firstchoice or probabilistic with the probability of a particular product being chosen is related to its distance from the customer's ideal point Product design optimization based on the MDS approach was introduced by Shocker and Srinivasan (1974), has since been pursued by several other researchers (see, for example, Zufreyden 1979, Hauser and Simmie 1981, Gavish, Horsky and Srikanth 1983, Sudharshan, May and Shocker 1987, and Eliashberg and Manrai 1989) The objec tives commonly considered include maximizing incremental profit and maximizing market share Albers (1976) and Sudharshan, May and Gruca (1988) extend this line of research to a product line In the typical Conjoint Analysis approach, which is the methodology used in this study, each at tribute is specified at one of several potential discrete levels In most formulations, the overall utility of the product for a given customer is given by the sum of the idiosyncratic part worth of the level at which each attribute is active The bulk of this research employs a deterministic firstchoice selection criterion A customer chooses the product with highest utility; alternatively, if price is considered as an extrinsic attribute, the product which provides the maximum surplus utility net of price, is selected Optimal product design based on conjoint analysis was first developed by Zufreyden (1977) for the objective of maximizing market share which has since been extended by Green, Carroll and Goldberg (1981) Other objectives that have been studied in the context of conjoint analysis include maximizing seller's return (Green and Kreiger 1985, Kohli and Krish namurthi 1987, Dobson and Kalish 1988, McBride and Zufreyden 1988) and maximizing buyer's welfare (Green and Kreiger 1985) In their recent work, Kohli and Sukumar (1990) extend the ap proach proposed by Kohli and Krishnamurthi (1987) to include all three objectives for introducing a product line Much of the existing research on product design does not explicitly consider the cost of providing the product As Johnson (1974) notes, these studies "assume that these versions (of product) are all feasible from a manufacturing and pricing standpoint, that we could produce any one of them, and we wish to choose the "best" version" A notable exception is Dobson and Kalish (1988) who consider both fixed and variable manufacturing costs of each product, and also consider price to be an extrinsic variable They construct a general model for selecting a line of products from a prespecified set of candidate products, and construct a two stage heuristic to obtain the approximate solution However, Dobson and Kalish do not explicitly consider the process selection decision In imputing the manufacturing costs to a product, they assume, in effect, that this decision is made independently and the optimal process is used for each product The model developed in this study addresses the introduction of a single new product for the objective of maximizing the producer's incremental profit The significant point of departure of this work from previous research on product design lies in integrating the product design and process selection decisions Unlike the DobsonKalish model, we consider each attribute level explicitly, and build the optimal (or nearoptimal) product profile directly from these levels Process selection is integrated into the product design problem by explicitly considering the alternative processes available, and the associated fixed and variable costs, for providing an attribute at a given level The overall decision involves simultaneously determining the levels at which each attribute will be present in the new product(s) as well as the processes used for providing these attribute levels In addition, akin to the DobsonKalish model, we treat product price as an extrinsic decision variable The incorporation of manufacturing costs into the model enables us to consider the tradeoff between using the processes currently available within the company and buying new equipment Because the new product is likely to share a number of common features with existing products (Srinivasan and Shocker 1979), the current manufacturing facility may be capable of providing certain attribute levels with negligible increase in fixed costs, while on the other hand, new equipment has the poten tial of reducing variable costs Furthermore, the model provides a basis for evaluating the economic worth of process flexibility For example, consider the decision of selecting between a (relatively inflexible) process that can provide only a limited number of attributes, and an alternative process capable of providing a wider range of attributes, albeit less efficiently The outcome of this decision clearly depends upon the mix of attributes under consideration, as well as the demand volume generated by the customers who switch to the new product Similarly, whether or not an attribute will be present at a given level depends upon the associated manufacturing cost, in addition to the additional revenue that it will generate The paper is organized as follows §2 discusses the major characteristics and assumptions of the model We formulate the problem as a nonlinear mixed integer program, and show that it is NP hard In §3, we present an iterative heuristic solution procedure that decomposes the problem into product design and process selection subproblems The performance of this heuristic is evaluated in §4 In addition, we demonstrate the merit of adopting the integrated approach over the sequential approach to product design and process selection, and relate it to various model parameters §5 summarizes the main results of this study Proofs of mathematical results stated in the paper can be found in Appendix 1 2 Problem Description The model is based on the conjoint analysis approach to estimating consumer preferences The product to be designed is comprised of K attributes A given attribute k 6 /C is realized in the product at exactly one of Jjt discrete levels Some of these attributes can be options which occur at two levels 'present' and 'absent' The set of levels for attribute k is denoted by J^ A product profile is denoted by X = (Xi, ,Xk), where Xk = (in, ,xj k k) T X — (1,2, ,/) denotes the set of customers A given customer i G J represents either an individual or a segment The weight p, is a measure of segment population and product purchase frequency for customer i Let Wijk denote the part worth of attribute k at level j for customer i Consistent with the most frequently used formulations of conjoint analysis, we assume that the utility U{ of any product X for customer i, i = 1, ,/ is the sum of the part worths of individual attributes; i e, U{ = <7k<7]WijkXjk' We also assume that the customer employs a deterministic firstchoice selection criterion based on maximizing his/her surplus Therefore, given the utility £/,, price 7r and surplus u,(= U{ — it) of the new product, customer i will switch if w, > u° where v,® refers to the surplus of the product currently purchased by customer i [Uf and icf are similarly defined] /, denotes the marginal contribution made by customer i to the firm; it is nonzero only if i is a customer of one of the existing products made by the firm The model developed in this study does not address the competitive reaction to product design decision made by the producer Thus, the situations modeled here are that of no competition or passive competition in the sense of Dobson and Kalish (1988) The set of candidate processes is denoted by M, and \M\ = M Each process m € M has a fixed cost of f m , and a variable cost of Vjk m for producing attribute k at level j In this paper, a process denotes an entity that can deliver an attribute at a given level Thus, a process can be a single workcenter, a manufacturing cell or even an entire plant; it could also denote a subcontractor We assume that each process has unlimited capacity While, as we discuss later in §32, it is possible to include these constraints in the overall solution approach, doing so introduces discontinuities that obscure the useful insights otherwise available from a basic model Aside from the assumptions made above, the model is quite general No structure is imposed on the part worths which can be defined arbitrarily in the multiattribute space for the individual customers The model allows for the cannibalization of existing customers by the new product Similarly, in regard to the process, no restriction is placed on the values that the fixed and variable costs can take The formulation also permits process flexibility, i e, a given process can be used for producing more than one attribute The integrated product design and process selection problem (PDPS) is formulated as the following mathematical program: PDPS Z= max ^2(irpili)si ^ f m q m ^PiSi I 5Z ]C S v JkmZjkm I (1) i€l meM i£l \meM k^fC j&J k J subject to H ]C w 'jkXjk * u ° < Bs t Vz (2) keiCjeJk * ~ H S w *3k x jk + «? < 5 (1 5,) Vi (3) ^x^l Vk (4) ^ ZjJfcm > Xj* Vj, k (5) ^fcm < ?m Vj, fc, m (6) ir > 0;si,Zjkm,Xjk,q m € (0,1) Vi,j,k,m (7) where 5, = 1 if customer i switches to the new product, otherwise; Xjk = 1 if attribute k is provided at level j in the new product, otherwise; q m — 1 if process m is selected, otherwise; and Zjkm = 1 if level j of attribute A: is assigned to process m, otherwise Expression (1) states the objective of maximizing the difference between net revenue total revenue less loss due to cannibalization, and incremental fixed and variable costs Disjunctive constraints (2) and (3) enforce the product selection criterion for each customer; the first term in (2) is the total utility U x provided by the product to customer i Constraint (4) requires each attribute to be specified at exactly one level Constraints (5) and (6) guarantee that the selected level of each attribute is assigned to at least one process and the appropriate variable and fixed costs are taken into account Finally, constraints (7) specify the nature of the variables This formulation can be used to answer questions such as: • Should a new product be introduced at all? • Is it better to buy a flexible machine that is capable of providing a number of attributes or should dedicated machines be purchased? • Should a new option, favored by a large number of customers, be offered even if it requires significant fixed expenditure? • If a company is thinking about expanding its current line of products, which of the attribute levels currently being offered should be duplicated in order to minimize incremental fixed costs? The following result indicates that it is unlikely that an efficient procedure for solving this problem exactly can be constructed Remark 1 PDPS is NPhard in the strong sense In view of the computational complexity of PDPS, we construct a heuristic solution approach for solving it 3 Heuristic Solution Procedure The formulation of PDPS given by (l)(7) indicates that it comprises two subproblems: (l)(5) and (7) define the problem of determining attribute levels, while (1), (5)(7) specify the problem of determining the processes (5) provides the coupling constraints between these two subproblems; also, variables s, appear in both subproblems The proposed heuristic solution procedure exploits this structure by decomposing PDPS into the subproblems which are solved iteratively 31 The Basic Algorithm A brief statement of the algorithm is given below Algorithm BasicDesign Step 1: Initialization: Determine initial product profile X 1 by selecting appropriate values of Xjk,k = 1, , K, j = 1, , Jk Set n = 1, Z° = 0 Step 2: Process Selection Problem: For the given product X n at iteration n, determine the optimal set of processes, the optimal set of switching customers and the optimal price Let the set of processes selected be M n Determine the profit Z n corresponding to X n and M n Stop if (Z n — Z n ~ l )/Z n < e Else, set n <— n + 1, and go to step 3 Step 3: Attribute Level Selection Problem: For the given set of processes M n ~ l , find the best product profile X n Stop if X n = X n_1 Else, go to step 2 The initial product profile can be determined in one of several ways For example, any one of the existing products can serve as the starting profile An approach to obtaining the initial solution that we found to be particularly effective in our computational studies was to solve the product design problem given in step 3 with all processes being available, i e, M° = M However, the performance of the algorithm depends more critically on solving Steps 2 and 3 efficiently The solution approaches to these two problems are now discussed 32 The Process Selection Problem Consider the problem of determining the optimal set of processes for a given product X Let jk denote the level at which attribute k,k = 1,2,, A' is active in this product Its utility for customer i is U{ = J2keic w *Jkk The resulting problem is PSP Z(X) = max ^2(irpiIi)si J2 /mtfm^P' 5 '! ]C Yl HC V JkmZjkm subject to Ui 7T M? < Bs % Vl (8) irUi + v!j 1 Vfc (10) Zj k km < q m Vk,m (11) * > 0;s,, z Jk km,q m e (0, 1) Vz',A;,m (12) Now consider a restricted version of (PSP) with n = ir' The set of customers J„/ who switch to the new product is J T , = {i\Ui Ui > z'} (13) Let P„i = J2iei , Pi represent the total population of the switching customers The restricted problem can be written as RPSP Z(X,7r') = max subject to m€M \m€M k£)C (10), (11), and z Jk km,qm € {0, 1} Vfc,m The first term in the objective is a constant with respect to the problem variables; it can, therefore, be ignored for the purpose of finding the optimal solution The remaining problem has the structure of the uncapacitated facility location problem (UFL) if we treat attribute levels jk as the unit demand points and the processes m as the candidate location sites f m is the fixed cost of opening a facility at location m, and P K iVj k k m is the cost of satisfying the demand at jk from location m Although UFL is NPhard, efficient solution procedures are available for obtaining strong bounds and for solving reasonably large problems within acceptable computation time In our computational study, we use the dual ascent procedure DUALOC developed by Erlenkotter (1978) Let Z'(X,7r') denote the optimal solution to UFL, then Z(X,w') = n'Pi r , £ / t Z'(X,7r') The solution to PSP is given by Z{X) = max^ZiX,*) = Z(X,ir*) Let <§, = U{ — u° The following result indicates that the search for ir* involves considering at most / values of n Proposition! K* E {61,62, , Si} Consequently, at each iteration, we need to solve at most / uncapacitated facility location problems in order to determine the optimal set of processes As shown in the proof of Proposition 1, this step generates the best price and the set of switching customers as well If we impose capacity limitations on individual processes then (11) is replaced by constraints of the form P*>Z] k km < CAP m q m Vfc,m where CAP m is the capacity of process m In this case, the solution approach to PSP essentially requires solving a number of capacitated facility location (CFL) problems, instead of the UFL prob lems considered here While CFL is harder to solve optimally, several heuristic solution methods exist for it so that from an algorithmic standpoint, capacity constraints can be included within the solution approach 33 The AttributeLevel Selection Problem Now consider the problem for determining the optimal set of product attributes given a set of processes M° = {m\q m = 1} Let f(M°)= £ f m , and m€M° v' ]k = min meM o{vj k m} = v ]krn , Clearly, for a given (j,k), Zjk m equals 1 for m = m', and equals for all other m The attributelevel selection problem can now be stated as ASP KM ) Z(M°) = max £ «6I ke>Cj€Jk subject to (2), (3) (4), and s t ,x jk e {0,1} V«,i,* ASP generalizes the model proposed by Kohli and Sukumar (1990) for the seller's return problem to include product price as an extrinsic decision variable We construct a heuristic solution method that extends the KohliSukumar algorithm to incorporate this generalization This procedure uses a dynamic programming like approach in which each attribute is treated as a stage, and individual attribute levels are the states Starting with attribute 1, this method successively performs a local optimization with respect to adjacent attributes that is followed by attribute augmentation Specifically, at step k of the procedure, only attributes k and k + 1 are considered Let J t — \Jt\, t = l,,K For a level j 6 Jk+i, Jk partial product profiles are constructed by associating each r E Jk with j Of these Jk profiles, the profile (r*,j) that maximizes profit is selected, and r* is merged into j The next iterative step involving attributes k + 1 and k + 2 is then solved with respect to these augmented attribute levels for attribute k + 1 Thus the heuristic forms partial product profiles of increasing cardinality in attribute space, with the profile at the end of stage k consisting of the first k + 1 attributes A formal description of the procedure now follows Algorithm BuildProduct Step 1: Initialization: For each customer i, determine the "partial price" of attribute k as 0* = *?U? k /U? where Uf k is the part worth of attribute k to customer i in the product that i buys currently Set fc = l Step 2: Recursion' a Local Optimization: At step k, for each level of attribute k+l, determine the level r* of attribute k that maximizes the overall contribution b Attribute Augmentation : Set v' hk+l = v' hk+l + v r k Step 3: Termination: If k < K — 1, set k = k + 1, and go to step 2 Else, determine the optimal level fa for attribute K Set x 3 k — 1 if J = j^; Xjk = 0, otherwise Do a backward pass; for k = K — 1, , 1, set x T k = 1 if r = r* and x ]t k+\ = 1; x r k — 0, otherwise The major step in this algorithm involves local optimization at each stage For a given level j of attribute k + 1, this problem can be formulated as: Pl(j,*+1) r*j = arg max r€Jk ^ (vi{* ~ v' jM1 v' rk ) /,) s { (14) subject to >ij,k+i + ™ 0 Equation (14) enforces local optimization with respect to attributes k and k + 1, while equations (15) and (16) insure that customer i will switch to the partial product if and only if it provides a higher surplus than the surplus offered by the current partial product To solve Pl(j, k + 1), we first find the optimal price 7r* corresponding to each r £ J7jt The maximum price that customer i is willing to pay to switch to the partial product defined by levels r and j for attributes k and k + 1, respectively, is given by e % rj = Wij,k+l + Wirk ~ [U°k+l + U?k ~ 0*k ~ ^i,Jfe+l] The profit corresponding to a price of e' is given by Eir = Y^M e n ~ v 'j,k+i ~ v rj) l g] ged where Q = {g\g G J, e 9 r > e l rj } Arguments similar to those used in the proof of Proposition 1 yield Consequently, the maximal profit corresponding to level r of attribute k is given by E*j = max ie x{E tT } Pl(j,k + 1) is then solved by r*j = arg max r€ j k {E*j} At step 3 of BuildProduct, the optimal attribute level is given by fa — arg max je j K {Ej}, where Ej = E*j Thus algorithm BasicDesign essentially iterates between the product and the process spaces, thereby dealing separately with problems of reduced dimensionality While it is difficult to analyze its convergence properties theoretically, in all our computational experiments, it was found to converge quite rapidly However, there are instances in which it may converge to a solution that is only locally optimal In order to overcome this drawback, we imbed this algorithm within a simulated annealing based approach This enhancement is now described 11 34 Algorithm Refinement Based on Simulated Annealing Simulated annealing has been successfully employed for solving some difficult problems such as graph partitioning (Johnson et al 1989), pattern recognition (Geman and Geman 1984), VLSI design (Kirkpatrick, Gelatt and Vecchi 1983), single machine minimum tardiness schedule (Matsuo, Suh and Sullivan 1987a), job shop minimum makespan (Matsuo, Suh and Sullivan 1987b) and operation partitioning ( Ahmadi and Tang 1991 ) We give below a brief description of this approach For details, the interested reader is referred to Kirkpatrick et al (1983), and Johnson et al (1989) Consider the following problem: max h(y), subject to y 6 y where h(y) is a realvalued function on domain y Each element y 6 y has an associated set of neighborsM(y) such that any element y' 6 M(y) can be reached from y by a onestep perturbation A typical ascent algorithm based on neighborhood search moves from a given y to its neighbor y' if h(y') > h(y) If there is no such neighbor, then the algorithm terminates having returned y as the best solution If h(y) is not concave, such an algorithm will frequently yield solutions that are only locally optimal In contrast, simulated annealing permits occasional downhill moves, and thereby, provides a mech anism to escape from a local optima Under simulated annealing, the probability that a move will be made from y to y' is given by a = exp{{h(y) h(y')}+ /TEMP(g)) where [t] + denotes max(0,t), and TEMP(p) is a positive number Thus, a profitable move will always be accepted; however, there is a nonzero probability of accepting an unprofitable move as well, a is a function of the difference in the objective function values at y and y', as well as the temperature TEMP(<7) at a given state g A simulated annealing algorithm goes through several states of gradually decreasing temperatures A commonlyused sequence of temperatures follows a geometric series given by TEMP(y) = r * TEMP(<7 — 1) where r is the cooling rate such that < r < 1 Clearly, the probability of accepting a downhill move decreases with a reduction in temperature The system is deemed to be frozen if there is virtually no change in the solution value at successive temperatures Under certain assumptions, it is possible to show ( Anily and Federgruen 1985; Geman and Geman 1984) the existence of certain values of r that guarantee that simulated 12 annealing will obtain the optimal solution in the limiting case Although it is conjectured that the rate of convergence may be slow, this approach has yielded good solutions for many practical problems within reasonable computation time For PDPS, we define the neighborhood of a given solution individually for the process and the product spaces In the process space, the neighborhood Af\{Q r ) of a given point Q r = (q[, ,q T M ) consists of all points Q 5 = (q{ , , q s M ) such that 9m = Qm for m = 1, ,Af; m ^ 71, and, Qn = 1 " Qu it can be seen that the neighborhood of Q r consists of M points Similarly, the neighborhood A/2(X r ) of a point X r = (X[, , A£) in the product space comprises all points X s such that X a k = XI ioik= 1,,A' k^n, X U = x )n (or j = l,,J k j ^ g, and, x s = 1 — x T It can be seen that the neighborhood of X r consists of Ylk=i(Jk ~ 1) points For a given pair (X r , Q s ) of points from the product and the process spaces, the optimum objective function value Z(Y rs ) can be obtained as follows For each (j, k) such that x r jk = 1, set Zjk m > — 1 where m' = arg minm^jkmWm = 1} is the machine with the minimum variable cost for producing attribute k at level j among all the open machines, and set all other Zjkm — 0 Next use the approach given in §32 to determine the optimal values of s, and 7r It follows, therefore, that a solution Y to PDPS is completely determined by the selection of the product profile and the set of open machines The parameters required for implementing this algorithm are the starting temperature INITTEMP; the cooling rate r; the termination threshold c; and the maximum values N\ and A r 2 that the counters which control the number of neighbors scanned can take A formal statement of the simulated annealing algorithm is given below The various steps are described in detail subsequently In the following, Z() represents the optimal objective function corresponding to solution (•), Y mc denotes the incumbent solution, and Z g is the best solution value obtained until temperature g 13 Algorithm IntegratedDesign Step 1: Initialization Set the initial solution Y° = (X°,Q°) to the solution obtained from algorithm BasicDesign Set the incumbent solution Y mc = Y° Also set TEMP(0)=INITTEMP; m = 0; g = 0; and Z = Z(Y°) Go to Step 2 Step 2: Annealing If ni > Nu go to Step 5 Else, set g =gl; TEMP(#) = r*TEMP(#+l); and n 2 = 0 Go to Step 3 Step 3: Neighborhood Scan a) Set n 2 < n 2 + 1 If n 2 < N 2 , fix m = 1, and go to Step 3b) Otherwise, set Z g = Z(Y mc ) If Z g < (1 + e)Z g i, then set n\ *— n\ + 1 Else, set n\ = 0 Go to Step 2 b) If ra > M, go to Step 3a) Else, determine the neighbor Q 1 of Q° by setting q^ = 1 — q^ Determine X 1 and Y 1 Go to Step 4 Step 4' Neighbor Selection If Z(Y X ) > Z(Y°), set Y° = Y* nc = Y 1 , set m < m+ 1, and go to step 3b) Otherwise, compute a = expHZtY 1 ) Z(Y°)}/TEMP(^)] Generate a random number a from the uniform distribution [0,1] Set Y° = Y 1 if a > a Set ra <— ra + 1 Go to step 3b) Step 5: Reoptimization Determine the optimal solution Y* corresponding to the incumbent product profile X mc The algorithm is initialized with the solution obtained from BasicDesign in Step 1 Computational experience (see, for example, Johnson et al 1989, and Ahmadi and Tang 1981) indicates that good starting solutions usually enhance the performance of simulated annealing Step 2 implements the specified cooling schedule; it also determines whether the frozen state is reached This algorithm maintains a counter n\ that is incremented by one each time the incumbent solution value obtained at the end of the neighborhood search at any temperature does not exceed the incumbent solution 14 value at the previous temperature by the threshold c The system is deemed to be frozen if the counter value equals N\ At each temperature, Step 3 controls the generation of neighbors This is done by considering the neighborhood of the partial solution Q° through N2 cycles In any cycle, the algorithm generates each of the M neighbors of Q° in turn For any neighbor Q 1 , the approach given in §33 is used to determine the corresponding product profile X 1 Subsequently, Y 1 is determined from Q 1 and X 1 Step 4 in the algorithm executes the logic pertaining to the acceptance of a neighboring solution, and if necessary, updates the current and the incumbent solutions The solution obtained at the end of simulated annealing is reoptimized at Step 6 This is done by retaining the incumbent product profile X mc , and solving the process selection problem following the procedure given in §32 to determine the optimal processes, the optimal price and the optimal set of switching customers Several parameter values were tested for implementing the simulated annealing phase of algorithm IntegratedDesign The values actually used in our computational study were r = 090; N\ = 5; N2 = 10; and INITTEMP= 001 * Zq where Zq is the solution value obtained from BasicDesign 4 Computational Experience We conduct two sets of computational experiments The first set addresses the performance of algorithm IntegratedDesign with respect to the optimal solution, while the second set evaluates the relative merit of adopting the integrated approach over the sequential approach as a function of various problem parameters 41 Experimental Details In order to better focus on the impact of process characteristics, we keep certain customerspecific parameters fixed across all experiments For example, the part worths Wijk are generated initially through random sampling from the uniform distribution [60, 340]; the realized values are retained in all experiments Similarly, in the second set of experiments, the total number of customers / is fixed at 20 (/ is varied in the first set merely to generate a larger number of problem scenarios) Customer populations are sampled from the uniform distribution [200, 600] and the resulting values remain fixed subsequently In all cases, the number of levels is the same for all attributes, ie, \Jk\ = tj, Vfc Also, the marginal contributions /, = 0, Vz 15 In each problem instance, we generate 1/5 competing products; the active attribute levels for these products are assigned randomly These products are assigned prices sampled from the uniform distribution [aU ave , bU aV e], where U ave is a measure of the average utility across all customers and across all products currently available U aV e — Kw ave , where w ave is the mean realized part worth given by _ E, Hk Ej Wjk Wave — T T ~ IKt) and A' and 77 are, respectively, the number of attributes and the number of attribute levels consid ered in the problem instance The best product and the resulting surplus u® for any customer i are determined from the profiles of the competing products and their prices, as well as the part worths Wijk We vary a and b in our experiments to yield various values of the mean price of competing products TT ave = Uaveio* + b)/2 The problem parameters of interest are i) the number of attributes K, ii) the number of levels in each attribute 77, iii) the number of processes M, iv) the mean process fixed cost ///, v) the coefficient of variation of process fixed cost Q, vi) the coefficient of variation of variable cost £„, vii) the ratio p = p v /w ave of the mean variable cost to the mean part worth, and viii) the ratio i?ave/U ave which is a measure of the surplus enjoyed by the customers currently The base values of these parameters are given in Appendix 2 The actual fixed costs f m used for the various processes are obtained by sampling from a uniform distribution which has mean /z/, and for which the upper and lower limits are derived from pj and C/ Similarly, the actual variable costs Vjk m are obtained from a uniform distribution determined by n v and C« The first experiment considers 27 different scenarios comprising 3 values of the number of segments, and 9 combinations of the number of attributes and the number of attribute levels as shown in Table 1 The other problem parameters are retained at their base values indicated in Appendix 2 10 instances of each scenario are generated For a given instance, the optimal solution value Z opt is obtained by first explicitly enumerating all r/ A profiles For each of these profiles, the process selection problem is solved to determine the optimal set of processes and the optimal price corresponding to that profile, and consequently the profit value as well The optimal solution for the overall problem is the best profit value across all these product profiles For each problem instance, we compute the performance ratio PR tn t = {Z opt Z tnt )/(Z opt ), where Z, n< is the solution 16 value obtained from IntegratedDesign Table 1 reports the average value of PR in t across all 10 instances; also reported in parentheses is the number of times the optimal solution was obtained in these 10 instances For comparison purposes, we also report the corresponding performance ratio PR seq for the se quential approach, where PR seq = {Z opt Z seq )/(Z opt ) and Z seq is the sequential solution value In any problem instance, the sequential solution is obtained by first determining the product profile using algorithm BuildProduct ignoring the attribute level variable costs Vjk m These costs are taken into account at the subsequent stage when we solve the process selection problem to yield the optimal set of processes as well as the optimal price It can be seen that, while the sequential approach performs limited optimization with respect to the processes and the product price for the selected product profile, it lacks the integrated approach's ability to revise this profile subsequently The exponential growth in the number of product profiles to be generated explicitly limits the size of problems that can be considered in the first set of experiments An alternative approach of evaluating the performance of IntegratedDesign through the use of upper bounds, based on Lagrangean relaxation, did not yield satisfactory results We found that these bounds were quite weak even for small problems The major reason for the weakness of these bounds appears to be the fact that the attributelevel selection problem has very little structure; it is essentially a general integer program The second set of experiments examines the impact of eight parameters, which are varied one at a time while the others are retained at their base values, on the relative performance of the integrated approach visavis the sequential approach Algorithm IntegratedDesign is used for generating the integrated solution value while the sequential solution value is determined in the manner described above Each of M , K and r) are considered at the seven levels of 3, 5, 7, 9, 11, 13, 15 Similarly, C/ and Q v are tested at levels of 008, 016, 024, 032, 040, 048 and 056 [Note that the largest value that the coefficient of variation of a uniformly distributed nonnegative random variable can take is 058] fi f is considered at levels $60000, $120000, $180000, $240000, $300000, $360000, and $420000 Mean fixed cost values higher than $420000 result in many solutions with zero objective function values; consequently, they are not considered We test p at the seven levels of 01, 02, 03, 04, 05, 06, and 07 Finally, we generate problems for seven values of the ratio ^avel (Uave) ~ 060, 065, 070, 075, 080, 085 and 090 17 The results of the second set of experiments are shown in Tables 2 through 9 As in the first set, 10 problem instances are generated randomly for each scenario For reporting purposes, we take the average of the solution values Z seq and Z tnt across these instances under the sequential and integrated approaches, respectively We use the measures PR = Zi nt /Z aeq and A = Z tnt Z seq to evaluate the relative performance of the integrated approach In addition, we also record the average optimum product prices 7T, n< and 7r se<7 obtained under the two approaches in each problem scenario 42 Experimental Results Table 1 indicates that algorithm IntegratedDesign frequently finds the optimal solution Across the 27 scenarios and the 270 problem instances, it is 1% away from the optimal solution on average More importantly, its performance does not appear to be datadependent; the worst performance ratio for the integrated solution is 65% (averaged over 10 problems) It is also seen that, even for these small problems, the integrated approach yields substantially superior results to the sequential approach which is on average 16% away from the optimal solution INSERT TABLE 1 HERE Tables 2 and 3 deal, respectively, with the impact of the mean variable cost and the mean fixed cost on solution values As seen in Table 2, while both Z{ n t and Z seq decrease with an increase in p (= p v /w ave ), Z int decreases more slowly Consequently, except at very high values of p, AZ increases leading to an exponential increase in PR Furthermore, 7r, n * is more sensitive to variations in /> A similar result is obtained for fj,j as indicated in Table 3 although in this case, the solution values as well as PR are less sensitive to changes in /// INSERT TABLES 2 AND 3 HERE Tables 4 and 5 deal with the impact of the coefficient of variation in the fixed and the variable costs Q and £„, respectively In each case, both Z, n< and Z 3eq increase with an increase in the parameter value Recall that both approaches find the optimal set of processes and the optimal price, albeit for (possibly) different product profiles As ( v (£/) increases, the probability of finding processes with lower variable (fixed) costs to manufacture the profile selected by the sequential approach increases; this, in turn, results in higher profit values The integrated approach is similarly benefitted, so that 18 in Table 4, AZ does not change appreciably with £ v However, as Tables 5 shows, AZ tends to decrease with an increase in £/ Also, any change in the value of ( v has a greater impact on the Z values relative to a similar change in £/ INSERT TABLES 4 AND 5 HERE Table 6 considers the number of candidate processes M Both Z seq and Z{ nt increase with an increase in M which is attributable to the fact that as M increases, there is a increasing likelihood of finding processes with lower cost structures Note that, while both Z seq and Z jn < attenuate with A/, the incremental benefits of increasing the number of candidate processes are greater for the sequential approach which results in a decrease in both AZ and PR as M increases Nonetheless, the initial difference in the profits under these two approaches is large enough in that the sequential approach requires much larger values of M to attain comparable profit levels INSERT TABLE 6 HERE As seen in Table 7, the integrated approach is increasingly superior with an increase in the number of attributes, and the incremental benefit generally appears to be additive Clearly, this approach is able to make a better use of the cost advantages resulting from higher process flexibility, ie, the ability of any process to deliver an increasing number of attributes Similarly, Table 8 indicates that the relative performance of the integrated approach, as measured by AZ, increases with an increase in the number of attribute levels t] as well INSERT TABLES 7 AND 8 HERE In Table 9 we use the ratio of the average price 7r ave to the average utility U ave = (Kw ave ) of the products currently available as a surrogate to measure the intensity of the prevailing market competition Lower this ratio, higher is the surplus enjoyed currently by the average customer, and therefore, less likely (s)he is to switch to the new product As seen from the table, while increased competition clearly erodes the profits obtained under both approaches, the integrated approach is more robust especially at low values of x a ve/U ave signifying extensive competition INSERT TABLE 9 HERE 19 As seen from Tables 2 through 9, a common outcome across all the different scenarios tested in the second set is that the optimum product price x tnt under the integrated approach is consistently higher than the price Tr seq under the sequential approach This implies that the utility of the new product for the average switching customer is higher under the integrated approach In summary, these experiments reveal that the integrated approach is increasingly preferable as the problem instance becomes more tightly constrained Such a tightness could be brought about by the intensity of competition in the market measured by K a ve/U ave , that results in large consumer surpluses It also results from higher product complexity, expressed in terms of the number of attributes and the number of attribute levels In regard to the process, this tightness is caused by high variable and fixed process costs, and from having a limited number of alternative candidate processes 5 Discussion and Summary This paper models an integrated framework in which the decision on new product design is made jointly with the selection of optimal processes required to manufacture the product This problem is formulated as nonlinear integer program We construct a solution approach that has the concep tually appealing property of decomposing the problem into the product design and process selection subproblems that represent the marketing and the manufacturing aspects of this decision, while providing a mechanism to link these two subproblems together Our emphasis in this paper is on constructing a basic model for the integrated approach, and using this model to gain useful insights into productprocess interactions To this extent, we makes certain simplifying assumptions As discussed elsewhere in this paper, algorithmic extensions within such an approach are certainly possible; it is also possible, at a cost, to relax some of its assumptions We have chosen not to do so in order to avoid introducing discontinuities that detract from the insights that we obtain from our computational experience The significance of productprocess interactions at the system design level has been emphasized in the literature on concurrent engineering, simultaneous engineering, and quality functional deploy ment We believe that this study is one of the earliest attempts at modeling these interactions and proposing an integrated solution approach Furthermore, our computational experience also iden tifies conditions that heighten these interactions, and consequently, result in greater benefits from 20 adopting the integrated approach These conditions relate to more intensive market competition, greater product complexity, low contribution margins, and high fixed process costs With an increase in market competition, productprocess design integration becomes increasingly important in order to introduce products that sell well and that are profitable In a niche market where competition is nonexistent, the need for integrated design may not be paramount On the other hand, intensive competition is forcing the major automobile manufacturers to integrate their design and manufacturing activities Chrysler, for example, has built a billion dollar center in order to locate experts from different functional areas in the same facility (Woodruff and Lasly 1992) Similarly, Nissan claims that simultaneous engineering and close interaction between the design and manufacturing personnel played critically important roles in introducing Quest in the crowded minivan market (Narita 1991) In regard to product complexity, the computational study suggests that the integrated approach is more desirable for products with more attributes and/or more attribute levels As these two parameter values increase, product and process decisions become more interrelated, and techniques that consider the overall decision in totality become more useful The results of this study also show that the integrated approach is able to deliver a product with higher utility and is consequently able to charge a higher price as well The results also suggest that when variable costs are high, there is a greater need to carefully select the attribute levels A number of new products with novel, wellconceived attributes have failed during the growth stage of their life cycles primarily because the firms have underestimated the costs associated with providing these attributes A case in point is that of Ultrasofts Diapers (Swasy 1990) While the firm touted its design features such as the superabsorbent pulp material used in these diapers to keep babies dry, they underestimated the associated processing costs and the manufacturing problems that these features might entail Consequently, in spite of strong customer acceptance, this product flopped The difference in the values of ir int and ir seq indicates that, by explicitly accounting for the manufacturing costs, the integrated approach provides a more realistic assessment of the optimal price Similarly, adopting the integrated approach becomes more important for larger investments result ing in high fixed costs Again, there is empirical evidence to suggest that firms that have carefully evaluated both product design and process selection alternatives before making major investments 21 have been successful For example, before introducing its Sensor line of razors and blades, Gillette spent considerable time and effort in insuring that the stateoftheart technology in laser weld ing could indeed meet the required output rates without adversely affecting blade hardness and sharpness (Ingrassia 1992) The success of Sensor (43% of the nondisposable razor market in less than 3 years) and the higher price that it commands in the market testify to the wisdom of having considered the product design and the manufacturing decisions simultaneously In highlighting the above conditions, we do not mean to suggest that the benefits of adopting the integrated approach is limited to these conditions only Rather, under these conditions, the integrated approach is so significantly superior that its adoption is critical for achieving any measure of competitiveness Acknowledgements The authors thank Don Erlenkotter for providing the DUALOC code, and Marilyn Lucas for the extensive computational support This research was partly supported by a grant from the Research Board at the University of Illinois 22 References 1 Ahmadi, R H and C S Tang (1991), "An Operation Partitioning 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Vol 36, 14641478 22 Matsuo H, C J Suh and R S Sullivan (1987a), "A Controlled Search Simulated Annealing Method for the Single Machine Weighted Tardiness Problem," Working Paper #87122, Graduate School of Business, Univ of Texas, Austin, TX 23 Matsuo H, C J Suh and R S Sullivan (1987b), "A Controlled Search Simulated Annealing Method for General Job Shop Scheduling Problem," Working Paper, Graduate School of Business, Univ of Texas, Austin, TX 24 24 McBride, R D and F S Zufreyden (1988), "An Integer Programming Approach to the Optimal Product Line Selection Problem," Marketing Science, Vol 7, 126140 25 Narita, R (1991), "Designing Cars with "You" in Mind: The Hidden Source of Customer Satisfaction," presented at the University of Michigan Automotive Management Briefing Sem inar, Traverse City, MI, August 8 26 Shocker, A D and V Srinivasan (1974), "A Consumer Based Methodology for the Identifi cation of New Product Ideas," Management Science, Vol 20, 921937 27 Sudharshan, D, J H May and A D Shocker (1987), "A Simulation Comparison of Methods for New Product Location," Marketing Science, Vol 6, 182201 28 Sudharshan, D, J H May and T S Gruca (1988), "DIFFSTRAT: An Analytical Procedure for Generating New Product Concepts for a DifferentiatedType Strategy," European Journal of Operational Research, Vol 36, 5065 29 Swasy, A (1990), "Unexpected Woes Can Kill New Products," Wall Street Journal, October 9 30 Woodruff, D and E Lasly (1992), "Surge at Chrysler," Business Week, November 9, 8896 31 Zufreyden, F S (1977), "A Conjoint Measurement Based Approach for Optimal New Product Design and Product Positioning," in Analytical Approaches to Product and Market Planning, edited by A D Shocker, Marketing Science Institute, Cambridge, MA 32 Zufreyden, F S (1979), "ZIPMAPA ZeroOne Integer Programming Model for Market Seg mentation and Product Positioning," Journal of the Operational Research Society, Vol 30, 6376 25 Appendix 1 Proofs Remark 1 PDPS is NPhard in the strong sense Proof: The result is proved by restriction: we show that a special case of PDPS is NPhard in the strong sense Consider the case in which / = 1, l\ — 0, p, = 1, ttj = 0, Jk = 1, and tom = 1, Vfc Clearly, in an optimal solution, ir = K, and s\ = 1 PDPS then reduces to Z = max K ^ f m qm ]T] Vikm^lkm subject to ^Um < 9m VA:,m zikm,q m € (0, 1) Vfc,m This problem has the structure of the uncapacitated facility location (UFL) problem [see, for example, Erlenkotter 1974] The result follows from the observation that the vertex cover problem that is known to be NPhard in the strong sense (see, for example, Garey and Johnson 1979) can be transformed to UFL (Cornuejols, Nemhauser and Wolsey 1990) Proposition 1 x* £ {^i,#2> • • >^/} Proof: Order <$, such that 6^ < 6[ 2 ] < • • < <$[/], and let 6[ ] = 0 When tt = fy], it follows from (13) that Sj = 1 for j £ {[*]>[* + 1], • • , [/]}, and s : = for all other j s 3 remains unchanged for any value of tt in the interval (

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