Partner Selection with Dynamic Pricing under ...

Partner Selection with Dynamic Pricing under Uncertainty Condition in the Global Marketplace Yosi A. Hidayat† 1, Katsuhiko Takahashi2, Katsumi Morikawa3 and Kunihiro Hamada4 Department of Artificial Complex Systems Engineering 1, 2, 3 Department of Social and Environmental Engineering 4 Graduate School of Engineering, Hiroshima University, Higashi Hiroshima 7397527, JAPAN Email: [email protected], [email protected] 2, [email protected], [email protected] Lucia Diawati5 and Andi Cakravastia6 Department of Industrial Engineering Bandung Institute of Technology, Bandung 40132, INDONESIA Email: [email protected], [email protected] Abstract. A single company may do business in different types of marketplaces, both up and down of its supply chain. In the global situation and under uncertainty of market condition, the key to continue business success will lie in its ability to identify market opportunities in the downstream markets and simultaneously procure the resources needed from the appropriate partner to capture these opportunities from the upstream markets. Global supply chain gives impact to the business which will continue into the global trading by not only locating and forging profitably sustainable relationships with their customers and partners, but also anticipating uncertain demand condition in order to synchronize business activities with both of them. In this paper, we propose the quadratic programming model based on dynamic pricing in partner selection and supply chain planning on the global marketplace with both sell-side and buy-side by considering demand uncertainty factor. In particular, we consider a contract manufacturer who procures components from suppliers through a component marketplace and sells its manufactured sub-assemblies to original equipment manufacturers (OEMs), through a sub-assembly marketplace. Embedded with upstream and downstream marketplaces, we develop and present such a model that select a partner, synchronizes supply chain activities and optimizes the profit through optimal revenue pricing and cost minimization. Keywords: partner selection; demand uncertainty; dynamic pricing; optimal price; optimal quantity.

1. INTRODUCTION A single company may do business in different types of marketplaces, both up and down of its supply chain. In the global situation and under uncertainty of market condition, the key to continue business success will lie in its ability to identify market opportunities in the downstream markets and simultaneously procure the resources needed from the appropriate partner to capture these opportunities from the upstream markets. Global supply chain gives impact to the business which will continue into the global trading by not only locating and

forging profitably sustainable relationships with their customers and partners, but also anticipating uncertain demand condition in order to synchronize business activities with both of them. Previous literature still does not consider demand uncertainty and subsequently integrate it with pricing decision which has a linear relationship with the procurement and sales quantity decision. This linear relationship gives significant impact that results on the quadratic structure of revenue and total costs derived from a company in one supply chain configuration. In this paper, we propose a quadratic programming model based on dynamic pricing in partner selection and

________________________________________ † : Corresponding Author

944

APIEMS 2008 Proceedings of the 9th Asia Pasific Industrial Engineering & Management Systems Conference supply chain planning on the global marketplace with both sell-side and buy-side by considering demand uncertainty factor. Demand uncertainty as an external factor will be considered in this research in forms of probability of market demand which directly impacts on the supply chain downstream members. We also treat the price as dynamic decision variable. In particular, we consider a contract manufacturer who procures components from suppliers through a component marketplace and sells its manufactures sub-assemblies to original equipment manufacturers (OEMs), through a sub-assembly marketplace. Embedded with upstream and downstream marketplaces, we develop and present such a model that select a partner, synchronizes supply chain activities and optimizes the profit through optimal revenue pricing and cost minimization. We started this research by some of literature studies which are shown in section 2. We begin in section 3, by describing the problem we wish to address. In section 4, we formulate a quadratic programming model for integrated partner selection and dynamic pricing by considering demand uncertainty. We then proceed to present and discuss some computational result in section 5. And finally, we conclude in section 6 with some observation on the next research planning.

2. LITERATURE REVIEW There is significant amount of documented research in the area of operations research and management science in supply chain that addresses some of these issues related to dynamic pricing and partner selection. We review the literature in these areas one-by-one. In a supplier-buyer relationship, the partner selection process becomes an important strategic decision. Focusing on a single element (buyer only or supplier only) in the supply chain cannot assure the effectiveness of the network (Croom et al. 2000). In the field of partner selection, there have been a number of papers since the seminal work by Dickson (1966). Also, Chan et al. (2004) provide a comprehensive review and classification of pricing and inventory coordination problems discussed in the literature. Weber & Current (1993) discussed a multi-criteria analysis for vendor selection. They developed a model for minimizing total cost, late deliveries and supply rejection given the infrastructure constraints and constraints imposed by the company’s policy. Chaudhary et al. (1993) provided a linear programming model for vendor selection with price breaks. De Boer et al. (2001) provided a comprehensive review of published decision methods for vendor selection and classified them under a framework that takes into account the diversity of purchasing scenarios and covers all

phases of the vendor selection process. Degraeve et al. (2000) reviewed and evaluated a number of vendor selection models that presented by various researchers, by employing total cost of ownership as a basis for comparison. By solving all the models for a single real-life dataset of a purchasing problem they obtained the relative efficiency of the models and showed that mathematical programming models outperform rating models. Current and Weber (1994) extended the extensive literature in facility location problems to the solution of vendor selection problems. Li and O’Brien (1999) developed a model in supplier-buyer relationship in a hierarchical ways but in a sequential flow. In their research, after partner selection process, then at the operational level, manufacturing and logistics activities were optimized under the given targets. Hidayat et al. (2008) developed a model in supplier-buyer relationship in a hierarchical ways with a simultaneous flow in operational and strategic decisions by considering demand uncertainty as an external factor. The important thing that should be underlined in these partner selection researches is that while determining partner and optimal quantity, the related cost and price affecting model criteria had been set-up as parameters. This drawback will be accommodated in our proposed research. Snyder (2006) concluded his research by identifying four research avenues which are within the grasp of today’s operation research technology. One of the avenues is the multi echelon models. In this avenue, Snyder (2006) stated that there is a need for models that capture the costs of tactical and /or operational functions of the supply chain under uncertainty. In the condition with uncertainty, the overstock product cannot be used in the future because of product’s life cycle and product’s deterioration function, model and technology (Hidayat et al. 2008). Hidayat et al. (2008) also found that by considering demand uncertainty, the buyer will become more responsive to the market that impact to the expected lead time & delivery delay and more able to reduce the risk of under stock and over stock condition that impact to the expected total cost. With regards to dynamic pricing, Biller et al. (2005) generalized some of the concepts in yield management for coordinating production and inventory decisions in supply chains. Swann (2001) discussed strategies that incorporate pricing, production scheduling and inventory control under production capacity limits in a multi-period horizon where unmet sales are lost. Bhattacharjee and Ramesh (2000) developed a dynamic programming for efficient management of the marketing/manufacturing interface in the supply chain, through the appropriate pricing strategies. McGill and Van Ryzin (1999) review the research in transportation revenue management, with focus on airline pricing and provide an extensive bibliography. The

Nusa Dua, Bali – INDONESIA December 3rd – 5th, 2008 945

APIEMS 2008 Proceedings of the 9th Asia Pasific Industrial Engineering & Management Systems Conference important thing that should be underlined in these dynamic pricing researches is that while determining the price, the optimal quantity from the particular partner had been set-up as parameters. This drawback will also be accommodated in our proposed research. Our research here integrates uncertainty in forms of market demand probability information with strategic and operational decisions in a single framework. The proposed model will be able to capture the costs of tactical and /or operational functions of the supply chain under uncertainty. We present a model for supply chain planning that harnesses the information within global marketplaces. Specifically, we determine the optimal price and quantities for sales and procurement within the selected partner in the downstream and upstream marketplaces, select the supply chain configuration within the marketplaces that will allow us to meet the determined sales targets for the selected supply chain configuration. This decision is based upon the demand of goods in the downstream marketplaces in the supply chain after the members of downstream marketplace consider demand uncertainty from the market and supply of materials in the marketplaces upstream of supply chain. In particular, our analysis is in the context of global supply chain for components and sub-assemblies play an important role in the supply chain.

3. PROBLEM STATEMENT This part will be divided into three subsections, i.e.

supply chain system configuration, dynamic pricing, and demand uncertainty. By considering those three items, in a brief, our purpose in this paper is to develop a quadratic programming model for integrated supply chain planning for supply chain in the global marketplaces and in the process build a decision support tool for global marketplace participants.

3.1 System Configuration We assume a supply chain comprising a sub-assembly manufacturer and a number of component suppliers, and OEMs (buyers) in different geographical locations, interacting through global marketplaces. We assume a global marketplace for components through which the components suppliers sell a variety of components to the sub-assembly manufacturer. The sub-assembly manufacturer uses these components in the production of a variety of sub-assemblies. These sub-assemblies are then sold to OEMs through marketplaces for sub-assemblies. For the movement of goods between the various geographical locations, the sub-assembly manufacturer can procure the services of warehousing, transportation, and third party logistics companies through a logistics exchange. The supply chain configuration, including number of components, manufacturing facilities, suppliers, buyers, products, products’ composition, parameters, and decision variables, is shown in Figure 1.

Figure 1: Supply chain configuration


APIEMS 2008 Proceedings of the 9th Asia Pasific Industrial Engineering & Management Systems Conference 3.2 Dynamic Pricing Supply chain members seek information about supply function from the upstream supply chain members and demand functions from the downstream supply chain members and integrate them to the capacities and market information through negotiations prior to the transaction. They discover more and more about their partners during each of the many rounds of offers and counter-offers. We assume that the demand within their global supply chain is linearly related to the sales price per unit for the subassembly quoted by the manufacturer, as shown in Figure 2(a). Demand will be very low for high prices and will pick up if the price is lowered. This linear relationship will impact on the revenue generated from each buyer. Similarly, the supply of resources within the components as seen by the sub-assembly manufacturer is also linearly dependent on the unit price offered by the subassembly manufacturer in these marketplaces is greater and will be lower for the lower price. This linear relationship will impact on the costs resulted from each of component supplier (see Figure 2(b)).

Figure 1: Demand and supply function curves The sub-assembly manufacturer is aware of the demand curve for each of the buyers in the sub-assembly marketplace. The sub-assembly manufacturer needs to determine the optimal pricing strategy for a range of subassemblies and the corresponding demand that would maximize its revenue. The demand from the buyers in the market can be fulfilled from different manufacturing locations with the help of suppliers and warehousing companies. The logistics service providers have their own costs, capacity constraints and shipping schedules and so

do the warehousing companies. The sub-assembly manufacturers can determine the supply functions for the component suppliers, warehouse, and the management of ownership. It may be noticed that based on the description, the model presented herein differs from the traditional notion of dynamic pricing. Existing literature addressing pricing problems typically try to fix costs and prices based on actual demand so as to optimize profit. In this paper, we address the dual problem, namely the determination of optimal quantity for procurement and sales based on pricing information. In addition, one of the implicit assumptions in our model is that the participants trading within the marketplace have been pre-qualified by the market-maker with regards to their quality, integrity, and capabilities. This ensures that the sub-assembly manufacturer can safely select partners purely on the basis of price since all participants in the marketplace can be considered equally capable in terms of executing on the orders.

3.3 Demand Uncertainty In this paper, we consider demand uncertainty that affects the buyer in determining number of optimal order to the sub-assemblies manufacturer. Since future demand is usually uncertain, buyers building some arbitrary product to meet anticipated customer demand (Hidayat et al. 2008). In this research, the demand uncertainty from market only impact directly to the buyers. After buyers order to the sub assembly manufacturer, based on buyer’s demand function, the sub-assembly manufacturer determines the portion of the demand to each of sub-assemblies manufacturing facilities. Each subassembly manufacturing facility has the same component suppliers to provide the parts needed for making subassemblies. Each of component suppliers has its own supply function curve for each part. According to the characteristics of each supply curve, the sub-assemblies manufacturer determines the optimal quantity and the optimal price to their component suppliers. In this paper, we assume that the sub-assemblies manufacturer has two manufacturing facilities. According to buyers demand function, the sub-assemblies manufacturer divides some proportion of demand’s order to each of the manufacturing facilities. In the same way, the sub-assemblies manufacturer makes decisions about the optimal quantity and optimal price offer to the buyers. Supply and demand uncertainty in forms of the slope (a) and intersection (b) of supply and demand curves impacts the sub-assemblies to procure and sell some optimal quantities with optimal pricing from their component supplier (according to supplier’s supply function curves for each components)


APIEMS 2008 Proceedings of the 9th Asia Pasific Industrial Engineering & Management Systems Conference and to their buyers (according to buyer’s demand function curves for each products). Subsequently, we address the dual problem, which are the determination of optimal quantity for procurement and sales based on pricing determination in order to optimize profit of supply chain system.

4. MODEL DEVELOPMENT The basic insights of this paper are that profit as the criteria is generated from revenue subtracted with operations costs. The revenue and operation costs itself are affected by the determined price and the determined supply quantity (to sub-assemblies manufacturer’s component supplier) and sales quantity (from each sub-assemblies manufacturing facilities to the buyers). We set that this price and cost are not fixed as parameters in selecting partner, but they are in a linear relationship. Subsequently, the price and quantity are linearly related. This linear relationship makes impact on the total revenue and total costs that brings the model into a quadratic model. The linear relationship between the price (and cost from supplier point of view) and quantity is shown in Figure 2. These make the dynamic pricing decisions which will be proposed to the buyers and the component suppliers from sub-assemblies point of view. These problems are reflected in the objective function relationship between revenue and operational costs. According to these relationship, the model structure of the objective function will become quadratic programming, that different from previous researches in partner selection (i.e. linear programming (Li and O’Brien, 1999); multiobjective mixed-integer linear programming (Hidayat et al. 2008), etc).

4.1 Assumptions In developing the model, we use these following assumptions: a. The standard initial conditions with initial inventory, production, and transportation equal to zero are applied. b. The solution of this model determines the pricing strategy with the marketplace, the selection of suitable suppliers in the supply chain, and the synchronization of activities with them through uncertain market demand condition. Also, in the developed model, the following notations are used. Index i j k

Component supplier index (i=1,2,…,n) Sub-assembly supplier index (j=1,2,…, oi) Buyer index (k=1,2,…,uij)

ψ Θ t T

Component index (ψ = 1,2,…,w) Sub-assembly product type index (Θ=1,2,…,z) Time period index (t=1,2,…,T) Total time horizon of the model

Parameters aψi,. aΘk Slope of the supply/demand line for a resource. aψi is positive for supply graphs, whereas a Θk is negative for demand graphs and both of them represent the change in unit cost or price with respect to the quantity procured or produced. bψi., bΘk Intercept of the supply (bψi) or demand (bΘk) line for a resource. It represents the cost or price at which no demand or exists in the market. Within supply markets (upstream supply chain), bψi is the minimum price desired by the supplier for the component, before they would consider to produce it. Within sales markets (downstream supply chain), bΘk is the maximum price that the buyer is willing to pay. If the price is higher, the buyer will not procure anything from the market. RψΘ Unit production of one unit of sub-assembly product Θ will consume of component type ψ C Maximum availability of component CI Capacity availability for the storage space CM Production capacity availability DD Time period by which required quantity of subassembly is to be delivered to buyer P Production cost L Transportation lead-time for transportation of products TRmax Maximum transportation capacity for shipment P(D*) Probability of optimal quantity to be ordered by the buyers that reflects the demand uncertainty from market Cu Buyer’s understock cost Cs Buyer’s overstock cost TCb Buyer’s total cost (except C u and Cs) COGSb Buyer’s product selling price Variables I Inventory level S Quantity shipped Decision Variables SL* Service level negotiated with buyer M Quantity of sub-assembly produced D* Optimal quantity to be produced by the buyer according to market’s demand information Q Quantity of sub-assembly required (based on order information from buyers after considering demand uncertainty) COGS Optimal component price


APIEMS 2008 Proceedings of the 9th Asia Pasific Industrial Engineering & Management Systems Conference 4.1 Determining Quoted Demand and Quoted Service Level under Uncertainty Demand uncertainty from the market as an external factor in this proposed model is influenced by customer buying behavior that reflected by the potential benefits of demand forecasting and its probability in order to decrease the buyer’s risk of overstocking or shortage. Hidayat et al. (2008) stated that demand potential and its probability, material, production, and transportation costs (which is reflected by the total cost of buyer), under stock cost, overstock cost, product price (which is reflected by product’s cost of goods sold) will be considered in purpose to determine the optimal unit to be procured by the buyer. The optimal service level and demand are determined by using equations (1) and (2). Later on, we assumed that these values will be used as quoted demand and quoted service level. P( z ≥ D*) > SL* > P( z ≥ ( D * +1)) (1) P ( z ≥ D*) >

(TCb − Cs ) > P( z ≥ ( D * +1)) (COGSb + Cu − Cs )

(2)

4.2 Determining Optimal Quantity and Optimal Price of Components 4.3.1 Objective Function The basic insight of this paper is that profit as the criteria will be generated from revenue subtracted by operations costs. The revenue and operation costs itself are affected by the determined price and the determined supply quantity (to the sub-assemblies manufacturer’s component supplier) and sales quantity (to the buyers). Here, we set that these price and cost are not fixed as parameters in selecting partner, but they are in a linear relationship. Subsequently, the price and quantity are linearly related. This linear relationship makes impact to the total revenue and total costs that brings the model into a quadratic model. The linear relationship between the price (and cost from supplier point of view) and quantity is shown in Figure 2. These make the dynamic pricing decisions which will be proposed to the buyers and the component suppliers from the sub-assemblies manufacturer’s point of view. These decisions are reflected in the objective function relationship between revenue and operational costs. According to these relationship, the model structure of the objective function will become quadratic, that is different from previous researches in partner selection (i.e. linear programming (Li and O’Brien, 1999); multi-objective mixed-integer linear programming (Hidayat et al. 2008), etc).

4.3.2 Revenue As mentioned before, the objective function of this model is to maximize profit. Profit is generated by revenue and costs. The revenue and costs are dependent on both the choice of price and quantity for goods flowing through the network. Additionally, the unit price and quantity are linearly related. The revenue refers to the total sales of sub-assemblies products from the sub-assembly manufacturer to OEMs as the buyers. According to the buyers’ demand function curves and the linear relationship between optimal quantity and optimal price of each buyer’s sub-assembly product, there will be a quadratic structure on the generated revenue as shown in equation (3). Revenue =

z

oi uij T

∑ ∑ ∑ ∑ aΘk SΘjkt 2 + bΘk SΘjkt

(3)

Θ =1 j =1k =1t =1

4.3.3 Costs a.

Procurement Cost The procurement cost refers to the total cost of components procured by the sub-assembly manufacturer from their component suppliers. According to the suppliers’ supply function curves and the linear relationship between optimal quantity and optimal cost of each supplier’s component, there will be a quadratic structure on the procurement cost as shown in equation (4). Procurement Cost =

w

n T

2 + bΦiQΦit ∑ ∑ ∑ aΦiQΦit

(4)

Ψ =1i =1t =1

b.

Production Cost The production cost refers to the cost of manufacturing in the sub-assemblies manufacture facilities. This cost is not depend on both buyers’ demand function curves and suppliers’ supply function curves but this depend on the production process efficiency in each subassemblies manufacturing facility. According to this situation, the structure of the production cost will be linear, as shown in equation (5). Production Cost =

z

oi T

∑ ∑ ∑ PΘj M Θjt

(5)

Θ =1 j =1t =1

c.

Inventory cost of In-Transit Warehousing This cost refers to the total inventory cost before components reach sub-assembly manufacturing facilities or sub-assemblies products reach buyer’s facilities. The first term of this equation shows the inventory cost of components before reaching sub-assembly manufacturing


APIEMS 2008 Proceedings of the 9th Asia Pasific Industrial Engineering & Management Systems Conference facility in the in-transit warehouse facilities owned by the sub-assembly manufacturer. At the same situation, the second term of this equation shows the inventory cost of finished sub-assemblies products before reaching buyer’s facility in the in-transit warehouse facilities also owned by the sub-assembly manufacturer. In brief, this cost consists of the cost incurred for shipment of goods between the various facilities in the global marketplace. Each term has a quadratic structure because it is also depend on supply function curves of the warehousing and transportation ser vice providers. ⎤ ⎡ w n oi T In Transit Warehousing = ⎢ ∑ ∑ ∑ ∑ aΨij S 2 + bΨijt SΨijt ⎥ Ψijt ⎥ ⎢Ψ =1i =1 j =1t =1 ⎦ ⎣ ⎡ z oi uij T ⎤ + ⎢ ∑ ∑ ∑ ∑ aΘjk S 2 + bΘjkt S Θjkt ⎥ Θjkt ⎢Θ =1 j =1k =1t =1 ⎥ ⎣ ⎦

(6)

d.

Inventory Cost On-Site Warehousing This cost refers to the cost incurred for shipment of goods in the internal warehouse in the sub-assemblies manufacturing facilities. The first terms of this equation shows the inventory cost of components when waiting or queuing for manufacturing process in the sub-assembly manufacturing internal warehouse. The second and the third terms show the inventory cost of finished subassemblies products when waiting or queuing for shipping process in the sub-assembly manufacturing internal warehouse to the buyer’s facility, both direct shipping (the second term) or waiting list shipping along the negotiated due date (the third term). ⎡ w oi T ⎤ On Site Warehousing = ⎢ ∑ ∑ ∑ aΨj I 2 + bΨj IΨjt ⎥ Ψjt ⎢Ψ =1 j =1t =1 ⎥ ⎣ ⎦ ⎡ z oi T ⎤ + ⎢ ∑ ∑ ∑ a Θj I 2 + bΘj I Θjt ⎥ Θjt ⎢Θ =1 j =1t =1 ⎥ ⎣ ⎦ ⎡ z uij DDΘk ⎤ + ⎢ ∑ ∑ ∑ a Θk I 2 + bΘk I Θkt ⎥ (7) Θkt ⎢Θ =1 k =1 t =1 ⎥ ⎣ ⎦ By subtracting the revenue to all of the costs, we can determine the total profit of the optimal supply chain system.

4.3.4 Constraints According to the particular supply chain system in the global marketplaces (see Figure 1), we develop some constraints related to the system.

Constraints in Component Procurement a.

Production Capacity in terms of Volume The component suppliers would indicate a maximum amount that they can offer in a certain period of time based upon their production capacity limitations. The quantity that is procured from the component suppliers is less than the maximum they can offer. QΨit ≤ C Ψit for all Ψ ∈ w,i ∈ n,t ∈ T (8) b.

Inventory in Storage Facilities The component suppliers would deliver their goods to various storage facilities managed by warehousing companies on behalf of the sub-assembly manufacturer. These storage facilities may be near the manufacturing plants or far away from them. The procurement of components from the marketplace would add to these inventories at the end of each time period and the shipment of components will reduce the quantity in these inventories. The cost of maintaining a warehouse would be zero for goods delivered by the supplier directly to the manufacturing facilities. IΨi(t −1 ) + QΨit =

oi

∑ SΨijt + IΨi for allΨ ∈ w,i ∈ n,j ∈ oi ,t ∈ T

(9)

j =1

c.

Warehousing Inventory Capacity in terms of Volume The amount of inventory that can be managed is limited to the amount of warehousing space offered in the marketplace. Hence, the following constraint is applied. I Ψit ≤ CI Ψit for all Ψ ∈ w,i ∈ n,t ∈ T (10) d.

Transportation Capacity in terms of Volume The components in these inventories will be shipped out to the manufacturing facility. However, the quantity that can be transported in a single period is constrained by the maximum capacity that can be procured from the transportation marketplace. Hence, the amount that can be shipped is constrained. SΨijt ≤ TRmax Ψijt for all Ψ ∈ w,i ∈ n,j ∈ oi , t ∈ T (11) e.

Lead Time Delivery Delay The components that are shipped will arrive at the manufacturing facility after a certain delay equivalent to the transportation lead-time. When the warehouses are far away from the manufacturing facility, these lead-times will be significant, else they may be negligible. For items delivered directly to the manufacturing facility by the supplier, the lead time will be zero. ' SΨij (t + LΨij ) ≤ SΨ ijt for all Ψ ∈ w,i ∈ n,j ∈ oi , t ∈ T

(12)


APIEMS 2008 Proceedings of the 9th Asia Pasific Industrial Engineering & Management Systems Conference Constraints in Manufacturing Facilities f. a.

Inventory of Materials Component in On-site Storage of Manufacturing Facilities Once the components reach the manufacturer’s facilities, they add to the on-site inventory there, which is then consumed by the manufacturing process. The amount of inventory maintained is constrained by the warehouse space that can be procured. I Ψjt ≤ CI Ψjt for all Ψ ∈ w,j ∈ oi ,t ∈ T (13) b.

Adequate Availability Component for Sub-assembly Production Process However before the manufacturing process starting and the various component types be consumed, the subassembly manufacturer will need to check adequate availability of components that will be used in the subassembly production process. This imposes the following constraint on the component availability and the subassembly production. I Ψj (t −1) ≤

z

∑ RΘΨ M Θjt for all Ψ ∈ w,j ∈ oi ,Θ ∈ z, t ∈ T (14)

Θ =1

Inventory Replenishment in Sub-assembly Production Process However, once the production process begins the inventory of components drops and is replenished by incoming supplies. The inventory status for component types with the manufacturer can be determined as this given constraint below.

Warehousing Inventory Capacity in terms of Volume Again, there is a limit on the amount of storage place that can be procured from the marketplace for storing subassemblies. I Θjt ≤ CI Θjt for all j ∈ oi , Θ ∈ z , t ∈ T (18)

Constraints in Sub-Assembly Facilities and Sales a.

Logistics Marketplace Transportation Capacity in terms of Volume Transportation service providers transport the subassemblies from the manufacturing facilities to the buyer’s location. The amount that can be transported is limited by the maximum amount that is offered in the logistics marketplace. SΘjkt ≤ TRmaxΘjkt for all j ∈ oi , k ∈ uij , Θ ∈ z , t ∈ T (19) b.

Logistics Transportations Lead Time The sub-assemblies reach the buyers after a certain transportation lead-time. ' SΘjk (t + LΘjk ) = SΘ jkt for all j ∈ oi , k ∈ uij , Θ ∈ z, t ∈

c.

n

' I Ψj (t −1) + ∑ S Ψ ijt = i =1

Inventory Balancing of Buyer’s Facilities The sub-assemblies that reach the buyer add on to the amount supplied earlier. IΘk (t −1) +

( 15)

d.

Production Capacity of Manufacturing Facilities in terms of Volume The production within the manufacturer’s facility is constrained by the capacity of the manufacturing facility. M Θjt ≤ CM Θjt for all j ∈ oi , Θ ∈ z , t ∈ T (16) e.

Inventory Balancing Constraints of Finished Product in On Site Storage of Manufacturing Facilities Subsequent to production, the sub-assemblies are moved to an on-site storage facility, before they are shipped out to customers. The inventory balancing constraint for the sub-assembly inventory at the manufacturing locations is applied. uij

∑ SΘjkt + IΘjt

k =1

for all j ∈ oi , k ∈ uij , Θ ∈ z , t ∈ T

oi

∑ SΘjkt j =1

= IΘkt for all j ∈ oi , k ∈ uij , Θ ∈ z , t ∈ T (21)

d.

Θ =1

for all Ψ ∈ w,i ∈ n,j ∈ oi ,Θ ∈ z,t ∈ T

I Θj (t −1) + M Θjt =

c.

z

∑ RΘj (t −1) + I Ψjt

(20)

(17)

Warehousing Inventory Capacity in terms of Volume The amount of storage space available for the subassemblies is constrained by the amount available in the marketplace. I Θkt ≤ CI Θkt for all k ∈ u ij , Θ ∈ z , t ∈ T (22) e.

Due Date and Service Level Quoted during SupplierBuyer Negotiation The amount supplied to the buyers till their desired delivery date need to be within the service levels quoted to them during the negotiation in the sub-assembly marketplace. I Θk (t + DDΘk ) ≥ SLΘk DΘk for all k ∈ u ij , Θ ∈ z , t ∈ T (23)

5. MODEL SOLVING AND ANALYSIS By considering the specific structures of supply chain, we will show the effectiveness of the proposed model. In this numerical example, first we determine the economic order quantity and optimal service level from the buyer by


APIEMS 2008 Proceedings of the 9th Asia Pasific Industrial Engineering & Management Systems Conference considering demand uncertainty from the market. After finding the optimal economic order and service level, the buyers inform the order at the beginning of planning horizon to the sub-assemblies manufacturer. We assume here that sub-assemblies manufacturer has the information about the buyers demand function curves and also the component suppliers supply function curves for each component. By considering this information, the subassemblies manufacturer determines the optimal quantity to be procured from their suppliers for each components and the optimal price they offer to the suppliers. Subsequently, they also determine the portion of buyer’s order from each of sub-assemblies manufacturing facilities according to buyer’s demand function curves. The model was developed and solved for a scenario

with 3 component suppliers, 2 sub-assembly manufacturing facilities locations and 2 buyers. The manufacturing facilities make 2 different types of sub-assemblies from a combination of 3 different component types. Furthermore, the two sub-assemblies products are manufactured from a mix of components. Product 1 requires 1 unit each of components I, II, and III, whereas product 2 requires 2 unit of component I, and 1 unit of component II. In such a situation, it is quite possible to gain from economies of scale in the collective ordering and transportation of materials, which are used in the manufacture of multiple models. The time horizon for model is taken as 6 periods. Numerical experiment for operational decisions uses the data shown in Table 1.

Table 1: Data for operational decision Product 1 Buyers

Demand Lot Size (D)

P(D)

P(z>D)

1

70 80 90 100 125 150 70 80 90 100 125 150

0.3 0.2 0.2 0.15 0.1 0.05 0.03 0.05 0.07 0.1 0.25 0.5

1 0.7 0.5 0.3 0.15 0.05 1 0.97 0.92 0.85 0.75 0.5

2

Product 2 Decision Parameters

Demand Lot Size (D)

P(D)

P(z>D)

70 80 90 100 125 150 70 80 90 100 125 150

0.05 0.1 0.3 0.2 0.2 0.15 0.2 0.3 0.1 0.25 0.1 0.05

1 0.95 0.85 0.55 0.35 0.15 1 0.8 0.5 0.4 0.15 0.05

Cu = $500 Cs = $300 TCb = $3,500 COGSb = $4,400

Cu = $600 Cs = $100 TCb = $3,700 COGSb = $4,300

The supply functions for the component suppliers, war ehousing and transportation service providers were assume d. A representative’s data of the parameters for the supply f unction of the component suppliers is given in Table 2.

2

3

Component I II III I II III I II III

aψi 0.002 0.003 0.0016 0.0023 0.0022 0.0017 0.0015 0.0019 0.0021

Buyer I II

bψi 800 700 850 900 800 750 850 900 950

On the sales side, the sub-assembly manufacturer was faced with decisions related to the demand curves of the various buyers as given in Table 3.

Cu = $600 Cs = $100 TCb = $3,700 COGSb = $4,000

Cu = $500 Cs = $160 TCb = $3,500 COGSb = $4,800

Table 3: Parameters for the buyer’s demand functions

Table 2: Parameters for the suppliers’ supply function Supplier 1

Decision Parameters

Product 1 2 1 2

aΘk 0.17 0.21 0.20 0.23

bΘk 4000 3700 4500 3500

The slopes for the demand functions are higher than the slopes for the supply functions of the component supplier, because it is argued that due to the fact that the finished goods have more value, so the difference between price and unit increase of the quantity will be greater on the demand side as compared to the supply side. Similar, the intercept is greater on the demand side representing the higher value of the sub-assemblies sold as compared to the cost of warehousing service providers. However, since the cost of warehousing and transportation was assumed to be much lower compared to the cost of the components and the prices of the sub-assemblies, then the values for their


APIEMS 2008 Proceedings of the 9th Asia Pasific Industrial Engineering & Management Systems Conference into the supply and demand functions. The optimal prices averaged over the time horizon are shown in Table 5. Only partial demand, within the constraints of the service levels, is fulfilled of Product 2, due to the limitations of the maximum amount of resources that can be procured from the marketplaces.

intercepts (b) were much lower than the value of the intercepts for the component supply and sub-assembly demand functions. The demand of the buyers is also determined from the marketplace by considering the demand uncertainty factor and a service level quoted to them using operational data in Table 1. By using equations (1) and (2), we can find quoted demand and service level of buyers as shown in Table 4.

Table 5: Optimal price and optimal quantity flows through the supply chain structure

Table 4: Buyer’s optimal order (D*) and quoted service level (SL*) Buyer I II

Product 1 2 1 2

Demand 80 90 125 80

Procure From & Supply To

Service Level 70% 80% 75% 65%

Supplier 1

Supplier 2

The problem is solved using Lingo 8.0. Even for such a simple set-up, the number of variables and constraints encountered are around 512 and 680 respectively. Hence, it can be expected that for real-life situations, the problem can get too large. Fortunately, LINGO 8.0 can ease the solution process. In addition, since the underlying structure of the formulation is a network flow model algorithms similar to the network simplex may be investigated to identify if they would be able to solve the model more efficiently. The optimal quantity and optimal cost and price of procurement and sales decision, consolidated over the entire time horizon are obtained as shown in Figure 3. The profit earned from the operation of the supply chain in the optimal manner is expected to be $744,250. The negotiated prices, for consolidated procurement across all manufacturing facilities, associated with the above optimal quantities can be calculated by plugging in the quantities Optimal Order Quantity (K*)

Supplier 3

Buyer I

Buyer II

Component & Products

Optimal Quantity

Optimal Price

Component I

247

$800.5

Component II

131

$700.4

Component III

66

$850.1

Component I

115

$900.3

Component II

170

$800.4

Component III

100

$750.2

Component I

135

$850.2

Component II

50

$900.1

Component III

40

$950.1

Product

1

80

$3,986.4

Product

2

73

$3,684.8

Product

1

125

$4,475.0

Product

2

74

$3,483.0

Optimal Service Level

Product Price

information and technology flow Assembly Component Manufacturer Set

Component Supplier Set

C1

C2

C3

(88, 39, 0) (159, 92, 66)

A1

(65, 70, 50) (50, 100, 50) (75, 50, 40) (60, 0, 0)

Buyer Set

(56,70)

B1

(24,3)

Demand Uncertainties

(33,0) A2

Quantity Supplied of (Component I, Component II, Component III)

(92,74)

B2

Quantity Supplied of (Product I, Product II)

physical flow Component Product

Sub-Assemblies Product

Figure 3: Supply chain flow: the optimal quantity and optimal cost/price of procurement and sales decision, consolidated over the entire time horizon by considering demand uncertainty from the market


APIEMS 2008 Proceedings of the 9th Asia Pasific Industrial Engineering & Management Systems Conference To see the effectiveness of the proposed model, we would like to compare the effectiveness of proposed model before and after considering linear relationship between price and quantity from the supply and demand function curves. In the condition without considering supply and demand function curves, we used the reference values in the intercepts (b) of each curves. As explained before, the intercept of the curves represents the cost or price at which no demand or exists in the market. Within supply markets, it is the minimum price desired by the seller for the product, before we would consider selling it. Within procurement

markets, it is the maximum price that the buyer is willing to pay. Procurement cost mainly contributes in the total cost (in the quadratic structure, it contributes 60.5% from the total revenue generated from the buyers). To show the effectiveness of the proposed model, next we will compare the impact of procurement cost and sales revenue to the total profit before and after considering supply and demand function curves. The comparison of these two scenarios will be shown in Table 6.

Table 6: Comparison of model effectiveness before and after considering linear relationship between optimal quantity and optimal sales price or optimal procurement cost Buyer I

II

Supplier 1

2

3

Product

aΘk

bΘk

Optimal

Revenue

Revenue

(Quadratic Structure)

( Linear Structure)

Optimal Price Quantity

Differences

1

0.17

4000

80

$3,986.4

$321,088.0

$320,000.0

$1,088.0

2

0.21

3700

73

$3,684.8

$271,219.1

$270,100.0

$1,119.1

1

0.2

4500

125

$4,475.0

$565,625.0

$562,500.0

$3,125.0

2

0.23

3500

74

$3,483.0

$260,259.5

$259,000.0

$1,259.5

Total Revenue

$1,418,191.6

$1,411,600.0

$6,591.6

Optimal

Total Cost

Total Cost

(Quadratic Structure)

(Linear Structure)

$800.5

$197,722.0

$197,600.0

$122.0

131

$700.4

$91,751.5

$91,700.0

$51.5

850

66

$850.1

$56,107.0

$56,100.0

$7.0

0.0023

900

115

$900.3

$103,530.4

$103,500.0

$30.4

II

0.0022

800

170

$800.4

$136,063.6

$136,000.0

$63.6

III

0.0017

750

100

$750.2

$75,017.0

$75,000.0

$17.0

I

0.0015

850

135

$850.2

$114,777.3

$114,750.0

$27.3

II

0.0019

900

50

$900.1

$45,004.8

$45,000.0

$4.8

III

0.0021

950

40

$950.1

$38,003.4

$38,000.0

$3.4

Total Cost

$857,976.9

$857,650.0

$326.9

Profit

$560,214.7

$553,950.0

$6,264.7

aψi

bψi

I

0.002

800

247

II

0.003

700

III

0.0016

I

Component

Optimal Cost Quantity

As shown from the table, we can see that the proposed model gives a better result by considering the linear relationship between optimal quantity with the optimal price of procurement and sales. The proposed model can increase 1.12% profit by increasing 0.46% of revenues and by only increasing 0.04% of procurement cost.

Differences

Hence, the quadratic programming model provides an integrated strategic-level dynamic pricing and partner selection tool and a low level operational determination of sales and procurement quantity tool as well.


APIEMS 2008 Proceedings of the 9th Asia Pasific Industrial Engineering & Management Systems Conference 6. CONCLUSION Here we may draw the following conclusions. A. This research develops a quadratic programming model for dynamic pricing optimal quantity decisions by considering demand uncertainty. B. The global structures of supply chain consist of component suppliers, sub-assemblies manufacturer, and buyers supported by warehousing and transportation service providers are being an example. C. This research provides a quantitative view of a decision model of number of quantity procured from the upstream supply chain and number of quantity sold to the downstream supply chain. Simultaneously, the optimal price proposed to buyers and optimal costs proposed to the suppliers are also decided. D. The numerical result shows that by knowing the information about demand uncertainty, threatening the quantity and cost or price in a linear relationship can successfully increase the total profit of supply chain operation. E. The research can be extended by synchronizing production activities of the sub-assembly manufacturer, supply capacity, and production capacity and provide manufacturing, assembly, and transportation schedules for the selected supply chain configuration. F. Scheduling can also be addressed in the model through the determination of procurement levels, transportation levels, and production level for each time period.

Current, J. R and Weber, C. A (1994) Application of facility location modeling constructs to vendor selection problems, European Journal of Operations Research, 76, 387-392. de Boer, L., Labro, E., and Roodhooft, F. (2000) A review of methods supporting supplier selection, European Journal of Purchasing and Supply Management, 7, 75-89. Degraeve, Z., Labro, E., and Roodhooft, F. (2000) An evaluation of vendor selection methods from a total cost of ownership perspective, European Journal of Operations Research, 125, 34-58. Hidayat, Y. A., Takahashi, K., Morikawa, K., Hamada, K., Diawati, L., and Cakravastia. A. (2008) A quantitative model of partner selection by considering demand uncertainty, Proceedings of the 9th International Conference on Industrial Management, Japan, 307-316. Li, D., and O’Brien, C. (1999) Integrated decision modeling of supply chain efficiency, International Journal of Production Economics, 59, 147-157. McGill, J. I. and Van Ryzin G. J. (1999) Revenue management: Research overview and prospects, Transportation Science, 3, 233-256. Snyder, L. V. (2006) Facility location under uncertainty: a review, IEE Transactions, 38, 537–554. Weber C. A. and Current J. R. (1993) A multiobjective approach to vendor selection, European Journal of Operations Research, 68, 173-184.

REFERENCES Bhattacharjee, S. and Ramesh, R. (2000) A multiperiod profit maximizing model for retail supply chain management: An integration of demand and supply-side mechanisms, European Journal of Operations Research, 122, 84-601. Biller, S., Chan, L. M. A., Simchi-Levi, D., and Swann, J. (2005) Dynamic pricing and the direct tocustomer model in the automotive industry, Electron Commerce Journal, 5, 309-334. Chan, L. M. A., Shen, Z. J. M., Simchi-Levi, D., and Swann, J. (2004) Coordination of pricing and inventory decisions: a survey and classification. Handbook of quantitative supply chain analysis: Modelling in the enusiness era (eds) D. Simchi-Levi, SD Wu, Z.J.M. Shen (Boston, MA: Kluwer Academic), 335-392. Chaudhry, S. S., Frost, F. G., and Zydiak, J. L. (1993) Vendor selection with price breaks, European Journal of Operations Research, 70, 52-66.

AUTHOR BIOGRAPHIES Yosi A. Hidayat is a doctoral student at Department of Artificial Complex Systems Engineering, Graduate School of Engineering, Hiroshima University. She received her Master degree at Department of Industrial Engineering, Bandung Institute of Technology (ITB) in 2007. Her research interests include technology transfer and supply strategy in supply chain management. Her email address is Katsuhiko Takahashi is a Professor at Department of Artificial Complex Systems Engineering, Graduate School of Engineering, Hiroshima University. He received his Doctoral degree from Waseda University. His research interests include production system and supply chain management. His email address is


APIEMS 2008 Proceedings of the 9th Asia Pasific Industrial Engineering & Management Systems Conference Katsumi Morikawa is an Associate Professor at Department of Artificial Complex Systems Engineering, Graduate School of Engineering, Hiroshima University. He received his Doctoral degree from Hiroshima University. His research interests include production planning, scheduling, and human-computer interactive systems. His email address is

Lucia Diawati is a faculty member of Department of Industrial Engineering, Faculty of Industrial Technology, Institut Teknologi Bandung, Indonesia. She received her Doctoral degree from Keio University, Japan. Her research interests include management of technology and product design & development. Her email address is

Kunihiro Hamada is an Associate Professor at Department of Social and Environmental Systems Engineering, Graduate School of Engineering, Hiroshima University. He received his Doctoral degree from the University of Tokyo. His research interests include system engineering, ship engineering, and marine engineering. His email address is

Andi Cakravastia is a faculty member of Department of Industrial Engineering, Faculty of Industrial Technology, Institut Teknologi Bandung, Indonesia. He received his Doctoral degree from Hiroshima University. His research interests include supply chain management and management of technology. His email address is
