Contemporary Logistics 03 (2011) 1838-739X Contents lists available at SEI Contemporary Logistics journal homepage: www.seiofbluemountain.com Research on Service Capacity Coordination Strategy in Product Servitization Supply Chain Shujun Yao 1, 2, Juhong Chen 1 1. School of Economic and Management, Xi an University of Technology, Xi an, 710054, China 2. School of Management, Xi an University of Finance & Economics, Xi an, 710100, China K E Y W O R D S A B S T R A C T Service outsourcing, Service capacity, Stochastic service demand, Supply chain This paper introduces a three-echelon product Service-oriented supply chain consisting of specialized service function provider, service integrator and customer. Service integrator purchases service capacity from specialized service function provider and sales the added service to customer facing with a price sensitive stochastic demand market. The purpose of service integrator is to meet expected profit maximization through the optimal service capacity order quantity and price of integrated services. Specialized functions service provider identifies the best service capacity price to maximize the expected profit. Establishing the revenue model and supply chain coordination model in product Service-oriented supply chain based on service capacity. Through the numerical example, we find that service capability has an important influence on product Service-oriented supply chain coordination performance. ST. PLUM-BLOSSOM PRESS PTY LTD 1 Introduction The definition of supply chain in domestic and foreign literatures concentrated on logistics flow, information flow and capital flow in the process from the raw material supply to final product delivery, ignoring service elements in the supply chain [1]. "Service oriented product supply chain" is the earliest proposed by Johnsonetal in 2008 [2]. In the product service oriented supply chain, service integrators accept various customer service requirements, design these service requirements, and outsource every well designed service package to professional function provider. After completion of service processing, the service integrators synthetize the completed service packages and provide a customized, integrated solutions for customer with product and service. [4] The recent literatures dedicated to the study of supply chain management coordinate strategy. Chenetal believed that reduce the supply chain cost, optimize the structure of incentive to improve supply chain members of the cooperation between enterprises, [5] improving the overall performance of the supply chain. Weng firstly put forward the service level, but not explicitly considered the capacity loss cost. However, this paper focuses on the price sensitivity of stochastic demand situation, Service integrator determines reasonable service provider, function service provider determines reasonable service ability price. When the service integrator does not undertake service capacity surplus and insufficient risk, function service provider can design product servitization supply chain coordination mechanism by effectively control service capacity. English edition copyright ST. PLUM-BLOSSOM PRESS PTY LTD DOI:10.5503/J.CL.2011.03.013 77
2 Product Servitization Supply Chain Structure Model We use a state model to research the product servitization supply chain. In this structure model, function service provider has w units service capacities. The service integrator purchases service capacities from function service provider, and sales the integrated value-added service capacities, to customers in the market with unit price p. Product servitization supply chain model shown in figure 1: (1) Fig.1 Three-echelon product Servitization supply chain model f Service integrator faces a price sensitive and stochastic service demand market, with random service demand function ( ) x x p, which means probability distribution that service demand along with the service demand price changes. The linear demand relationship between service demand and price for: = d αp d α > 0 Equation (1) describes the maximum potential market standard of the linear service demand curve:d. Price sensitive coefficient α. b, + b belongs to uniform distribution. b is the service demand range parameter. f ( ) x x p, the expected profit of service integrator is : Based on the probability distribution of price stochastic demand: + b SIP(, ) = [( ) ] x( ) X + [( ) ] x( ) P p wx f x pd p wf x pdx The former of equation (2) is expected profit as service demand is less than service capacity. The latter is expected profit as service demand is more than service capacity. The expected profit of function service provider is equal to service capabilities multiplies service capacity unit price w. The capacity cost structure of function service provider consists of service capacity unit cost c and Scale economic cost e. Parameter c is service capacity cost when scale economy is constant [10]. Parameter e is capacity management cost caused by Scale economic infrastructure [6][11]. So the expected profit of function service provider can be defined as: 2 FSP( ) = w ( c + e ). Problems faced by service integrator are how many service capacities should be purchased from function service provider ( ) and with what kind of service integrated capacity price to control customer market ( p ). But the objective of function service provider is to setting an optimal service unit price ( w ) for service integrator so that achieving maximum expected profit. Service demand is stochastic, causing function service provider has service capacity surplus and service capacity insufficient two p ) and service capacity insufficient cost ( IC( p, ) ). situations, thus leading to service capacity surplus cost ( SC(, ) SC( p, ) = [( w r)( x)] f ( x p) dx b + b IC( p, ) = ( ) x ( ) k x f x p dx x (2) (3) (4) (5) Where the parameter r represents the salvage value of service capacity surplus, and the parameter k is the opportunity cost of lost sales due to service capacity insufficient. In the product servitization supply chain, the service integrator is close to the market and easy to collect service demand information and service capacity information of function service provider, effectively choose appropriate function service provider for cooperation, determines a reasonable price of integrated service capacity for the end customer ( p ). By adjusting service capacity, function service provider coordinates and controls the entire product servitization supply chain, and undertakes risk cost under the circumstance of service capacity surplus and service capacity insufficient. 3 Product Servitization Supply Chain Coordination Mechanism 78
In these circumstances, assuming a core service-oriented enterprise from joint decision-making perspective between function service providers and service integrator, realize performance optimization of the entire product servitization supply chain. Therefore, the total expected profit of product servitization supply chain is the expected profit of function service provider and service integrator minus service capacity surplus cost ( SC( p, ) ) and service capacity insufficient cost ( IC( p, ) ): R ( p, ) = SIP( p, ) + FSP( ) SC( p, ) IC( p, ) 1 p have been defined in equation(2),(3),(4). In the price sensitive stochastic demand conditions of uniform distribution, the total expected profit of product servitization supply chain equivalence in: Where SIP( p,fsp(, ),SC( ) p,ic(, ), ) 2 p 4 ( be + r k ) R 1( p, ) = ( ) (( p + k)( d p + b) 2 bc r( d p b)) + 2b 2 2 ( r p)( d p b) k( d p + b) + * ( r k ) + 3b p = k 2 2 * d( k 2) + b k + 1 + α( k 2 4 α ) r k = k 2 4 Numerical Example Analysis (7) When the price of integrated service is greater than the salvage value of unused capacity (p > r) and the range parameter b is bounded above, it can be shown in Lemma1 that the objective function in equation (10) is strictly jointly concave, thereby ensuring the existence of a unique optimal solution. The optimal solution of integrated service price made by service integrator is: The optimal solution of service capacity made by function service provider: ( ) This section is a numerical analysis of products, mainly research how price sensitive coefficient α and service capacity unit cost c affect performance of the whole supply service products, and use the statistical analysis table to illustrate. (6) Table 1 Benchmark parameter table parameter Benchmark Zero-price expected demand:d 100 Price sensitivity parameter:α 2 Range parameter of uniform distribution:b 20 Service capacity unit price:c 0.5 Diseconomy scale parameter:e 0.1 Salvage value of per unit over capacity:r 5 Opportunity cost of lost sale due to under capacity:k 8 Table 2 The key parameters affect numerical PSP: α 1.5 1.6 1.7 1.8 1.9 2 PSSC-TP:1 R 1258.9 1245.5 1145.7 1088.2 1012.6 987.6 SCUP:c 0.1 0.2 0.3 0.4 0.5 0.6 PSSC-TP:1 R 1098.5 1032.6 986.56 932.4 894.21 856.6 PSP:Price sensitivity parameter:α SCUP:Service capacity unit price:c PSSC-TP:product servitization supply chain-total profit 79
Fig.2 Price sensitivity affect supply chain performance Fig.3 Service capacity affect supply chain performance 5 Conclusion A three-echelon product Service-oriented supply chain consisting of specialized service function provider, service integrator and customer has been studied in this paper. Service integrator purchases service capacity from specialized service function provider and sales the added service to customer, who is faced with a price sensitive stochastic demand market. The purpose of service integrator is to meet expected profit maximization through the optimal service capacity order quantity and price of integrated services. Specialized functions service provider identifies the best service capacity price to maximize the expected profit. Establishing the revenue model and supply chain coordination mechanism model in product Service-oriented supply chain based on service capacity. Through numerical example study in this paper, we find: First, in the process of constructing product servitization supply chain coordination mechanism, We will realize maximization of whole supply chain performance, as multiple nodes enterprise competitive strategy are consistent. Second, Compared to other nodes enterprise, the enterprise can obtain higher returns from product servitization supply chain coordination of service products. However, this model has the following limitations: First, this paper merely study a harmonious relationship between service integrator and function service provider, without considering the reality of life and a pair of among them for more than coordinating relations. Second, the price sensitivity service demand just follows uniform distribution in our model. In the future, we should relax restrictions on service products, further study of supply chain coordination strategy. 80
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