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An order quantity negotiation model for distributor-driven supply chains
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Int. J. Production Economics 111 (2008) 147–158 www.elsevier.com/locate/ijpe
An order quantity negotiation model for distributor-driven supply chains Hosang Junga,, Bongju Jeongb, Chi-Guhn Leec a
Samsung Economic Research Institute, 191 Hangangno 2-Ga, Yongsan-ku, Seoul 140-702, South Korea Department of Information and Industrial Engineering, Yonsei University, 134 Shinchon-dong, Seodaemun-ku, Seoul 120-749, South Korea c Department of Mechanical and Industrial Engineering, University of Toronto, 5 King’s College Road, Toronto, Ont. M5S 3G8, Canada
b
Received 2 October 2004; accepted 13 December 2006 Available online 14 January 2007
Abstract We propose a negotiation process to find a contract for a distributor and a manufacturer in a supply chain. The contract is to determine supply quantities from the manufacturer to the distributor for multiple products from different production facilities over time for given prices set by the market. This negotiation process is for distributor-driven supply chains in that the distributor leads the negotiation process by submitting its profit-maximizing order quantities within, while the manufacturer can supply up to the ordered quantities. Numerical studies demonstrate that the proposed negotiation process, while requiring the minimum information revelation to partners, achieves small gap from the solutions of ideal centralized planning model that requires complete information sharing. r 2007 Elsevier B.V. All rights reserved. Keywords: Quantity negotiation; Distributor-driven supply chains; Supply chain planning; Decentralized planning model
1. Introduction Despite the excitements over the surge of e-Commerce fueled by the business-to-consumer (B2C) market around the turn of the century, buying and selling goods between companies still remains the most old-fashioned procedures. The process generally gets started by a company who needs products (possibly services or even information). The company, a buyer in this transaction, first prepares specifications for the product and sends the purchase order to a supplier (or sometimes Corresponding author. Tel: +82 2 3780 8341; fax: +82 2 3780 8108. E-mail address: [email protected] (H. Jung).
suppliers). The supplier may return with a commitment for either the full or partial order quantities depending on its current production capacity and/or profit structure. If the supplier reports shortages, the buyer may want to adjust its original order quantities, in which case the negotiation continues. Otherwise, the procurement process ends and both enter a contract. In this research, we propose a negotiation process for a buyer and a seller to determine supply quantities when the price is set by local markets. The buyer owns a network of distribution centers and has access to multiple markets, and a seller owns a network of manufacturing facilities. The buyer and the seller seek for a contract that specifies supply quantities of multiple products from many
0925-5273/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.ijpe.2006.12.054
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production locations owned by the seller over time at the price set by the market. In the iterative negotiation process, the buyer has the freedom of requesting any quantities, and the seller is not allowed to supply more than requested, but is also under no obligation to meet the whole demand. Traditionally, manufacturers either have distribution operations internally or rely on professional distributor externally. As the complexity of supply chain increases and the market becomes increasingly competitive, many manufacturers realized that distribution operations are not their core competence and outsource these operations. In line with this change of environments, a professional distributor has emerged to manage, control, and deliver logistics activities on behalf of the manufacturer (Hertz and Alfredsson, 2003). More recently, some professional distributors expand their service portfolio to more advanced and complex services such as planning and coordination of supply chain. Also, the direct access to the customers endows the distributors with opportunities to constantly extend their control from only distribution task to the coordination of the whole supply chain. According to Andersen Consulting Co. (Gattorna, 1998), professional distributors will gain more powerful positions as a global coordinators of the whole supply chain in the near future. Such a situation is often encountered with functional products as opposed to innovative products. Functional products include the staples that people buy regularly from their nearby stores to satisfy basic needs. They show stable, predictable demand, and long life cycles. Their stability invites competition, which often leads to large supplierbases, low profit margins and little room for sellers to negotiate around especially in terms of price. In other words, the price of functional products is set by the market (Fisher, 1997). The only options for the seller are either meeting the whole demand at the given price, or rejecting part of or the whole demand. In this sense, we call such supply chains ‘‘distributor-driven’’ supply chains. Although there is a large body of research on supply chain planning in various contexts, planning of distributor-driven supply chains has not gained much attention from the research community. Most studies focus on the integration of different functions of supply chains and assume a complete sharing of information between entities in a supply chain. For example, production-distribution planning (Vidal and Goetschalckx, 1997; Erengu¨c- et al.,
1999; Sarimento and Nagi, 1999; Dhaenens-Flipo and Finke, 2001; Goetschalckx et al., 2002) and supplier or partner selection problems (Weber et al., 1990; Viswanadham and Gaonkar, 2003; Amid et al., 2006; Liao and Rittscher, 2007; Huang and Keskar, 2007) are representative cases. This usually gives rise to a centralized supply chain planning problem where a single decision maker has the full authority to operate the whole supply chain, which might not be entirely realistic. Due to the high complexity of the centralized supply chain planning model, heuristic approaches have often been used (Shapiro, 2001). Recently, some researchers began to raise questions about the unrealistic assumption of complete information sharing between private companies. Decentralized models for production and/or distribution planning problems have been based on two different approaches, namely, mathematical decomposition methods (Barbarosog˘lu and O¨zgu¨r, 1999; Jung et al., 2006) and auction theoretic methods (Kutanoglu and Wu, 1999; Ertogral and Wu, 2000). Their research, however, assumes the presence of an extra coordinator with a complete control over the whole supply chain, and there is no guarantee for feasibility of the final solution due to the duality gap or the oscillation of mathematical decomposition methods. In summary, the literature on supply chain planning shows two shortfalls: centralized models using complete information sharing between private companies do not reflect the reality in the business world, and existing decentralized approaches do not guarantee the feasibility of the final solution. The negotiation process we propose in the paper attempts to address these limitations in that (1) both the seller and the buyer reveal the minimum information regarding their own private business to their negotiation partner and (2) the proposed negotiation process converges to a feasible supply chain plan that has been empirically shown to be close to an optimal supply chain plan. The buyer reveals order quantities to the seller, and the seller simply reports shortages, if any, in supply quantities to the buyer. Therefore, the only information exchanged in the negotiation process is the order quantity and the supply quantity. In addition, it will be empirically shown that the proposed negotiation process generates a near optimal supply chain plan similar to an ideal centralized supply chain planning process based on complete information sharing.
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In the rest of the paper, we will call the buyer ‘‘distributor’’ and call the seller ‘‘manufacturer’’ for ease of explanation. This paper is organized as follows. Section 2 introduces the distributor-driven supply chain, and Section 3 presents the negotiation process along with convergence of the process. Section 4 gives the numerical study for performance validation. Finally, Section 5 summarizes conclusions and future research directions. 2. Distributor-driven supply chain In this section, we will propose a situation in which a distributor and a manufacturer agree to participate in a negotiation to find a profitmaximizing supply chain plan by revealing only minimum information to their partners. The distributor leads the negotiation by setting the order quantities for each production facility of the manufacturer over a given planning horizon. The manufacturer passively reacts to the distributor’s request by committing to meet either the full or the partial orders. The order quantities are the result of profit maximization efforts of the distributor with the considerations of transportation costs, inventory carrying costs, inventory holding capacity at distribution centers, size of markets, sale price of products in each market, wholesale price of products from each of the production facilities, etc. A distribution planning model for the profitmaximizing distributor will be given later in the paper. Once the order quantities are submitted, the manufacturer has to decide how much of the order quantities should be satisfied in order to maximize the profit. The manufacturer may supply less than requested, but may not do more. The profitmaximizing manufacturer should consider product-specific production costs, inventory capacity, production capacity at different production facilities, and inventory carrying costs. These costs vary at different locations and change over time. A production-planning model for the manufacturer will also be given later in the paper. As described above, the negotiation process is led by the distributor, and the manufacturer reacts by determining how much of the order quantities can be fulfilled. Throughout the negotiation process, neither the distributor nor the manufacturer wants to reveal their private information such as cost- and capacity-related information. The distributor simply submits order quantities, and the
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manufacturer meets the requested demand to the extent that it maximizes the profit. The order quantities and supplier quantities must be the minimum information that negotiating parties may ever share. 3. An order quantity negotiation model As mentioned in the previous section, a negotiation begins by a distributor who submits order quantities over a planning horizon to a manufacturer. For an easier exposition of the negotiation process, we name the distributor ‘‘distribution agent (DA)’’ and the manufacturer ‘‘production agent (PA)’’ in the paper. DA generates a distribution plan for multiple products over a given planning horizon that maximizes the profit of the distributor, whereas PA generates a production plan, in response to order quantities submitted by DA, for multiple production facilities that produce multiple products over time in order to maximize the profit of the manufacturer. The basic steps in the quantity negotiation process (QNP) can be summarized as follows: Step 1: DA generates a distribution plan of multiple products over a given planning horizon and submits order quantities at different locations to PA. Step 2: PA generates a profit maximizing-production plan for the given order quantities with an option to supply the full or the partial quantities requested. PA reports to DA any shortage amounts of each product at each production facility over time. Step 3: If there is no shortage reported by PA, the negotiation is completed. Otherwise, DA generates a distribution plan so that the order quantity of each product at each production facility does not exceed the committed supply quantity of the product at each production facility. DA then resubmits the new order quantities to PA, and returns to Step 2. In addition, the following assumptions are employed in the proposed negotiation: A1. Manufacturer is not allowed to supply more than requested. A2. Demands for all products in all markets are known to only the distributor. A3. Manufacturer is solely responsible for all production-related information (e.g., production
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cost and capacity), while the distributor is solely responsible for all distribution-related information (e.g., transportation cost and inventory carrying cost of distribution centers). A4. Unit production costs (private information and known to the manufacturer only) vary across different locations, periods, and product types. A5. Unit inventory carrying costs at production facilities (private information and known to the manufacturer only) vary across different locations, periods, and product types. A6. Unit inventory carrying costs at distribution centers (private information and known to the distributor only) vary across different locations, periods, and product types A7. Inventory capacities at production facilities (private information and known to the manufacturer only) and vary across different locations and periods. A8. Inventory capacities at distribution centers (private information and known to the distributor only) and vary across different locations and periods. A9. Production capacities (private information and known to the manufacturer only) may vary between different production facilities and different periods. A10. Production lead-time and transportation time between locations are negligible. A11. The internal transportation between the production facilities of the manufacturer is not allowed. Assumption A1 simply states that supplying more than requested is not acceptable. Assumption A2 indicates that the distributor manages information on the market including demand in the distributordriven supply chain. Assumption A3 is to show that the current supply chain is decentralized, and the manufacturer and the distributor are running their own local databases regarding production and distribution, respectively. Assumption A4–A9 are often found in many deterministic planning models. Both the manufacturer and the distributor participating in the same supply chain may have other business partners to whom they may have to dedicate their capacities. Commitments to their business partners may vary in time and in locations and consequently their capacities available for the
current negotiation may vary. Moreover, allowance of changing capacity in time and in location makes the proposed model more general. Assumption A10 indicates production and transportation lead time are assumed to be zero, without loss of generality. The implication of assumption A11 is that excessive capacity of adjacent facilities may not be used. It is often the case that production facilities are considerable miles apart and transportation of products between locations is exclusively done by the distributor. As shortages are reported from any production facility, it is very likely that the distributor increases the order from adjacent production facilities or adjacent periods, which essentially results in moving capacity between production facilities or periods. Before proceeding to a local planning model of each agent, we investigate a centralized supply chain planning (CSCP) model. The CSCP model assumes that all the necessary information can be collected from the overall supply chain and processed freely in the central joint planning department between the manufacturer and the distributor. To formulate the model, the following parameters and decision variables are required: Parameters F D M N P Dkmt pkmt wkft rkft Tkijt hkft h^kdt Hft H^ dt Cft
set of production facilities set of distribution centers set of markets set of all locations (i.e., N ¼ D[F[M) set of products demand for product k in market m in period t market price per one unit of product k sold in market m in period t wholesale price of product k manufactured at production facility f in period t unit production cost of product k at production facility f in period t cost of transporting one unit of product k from location i to location j in period t unit inventory carrying cost of product k in production facility f in period t unit inventory carrying cost of product k in distribution center d in period t inventory capacity in production facility f in period t inventory capacity in distribution center d in period t production capacity in production facility f in period t
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ckf
production capacity required to produce one unit of product k in production facility f storage space required for one unit of product k
vk
Variables xkft
production quantity of product k at production facility f in period t transportation quantity of product k from location i to location j in period t ending inventory level of product k in production facility f in period t ending inventory level of product k in distribution center d in period t
ykijt Ikft I^kdt
Now, the CSCP model is given as follows: Max
X
pkmt
k;t;m
( X X
ykdmt
d
T kijt ykijt
i2N;j2N
k;t
þ
!
X
X
wkft
k;f ;t
X
h^kdt I^kdt
X
d
! ykfdt
X
X
d
wkft
f
X
!) ykfdt
d
rkft xkft þ hkft I kft
I kft þ xkft
X
ykfdt ¼ I kftþ1
8k; f ; t,
(2)
d
I^kdt þ
X
ykfdt
f
X
X
ykdmt ¼ I^kdtþ1
8k; d; t,
(3)
m
ykdmt pDkmt
8k; m; t,
vk I^kdt pH^ dt
8d; t,
(5)
vk I kft pH ft
8f ; t,
(6)
ckf xkft pC ft
8f ; t,
(7)
(4)
d
X
inventory costs in all periods in the given planning horizon; in addition, the central joint planning department knows all such information of the whole distribution network, including future demands in all markets, transportation costs, and inventory capacities in all distribution centers over all periods in the given planning horizon. In fact, the manufacturer would be very reluctant to reveal such information to their business partners, and vice versa. In the above model, the objective function (1) tries to maximize the total profit of the distributor (i.e., sales revenue minus the total cost of the distributor) and the manufacturer (i.e., the payment from the distributor minus the total cost of the manufacturer) simultaneously. Constraints (2) are inventory balance equations for production facilities, while constraints (3) are flow conservation equations between production facilities and markets via distribution centers. Constraints (4) ensure that the distributor may not provide more than market demands. Constraints (5) and (6) are to make sure inventory carrying capacity is not violated. Constraints (7) are to limit the production quantities to be less than or equal to production capacity in each of the production facilities.
k;f ;t
ð1Þ s.t.
3.1. A distribution planning model for DA We propose a linear programming model for the profit maximization of DA. To define a distribution-planning model for DA, we define a new parameter in addition to those introduced before as follows: Parameters C^ ft
aggregate production capacity at production facility f in period t as perceived by DA based on the shortage reported by PA. C^ ft are initially set at N (or a very big number) until PA reports a shortage for product k at production facility f in period t.
k
X k
X
151
k
xkft ; I kft ; I^kdt ; ykijt X0
8k; f ; d; i; j; t.
A distribution planning model of DA is given as follows:tvs
(8)
As mentioned above, the CSCP model is based on the assumption that the central joint planning department knows everything about all of the production facilities, including production capacities, inventory capacities, production costs, and
Max
X k;t;m
pkmt
X
( X X k;t
! ykdmt
d
i2N;j2N
T kijt ykijt þ
X d
h^kdt I^kdt þ
X f
wkft
X
!) ykfdt
d
ð9Þ
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Subject to X X ykfdt ykdmt ¼ I^kdtþ1 I^kdt þ X
8k; d; t,
(10)
m
f
ykdmt pDkmt
8k; m; t,
(11)
vk I^kdt pH^ dt
8d; t,
(12)
those introduced before, we define a new decision variable as follows: Variables supply shortage quantity of product k at production facility f in period t
bkft
d
X k
XX k
ykfdt pC^ ft
8f ; t,
(13)
8k; d; i; j; t.
(14)
d
I^kdt ; ykijt X0
A production planning model of PA for given order quantities Okft (order for product k from production facility f in period t) is given as follows: X X Max ðwkft ðOkft bkft ÞÞ ðrkft xkft þ hkft I kft Þ k;f ;t
The objective function (9) is to maximize the sum of all sales revenue minus transportation costs between and distribution cenP production facilities ters k;t;f ;d T kfdt ykfdt , between distribution centers P and markets k;t;d;m T kdmt ykdmt , the total inventory P
carrying costs at distribution centers ^ ^ k;t;d hkdt I kdt , and the total purchase cost paid
to PA based on the wholesale prices P set prior to the P . Constraints negotiation k;t;f wkft d ykfdt (10)–(12) are from constraints (3)–(5) of the CSCP model. Constraints (13) are to limit aggregate order quantity at a location to be less than or equal to the perceived aggregate production capacity at the location where PA reports shortages. The production capacity required to produce a single unit product varies between products and is unknown to the distributor. As a result, the distributor limits the sum of order quantities of all the products produced at a location as shown in constraints (13). How to set the order quantities with the output of solving the above model will be discussed again in Section 3.3. Note that the value of C^ ft is set based upon the shortage reported by PA, while all the others are the private information of DA. 3.2. A production planning model for PA PA plays a passive role in the proposed agentbased supply chain planning. Responding to the orders submitted by DA, PA will meet the demand only up to the point at which the profit is maximized, and then will report the shortage to DA. We propose a linear programming model for PA by which the manufacturer can maximize the profit for given order quantities. In addition to
k;f ;t
(15) s.t. I kft þ xkft Okft þ bkft ¼ I kftþ1 X vk I kft pH ft 8f ; t,
8k; f ; t,
(16) (17)
k
X
ckf xkft pC ft
8f ; t,
(18)
8k; f ; t.
(19)
k
xkft ; I kft ; bkft X0
The objective function (15) is to maximize the profit of the Pmanufacturer, which is the payment from DA k;f ;t ðwkft ðOkft bkft ÞÞ minus production costs combined P and inventory carrying k;f ;t ðrkft xkft þ hkft I kft Þ . Constraints (16) are inventory balance equations, and they ensure that PA may not supply more than requested, but may refuse to meet the full quantity. Constraints (17) and (18) are from constraints (6) and (7) of the CSCP model. In addition, the proposed planning model of PA can be decomposed into f separate linear programming models. 3.3. Information exchange between DA and PA The proposed negotiation process is designed to allow participating agents to reveal the minimum private business information to their negotiating partners. The minimum information that DA has to forward to PA includes order quantities, while the minimum information that PA has to provide to DA is supply quantities. As per common practice between any buyer and seller, the supply quantities may not exceed the order quantity but there is no practical mechanism to prevent the supplier (or seller) from untruthfully reporting its lack of
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capacity to meet the whole order quantities. Therefore, our negotiation process allows PA to report the shortage, not for the actual lack of production capacity, but for the profit maximization of the manufacturer. In each negotiation round, DA submits to PA order quantities for each product type from each production facility in each period. Such information is a result of solving the problem P given in Eqs. (9)–(14). In the linear program, d ykfdt is the order quantity for product k from production facility f in period t that is to be submitted to PA, and then to be used as Okft in PA. Upon DA’s submission of order quantities, PA builds the production planning problem shown in Eqs. (15)–(19) to find a profit maximizing production plan. The production plan specifies the production quantity of each product at each production facility in each period. The production quantity in the production plan can be less than the corresponding order quantity, and PA has to report the shortage amount (bkft), if any, to DA. With the reported shortage amount received from PA, DA will adjust its perceived aggregate production capacity at production facility f in period t. That is, the new distribution planning problemPof DA in the next negotiation round will assume k ðOkft bkft Þ as an upper bound of the aggregate order quantity ðC^ ft Þ at production facility f in period t. If no shortage is reported at production facility f in period t, DA maintains the same aggregate capacity limit as in the previous negotiation round. Note that the aggregate production capacity at production facility f in period t should remain unlimited as long as PA reports no shortages in all previous rounds at the location.
from PA to DA. Note that the production (distribution) planning problem is feasible for any given order quantities (reported shortages). A trivial feasible solution is to produce (order) 0 units of all products at all locations in all periods regardless of the given order quantities (reported shortages). Also note that the perceived production capacities are monotonically decreasing for all product at all locations in all periods due to the design of the negotiation process (once shortages are reported, DA never places orders requesting more units of any product than the perceived capacity of that particular product at all locations in all periods). When the perceived capacities are all 0, DA should place an order for 0 units of all products at all locations in all periods, in which case PA should report 0 shortages. The perceived capacities are monotonically decreasing as long as PA reports shortages. Otherwise, the negotiation terminates with a feasible supply chain plan that has none-zero production quantity and none-zero distribution quantity. The perceived capacities are monotonically decreasing, and are bounded below (the perceived capacities cannot be negative). In conclusion, the sequence of supply chain plans is guaranteed to be feasible and the sequence of perceived production capacities is monotonically decreasing and bounded below by zero componentwise. Therefore, the negotiation process is bound to terminate with a feasible supply chain plan eventually. Based on the above explanation, a more thorough proof is as follows.
3.4. Analysis
Proof. The feasible supply chain plan requires that both a distribution plan of DA and a production plan of PA are feasible, and that there is no conflict between the order quantity of DA and the supply P quantity of PA (i.e., k bkft ¼ 0 8f ; t ). First, ordering nothing in DA and producing nothing in PA are obvious feasible plans to both the production planning and distribution planning problems. Next, we should show the P proposed negotiation process is convergent in k bkft as zero 8f ; t, as negotiation rounds proceed. Since bkftpOkft is true from the property P of objective functionP(15) and Eq. (16), if k Okft converges then k bkft converges. Also, from
In this section, we will show that the proposed negotiation process should always be terminated with a feasible supply chain plan. Typically, when a centralized planning problem is decomposed into two sub-problems, which are locally optimized iteratively, convergence is often not guaranteed, and negotiation may continue indefinitely. However, the negotiation process proposed in the paper always terminates with feasible plans for DA and PA. A feasible supply chain plan is a collection of a feasible distribution plan for DA and a feasible production plan for PA with no shortage reported
Theorem 1. The proposed negotiation process is guaranteed to terminate with a feasible supply chain plan.
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P ^ Eq. k Okft (i.e., P P(13) if C ft converges then y ) converges. Thus, we can say that if k d kfdt P C^ ft converges then k bkft converges. For example, let us suppose that Oikft ; bikft ; i ^ C ft ; yikfdt indicate the value of each of the variables at the ith negotiation round, respectively. Each negotiation round is composed of DA running first and PA running next. P 1 ^1 From Eq. (13), k Okft pC ft is true after DA running. Also, after PA running, the supply shortage quantity, bkft1 8k; f ; t are delivered to DA, and P P P DA will use k O1kft k b1kft (when k b1kft 40) or P 1 2 C^ ft (when k b1kft ¼ 0) as C^ ft in the second negotiation round. Thus, in the second negotiation round, either P 1 P 2 ^2 P 1 P 1 ^1 k Okft pC ft ¼ k Okft k bkftoC ft (when k bkft 40) P 2 P 2 1 or k Okft pC^ ft ¼ C^ ft (when k b1kft ¼ 0) is true. i Consequently, C^ ft has a non-increasing sequence iþ1 i (i.e., C^ ft pC^ ft ) as negotiation rounds proceed, and i bounded from below. In other words, C^ ft will P i1 decrease whenever k bkft 40 (i.e., there exists at least one bi1 40). kft ^ PAs mentioned above, since C ft converges, also b converges. k kft Until the terminating condition of the negotiation P process (i.e., b ¼ 0 8f ; t ) is satisfied, the k kft negotiation process continues due to the design of i the negotiation process and it means that C^ ft can P i1 decrease continuously whenever k bkft 40. Also, P i the worstPcase, C^ ft ¼ 0 8f ; t makes k Oift ¼ 0, and leads to k bikft ¼ 0 8f ; t. & 4. Computational study In this section, experimental results are presented to demonstrate the performance of the proposed negotiation process in terms of solution quality and computational efficiency. To this end, the total profit of the supply chain at the end of the negotiation is compared with that of the CSCP model, and the number of iterations before the negotiation process converges is investigated for many randomly generated examples. 4.1. Experimental design We randomly generate 40 problem instances in four categories depending on tightness of PA’s capacity (Tm) and DA’s capacity (Td): (Tm,Td)A
{(High, High), (High, Low), (Low, High), (Low, Low)}. Production and distribution plans are heavily influenced by the capacity of PA and DA, and the information exchange between them. In this paper, production capacity is used for PA’s capacity, while the inventory capacity of the distribution center is considered for DA’s capacity. Because production capacity might directly affect whether products can be shipped in each production facility, we used production capacity as PA’s capacity rather than storage capacity. Also, we considered inventory capacity as DA’s capacity. For simplicity of experiments, the inventory carrying capacity at production facilities is set to unlimited. Tightness is defined as a ratio of the sum of demands to the sum of available capacity of all the planning period. Tightness of a problem instance is considered to be low if the ratio is 2/3 ¼ 0.67 (or the total demand is 67% of the total available capacity) and to be high if the ratio is 5/3 ¼ 1.67 (or the total demand is 167% of the total available capacity). It is expected that the number of negotiation rounds is larger as the capacity of DA and PA is more tightly constrained. As for the given parameters for experiments, we generated each of them as follows: demand is randomly generated from U(1500, 3500); two different ranges for the tightness factor are considered: low (0.6–0.8) or high (1.2–1.4). In addition, costs have been determined in the following way. The production cost is determined by rkft ¼ ckftk+ dkftf, where ckft is a random number chosen from U(45,55) to consider the effect of each product, dkft is a random number chosen from U(0,5) to consider the effect of each production facility, k is an index of products, and f is an index of production facilities. This is for generating the production cost in a systematic way: the product with a higher product index may have a higher production cost, while the production facility with a lower facility index may have a lower cost. Using this approach, we can make a distinction between products (e.g., a high valued product and a low valued product) and between facilities (e.g., high labor cost and low labor cost) in generating the production cost. The inventory carrying cost at production facilities is set to the half level of its production cost: hkft ¼ rkft/2. The sum of the inventory carrying cost at a distribution center and the transportation cost from a production facility to a customer zone might be expensive as the production cost of a product.
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category contains 10 problem instances and the profits shown in the table is the average of such 10 instances. As shown in Table 1, average percentile gap for all 40 problem sets is 5.8%. Profit loss due to negotiation process becomes smaller for both PA and DA when PA has shortage in capacity (category (High, High) and (High, Low)), while the profit loss becomes larger when PA has surplus in capacity (category (Low, High) and (Low, Low)). General trend is the loss in profit becomes smaller as PA has tighter capacity. If PA has tighter capacity, PA has no many alternative ways to generate a production plan and cannot help choosing a restricted solution of production part that may be equivalent to the production plan of the CSCP model. Such observation is confirmed by statistical analysis as summarized in Table 2. It is determined by statistical test that neither tightness of distributor’s capacity nor the product of tightness of manufacturer’s capacity and distributor’s capacity make any significant difference in the loss of profit due to the negotiation process. It is only tightness of manufacturer’s capacity that influences the quality of the final solution of the negotiation process as indicated in Table 2. Table 3 presents the average number of negotiation rounds in each category. The average number of rounds in all 40 problem instances is 21.45. It tends to take more rounds as manufacturer has tight capacity. This is again confirmed by statistical tests as shown in Table 4. If PA has enough capacity to generate a production plan with the requested order quantity by DA, then PA can make a proper production plan without reporting any shortage against the request of DA in a few negotiation rounds. Otherwise, DA
The inventory carrying cost at a distribution center is approximately set to P the half level of the production cost: h^kdt ¼ ð f rkft =2f Þ Uð0:8; 1:2Þ. The transportation cost between locations is approximately set to the quarter level P of the production cost as follows: T ¼ kfdt f rkft =4f P Uð0:8; 1:2Þ and T kdmt ¼ f rkft = 4f Uð0:8; 1:2Þ. Finally, the distributor’s sales price and the whole sale price of the manufacturer for one unit of product are set properly in consideration of the total production or distribution cost, respectively. For example, pkmt is chosen from U(800,850) and wkft is chosen from U(400,450). The gap between maximum profits from the CSCP model and from the final round of negotiation rounds will be compared to demonstrate the quality of solution, and the number of negotiation rounds will be used to show the computational performance of the negotiation process. In each of 40 problem instances, there are 4 product types, 10 production facilities, 5 distribution centers, 10 markets, and 12 planning periods. The negotiation process and the CSCP model are implemented using ILOG OPL Studio version 3.1 and MINITAB version 12.1 is used for statistical analysis. 4.2. Experimental results and analysis Table 1 shows profits achieved using the negotiation process and the CSCP model for 40 problem instances. The first column shows categories under which 40 problem instances are generated, and the rest of table shows (1) profits for the manufacturer and the distributor and (2) gap between profits for the manufacturer and the distributor from negotiation process and from the CSCP model. Each
Table 1 Solution quality comparison between centralized and decentralized problems Tm, Td
Profit of PA Ca
High, High High, Low Low, High Low, Low Average a
380, 382, 546, 543, 463,
Profit of DA Db
634 973 494 610 428
359, 360, 490, 495, 426,
643 763 426 623 614
The solution of centralized problem. The solution of the negotiation. c The % deviation. b
Gapc
C
5.5 5.8 10.3 8.8 7.6
346, 348, 516, 513, 431,
Total profit D
291 147 062 871 093
337, 337, 488, 489, 413,
465 182 240 704 148
Gap
C
D
2.5 3.1 5.4 4.7 3.9
726, 925 731, 121 1062, 556 1057, 481 894, 521
697, 697, 978, 985, 839,
Gap 108 944 666 327 761
4.1 4.5 7.9 6.8 5.8
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Table 2 The ANOVA results on the solution quality problem
Table 4 The ANOVA results on the computational burden problem
Source
DFa
SSb
AdjSSc
AdjMSd
Fe
Pf
Source
DFa
SSb
AdjSSc
AdjMSd
Fe
Pf
Tm Td Tm, Td Error
1 1 1 36
92.598 0.992 5.580 110.048
92.598 0.992 5.580 110.048
92.598 0.992 5.580 3.057
30.29 0.32 1.83
0.000g 0.572 0.185
Tm Td Tm, Td Error
1 1 1 36
435.60 0.10 25.60 314.60
435.60 0.10 25.60 314.60
435.60 0.10 25.60 8.74
49.85 0.01 2.93
0.000g 0.915 0.096
Total
39
209.219
Total
39
775.90
a
a
b
b
Degree of freedom. Sum of squares. c Adjusted sum of squares. d Adjusted means square. e Computed F-value. f Computed P-value. g The result is significant to a significant level of 0.05.
Degree of freedom. Sum of squares. c Adjusted sum of squares. d Adjusted means square. e Computed F-value. f Computed P-value. g The result is significant to a significant level of 0.05.
Table 3 The experimental results on the computational burden problem Tm
Td
No of iterations
High High Low Low
High Low High Low
23.9 25.6 18.9 17.4
may try to reduce its order quantity in order not to make any shortage in PA, and it requires more negotiation rounds. Tables 3 and 4 repeat the same observation that it took statistically less rounds of negotiation to reach the final plans for the manufacturer and the distributor as the manufacturer has surplus in capacity. To show the convergence of the proposed negotiation process, a graphical illustration of the negotiation process is given in Fig. 1, where unmet demands reported by PA, requested order quantities by DA, and profits of PA and DA in each negotiation round are plotted for one of the 10 problem instances of category (High, High). Fig. 1 is prepared using the following experimental result given in Table 5. As negotiation rounds proceed, both total order quantity and the profit of DA are decreasing, whereas the profit of PA is increasing as shown in Fig. 1(a). This is because the initial order quantity of DA has adjusted accordingly by the available supply quantity of PA throughout the negotiation rounds. In other words, the initial ideal distribution plan of DA, assuming the infinite product supply
Fig. 1. Example graphs on the convergence of the negotiation process, (a) convergence of the profits of DA and PA and (b) convergence of production and distribution plans through negotiation.
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Table 5 The experimental result for the example graphs Iteration
DA profit
PA profit
Supply shortage
Order from DA
Supply from PA
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
528,660 519,580 520,417 520,473 519,018 516,636 518,379 516,485 515,328 514,824 514,189 510,710 500,140 504,809 486,250 456,781 438,174 415,537 338,593
38,760 166,829 181,976 178,081 210,633 254,971 221,865 247,927 250,801 250,670 275,205 268,755 304,693 290,545 309,449 322,596 325,952 333,815 360,288
9080 6932 6560 6677 6075 5245 5925 5375 5252 4896 4843 4654 4266 4555 4280 3443 3050 2392 0
9656 9656 9656 9656 9656 9656 9656 9656 9656 9656 9656 9656 9656 9656 9656 9028 8683 8025 5633
576 2724 3096 2979 3581 4411 3731 4281 4404 4760 4813 5002 5390 5101 5376 5585 5633 5633 5633
from PA, has changed into a more realistic one as negotiation rounds proceed. In addition, as shown in Fig. 1(b), there exist no total unmet demands reported by PA at the end of the negotiation process, and it means that the total order quantity of DA is identical with the total possible supply quantity of PA properly.
For future research, the extended negotiation models considering vendors are needed. Also the implementation using real data in various distributor-driven supply chains should be followed to check the network traffic and extra cost problems.
5. Conclusions
Amid, A., Ghodsypour, S.H., O’Brien, C., 2006. Fuzzy multiobjective linear model for supplier selection in a supply chain. International Journal of Production Economics 104 (2), 394–407. Barbarosog˘lu, G., O¨zgu¨r, D., 1999. Hierarchical design of an integrated production and 2-echelon distribution system. European Journal of Operational Research 118, 464–484. Dhaenens-Flipo, C., Finke, G., 2001. An integrated model for an industrial production–distribution problem. IIE Transactions 33, 705–715. Erengu¨c- , S.S., Simpson, N.C., Vakharia, A.J., 1999. Integrated production/distribution planning in supply chains: An invited review. European Journal of Operational Research 115, 219–236. Ertogral, K., Wu, S.D., 2000. Auction-theoretic coordination of production planning in the supply chain. IIE Transactions 32, 931–940. Fisher, M.L., 1997. What is the right supply chain for your product? Harvard Business Review 75 (2), 105–116. Gattorna, J., 1998. Strategic Supply Chain Alignment: Best Practices in Supply Chain Management. Gower Pub Co. Goetschalckx, M., Vidal, C.J., Dogan, K., 2002. Modeling and design of global logistics systems: A review of integrated strategic and tactical models and design algorithms. European Journal of Operational Research 143, 1–18.
In this paper, we propose a negotiation process that can be easily implemented in an information system connecting a manufacturer and a distributor. Advantages of the proposed negotiation process include: (1) only minimum information is shared between a distributor and a manufacturer and (2) negotiation process is guaranteed to terminate with a feasible supply chain plan, which has been empirically shown to be close to optimal plan. Numerical studies show that the distribution and production plans at the end of negotiation are on average only 5.8% below the optimal solution of centralized planning based on full information sharing. The proposed mechanism can be used not only as a negotiation framework between companies who are reluctant to share their business information but also a decomposition scheme for a complex integrated planning problem.
References
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Hertz, S., Alfredsson, M., 2003. Strategic development of third party logistics providers. Industrial Marketing Management 32, 139–149. Huang, S.H., Keskar, H., 2007. Comprehensive and configurable metrics for supplier selection. International Journal of Production Economics 105 (2), 510–523. Jung, H., Jeong, B., Lee, C.G., 2006. Collaborative agent based supply chain planning for functional product markets. IE Interfaces 19 (1), 53–61. Kutanoglu, E., Wu, S.D., 1999. On combinatorial auction and Lagrangian relaxation for distributed resource scheduling. IIE Transactions 31, 813–826. Liao, Z., Rittscher, J., 2007. A multi-objective supplier selection model under stochastic demand conditions. International Journal of Production Economics 105 (1), 150–159.
Sarimento, A.M., Nagi, R., 1999. A review of integrated analysis of production–distribution systems. IIE Transactions 31, 1061–1074. Shapiro, J.F., 2001. Modeling the Supply Chain. Wadsworth Group, Pacific Grove, CA. Vidal, C.J., Goetschalckx, M., 1997. Strategic productiondistribution models: A critical review with emphasis on global supply chain models. European Journal of Operational Research 98, 1–18. Viswanadham, N., Gaonkar, R.S., 2003. Partner selection and synchronized planning in dynamic manufacturing networks. IEEE Transactions on Robotics and Automation 19 (1), 117–130. Weber, C.A., Current, J.R., Benton, W.C., 1990. Vendor selection criteria and methods. European Journal of Operational Research 50, 2–18.
Int. J. Production Economics 111 (2008) 147–158 www.elsevier.com/locate/ijpe
An order quantity negotiation model for distributor-driven supply chains Hosang Junga,, Bongju Jeongb, Chi-Guhn Leec a
Samsung Economic Research Institute, 191 Hangangno 2-Ga, Yongsan-ku, Seoul 140-702, South Korea Department of Information and Industrial Engineering, Yonsei University, 134 Shinchon-dong, Seodaemun-ku, Seoul 120-749, South Korea c Department of Mechanical and Industrial Engineering, University of Toronto, 5 King’s College Road, Toronto, Ont. M5S 3G8, Canada
b
Received 2 October 2004; accepted 13 December 2006 Available online 14 January 2007
Abstract We propose a negotiation process to find a contract for a distributor and a manufacturer in a supply chain. The contract is to determine supply quantities from the manufacturer to the distributor for multiple products from different production facilities over time for given prices set by the market. This negotiation process is for distributor-driven supply chains in that the distributor leads the negotiation process by submitting its profit-maximizing order quantities within, while the manufacturer can supply up to the ordered quantities. Numerical studies demonstrate that the proposed negotiation process, while requiring the minimum information revelation to partners, achieves small gap from the solutions of ideal centralized planning model that requires complete information sharing. r 2007 Elsevier B.V. All rights reserved. Keywords: Quantity negotiation; Distributor-driven supply chains; Supply chain planning; Decentralized planning model
1. Introduction Despite the excitements over the surge of e-Commerce fueled by the business-to-consumer (B2C) market around the turn of the century, buying and selling goods between companies still remains the most old-fashioned procedures. The process generally gets started by a company who needs products (possibly services or even information). The company, a buyer in this transaction, first prepares specifications for the product and sends the purchase order to a supplier (or sometimes Corresponding author. Tel: +82 2 3780 8341; fax: +82 2 3780 8108. E-mail address: [email protected] (H. Jung).
suppliers). The supplier may return with a commitment for either the full or partial order quantities depending on its current production capacity and/or profit structure. If the supplier reports shortages, the buyer may want to adjust its original order quantities, in which case the negotiation continues. Otherwise, the procurement process ends and both enter a contract. In this research, we propose a negotiation process for a buyer and a seller to determine supply quantities when the price is set by local markets. The buyer owns a network of distribution centers and has access to multiple markets, and a seller owns a network of manufacturing facilities. The buyer and the seller seek for a contract that specifies supply quantities of multiple products from many
0925-5273/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.ijpe.2006.12.054
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production locations owned by the seller over time at the price set by the market. In the iterative negotiation process, the buyer has the freedom of requesting any quantities, and the seller is not allowed to supply more than requested, but is also under no obligation to meet the whole demand. Traditionally, manufacturers either have distribution operations internally or rely on professional distributor externally. As the complexity of supply chain increases and the market becomes increasingly competitive, many manufacturers realized that distribution operations are not their core competence and outsource these operations. In line with this change of environments, a professional distributor has emerged to manage, control, and deliver logistics activities on behalf of the manufacturer (Hertz and Alfredsson, 2003). More recently, some professional distributors expand their service portfolio to more advanced and complex services such as planning and coordination of supply chain. Also, the direct access to the customers endows the distributors with opportunities to constantly extend their control from only distribution task to the coordination of the whole supply chain. According to Andersen Consulting Co. (Gattorna, 1998), professional distributors will gain more powerful positions as a global coordinators of the whole supply chain in the near future. Such a situation is often encountered with functional products as opposed to innovative products. Functional products include the staples that people buy regularly from their nearby stores to satisfy basic needs. They show stable, predictable demand, and long life cycles. Their stability invites competition, which often leads to large supplierbases, low profit margins and little room for sellers to negotiate around especially in terms of price. In other words, the price of functional products is set by the market (Fisher, 1997). The only options for the seller are either meeting the whole demand at the given price, or rejecting part of or the whole demand. In this sense, we call such supply chains ‘‘distributor-driven’’ supply chains. Although there is a large body of research on supply chain planning in various contexts, planning of distributor-driven supply chains has not gained much attention from the research community. Most studies focus on the integration of different functions of supply chains and assume a complete sharing of information between entities in a supply chain. For example, production-distribution planning (Vidal and Goetschalckx, 1997; Erengu¨c- et al.,
1999; Sarimento and Nagi, 1999; Dhaenens-Flipo and Finke, 2001; Goetschalckx et al., 2002) and supplier or partner selection problems (Weber et al., 1990; Viswanadham and Gaonkar, 2003; Amid et al., 2006; Liao and Rittscher, 2007; Huang and Keskar, 2007) are representative cases. This usually gives rise to a centralized supply chain planning problem where a single decision maker has the full authority to operate the whole supply chain, which might not be entirely realistic. Due to the high complexity of the centralized supply chain planning model, heuristic approaches have often been used (Shapiro, 2001). Recently, some researchers began to raise questions about the unrealistic assumption of complete information sharing between private companies. Decentralized models for production and/or distribution planning problems have been based on two different approaches, namely, mathematical decomposition methods (Barbarosog˘lu and O¨zgu¨r, 1999; Jung et al., 2006) and auction theoretic methods (Kutanoglu and Wu, 1999; Ertogral and Wu, 2000). Their research, however, assumes the presence of an extra coordinator with a complete control over the whole supply chain, and there is no guarantee for feasibility of the final solution due to the duality gap or the oscillation of mathematical decomposition methods. In summary, the literature on supply chain planning shows two shortfalls: centralized models using complete information sharing between private companies do not reflect the reality in the business world, and existing decentralized approaches do not guarantee the feasibility of the final solution. The negotiation process we propose in the paper attempts to address these limitations in that (1) both the seller and the buyer reveal the minimum information regarding their own private business to their negotiation partner and (2) the proposed negotiation process converges to a feasible supply chain plan that has been empirically shown to be close to an optimal supply chain plan. The buyer reveals order quantities to the seller, and the seller simply reports shortages, if any, in supply quantities to the buyer. Therefore, the only information exchanged in the negotiation process is the order quantity and the supply quantity. In addition, it will be empirically shown that the proposed negotiation process generates a near optimal supply chain plan similar to an ideal centralized supply chain planning process based on complete information sharing.
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In the rest of the paper, we will call the buyer ‘‘distributor’’ and call the seller ‘‘manufacturer’’ for ease of explanation. This paper is organized as follows. Section 2 introduces the distributor-driven supply chain, and Section 3 presents the negotiation process along with convergence of the process. Section 4 gives the numerical study for performance validation. Finally, Section 5 summarizes conclusions and future research directions. 2. Distributor-driven supply chain In this section, we will propose a situation in which a distributor and a manufacturer agree to participate in a negotiation to find a profitmaximizing supply chain plan by revealing only minimum information to their partners. The distributor leads the negotiation by setting the order quantities for each production facility of the manufacturer over a given planning horizon. The manufacturer passively reacts to the distributor’s request by committing to meet either the full or the partial orders. The order quantities are the result of profit maximization efforts of the distributor with the considerations of transportation costs, inventory carrying costs, inventory holding capacity at distribution centers, size of markets, sale price of products in each market, wholesale price of products from each of the production facilities, etc. A distribution planning model for the profitmaximizing distributor will be given later in the paper. Once the order quantities are submitted, the manufacturer has to decide how much of the order quantities should be satisfied in order to maximize the profit. The manufacturer may supply less than requested, but may not do more. The profitmaximizing manufacturer should consider product-specific production costs, inventory capacity, production capacity at different production facilities, and inventory carrying costs. These costs vary at different locations and change over time. A production-planning model for the manufacturer will also be given later in the paper. As described above, the negotiation process is led by the distributor, and the manufacturer reacts by determining how much of the order quantities can be fulfilled. Throughout the negotiation process, neither the distributor nor the manufacturer wants to reveal their private information such as cost- and capacity-related information. The distributor simply submits order quantities, and the
149
manufacturer meets the requested demand to the extent that it maximizes the profit. The order quantities and supplier quantities must be the minimum information that negotiating parties may ever share. 3. An order quantity negotiation model As mentioned in the previous section, a negotiation begins by a distributor who submits order quantities over a planning horizon to a manufacturer. For an easier exposition of the negotiation process, we name the distributor ‘‘distribution agent (DA)’’ and the manufacturer ‘‘production agent (PA)’’ in the paper. DA generates a distribution plan for multiple products over a given planning horizon that maximizes the profit of the distributor, whereas PA generates a production plan, in response to order quantities submitted by DA, for multiple production facilities that produce multiple products over time in order to maximize the profit of the manufacturer. The basic steps in the quantity negotiation process (QNP) can be summarized as follows: Step 1: DA generates a distribution plan of multiple products over a given planning horizon and submits order quantities at different locations to PA. Step 2: PA generates a profit maximizing-production plan for the given order quantities with an option to supply the full or the partial quantities requested. PA reports to DA any shortage amounts of each product at each production facility over time. Step 3: If there is no shortage reported by PA, the negotiation is completed. Otherwise, DA generates a distribution plan so that the order quantity of each product at each production facility does not exceed the committed supply quantity of the product at each production facility. DA then resubmits the new order quantities to PA, and returns to Step 2. In addition, the following assumptions are employed in the proposed negotiation: A1. Manufacturer is not allowed to supply more than requested. A2. Demands for all products in all markets are known to only the distributor. A3. Manufacturer is solely responsible for all production-related information (e.g., production
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cost and capacity), while the distributor is solely responsible for all distribution-related information (e.g., transportation cost and inventory carrying cost of distribution centers). A4. Unit production costs (private information and known to the manufacturer only) vary across different locations, periods, and product types. A5. Unit inventory carrying costs at production facilities (private information and known to the manufacturer only) vary across different locations, periods, and product types. A6. Unit inventory carrying costs at distribution centers (private information and known to the distributor only) vary across different locations, periods, and product types A7. Inventory capacities at production facilities (private information and known to the manufacturer only) and vary across different locations and periods. A8. Inventory capacities at distribution centers (private information and known to the distributor only) and vary across different locations and periods. A9. Production capacities (private information and known to the manufacturer only) may vary between different production facilities and different periods. A10. Production lead-time and transportation time between locations are negligible. A11. The internal transportation between the production facilities of the manufacturer is not allowed. Assumption A1 simply states that supplying more than requested is not acceptable. Assumption A2 indicates that the distributor manages information on the market including demand in the distributordriven supply chain. Assumption A3 is to show that the current supply chain is decentralized, and the manufacturer and the distributor are running their own local databases regarding production and distribution, respectively. Assumption A4–A9 are often found in many deterministic planning models. Both the manufacturer and the distributor participating in the same supply chain may have other business partners to whom they may have to dedicate their capacities. Commitments to their business partners may vary in time and in locations and consequently their capacities available for the
current negotiation may vary. Moreover, allowance of changing capacity in time and in location makes the proposed model more general. Assumption A10 indicates production and transportation lead time are assumed to be zero, without loss of generality. The implication of assumption A11 is that excessive capacity of adjacent facilities may not be used. It is often the case that production facilities are considerable miles apart and transportation of products between locations is exclusively done by the distributor. As shortages are reported from any production facility, it is very likely that the distributor increases the order from adjacent production facilities or adjacent periods, which essentially results in moving capacity between production facilities or periods. Before proceeding to a local planning model of each agent, we investigate a centralized supply chain planning (CSCP) model. The CSCP model assumes that all the necessary information can be collected from the overall supply chain and processed freely in the central joint planning department between the manufacturer and the distributor. To formulate the model, the following parameters and decision variables are required: Parameters F D M N P Dkmt pkmt wkft rkft Tkijt hkft h^kdt Hft H^ dt Cft
set of production facilities set of distribution centers set of markets set of all locations (i.e., N ¼ D[F[M) set of products demand for product k in market m in period t market price per one unit of product k sold in market m in period t wholesale price of product k manufactured at production facility f in period t unit production cost of product k at production facility f in period t cost of transporting one unit of product k from location i to location j in period t unit inventory carrying cost of product k in production facility f in period t unit inventory carrying cost of product k in distribution center d in period t inventory capacity in production facility f in period t inventory capacity in distribution center d in period t production capacity in production facility f in period t
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ckf
production capacity required to produce one unit of product k in production facility f storage space required for one unit of product k
vk
Variables xkft
production quantity of product k at production facility f in period t transportation quantity of product k from location i to location j in period t ending inventory level of product k in production facility f in period t ending inventory level of product k in distribution center d in period t
ykijt Ikft I^kdt
Now, the CSCP model is given as follows: Max
X
pkmt
k;t;m
( X X
ykdmt
d
T kijt ykijt
i2N;j2N
k;t
þ
!
X
X
wkft
k;f ;t
X
h^kdt I^kdt
X
d
! ykfdt
X
X
d
wkft
f
X
!) ykfdt
d
rkft xkft þ hkft I kft
I kft þ xkft
X
ykfdt ¼ I kftþ1
8k; f ; t,
(2)
d
I^kdt þ
X
ykfdt
f
X
X
ykdmt ¼ I^kdtþ1
8k; d; t,
(3)
m
ykdmt pDkmt
8k; m; t,
vk I^kdt pH^ dt
8d; t,
(5)
vk I kft pH ft
8f ; t,
(6)
ckf xkft pC ft
8f ; t,
(7)
(4)
d
X
inventory costs in all periods in the given planning horizon; in addition, the central joint planning department knows all such information of the whole distribution network, including future demands in all markets, transportation costs, and inventory capacities in all distribution centers over all periods in the given planning horizon. In fact, the manufacturer would be very reluctant to reveal such information to their business partners, and vice versa. In the above model, the objective function (1) tries to maximize the total profit of the distributor (i.e., sales revenue minus the total cost of the distributor) and the manufacturer (i.e., the payment from the distributor minus the total cost of the manufacturer) simultaneously. Constraints (2) are inventory balance equations for production facilities, while constraints (3) are flow conservation equations between production facilities and markets via distribution centers. Constraints (4) ensure that the distributor may not provide more than market demands. Constraints (5) and (6) are to make sure inventory carrying capacity is not violated. Constraints (7) are to limit the production quantities to be less than or equal to production capacity in each of the production facilities.
k;f ;t
ð1Þ s.t.
3.1. A distribution planning model for DA We propose a linear programming model for the profit maximization of DA. To define a distribution-planning model for DA, we define a new parameter in addition to those introduced before as follows: Parameters C^ ft
aggregate production capacity at production facility f in period t as perceived by DA based on the shortage reported by PA. C^ ft are initially set at N (or a very big number) until PA reports a shortage for product k at production facility f in period t.
k
X k
X
151
k
xkft ; I kft ; I^kdt ; ykijt X0
8k; f ; d; i; j; t.
A distribution planning model of DA is given as follows:tvs
(8)
As mentioned above, the CSCP model is based on the assumption that the central joint planning department knows everything about all of the production facilities, including production capacities, inventory capacities, production costs, and
Max
X k;t;m
pkmt
X
( X X k;t
! ykdmt
d
i2N;j2N
T kijt ykijt þ
X d
h^kdt I^kdt þ
X f
wkft
X
!) ykfdt
d
ð9Þ
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Subject to X X ykfdt ykdmt ¼ I^kdtþ1 I^kdt þ X
8k; d; t,
(10)
m
f
ykdmt pDkmt
8k; m; t,
(11)
vk I^kdt pH^ dt
8d; t,
(12)
those introduced before, we define a new decision variable as follows: Variables supply shortage quantity of product k at production facility f in period t
bkft
d
X k
XX k
ykfdt pC^ ft
8f ; t,
(13)
8k; d; i; j; t.
(14)
d
I^kdt ; ykijt X0
A production planning model of PA for given order quantities Okft (order for product k from production facility f in period t) is given as follows: X X Max ðwkft ðOkft bkft ÞÞ ðrkft xkft þ hkft I kft Þ k;f ;t
The objective function (9) is to maximize the sum of all sales revenue minus transportation costs between and distribution cenP production facilities ters k;t;f ;d T kfdt ykfdt , between distribution centers P and markets k;t;d;m T kdmt ykdmt , the total inventory P
carrying costs at distribution centers ^ ^ k;t;d hkdt I kdt , and the total purchase cost paid
to PA based on the wholesale prices P set prior to the P . Constraints negotiation k;t;f wkft d ykfdt (10)–(12) are from constraints (3)–(5) of the CSCP model. Constraints (13) are to limit aggregate order quantity at a location to be less than or equal to the perceived aggregate production capacity at the location where PA reports shortages. The production capacity required to produce a single unit product varies between products and is unknown to the distributor. As a result, the distributor limits the sum of order quantities of all the products produced at a location as shown in constraints (13). How to set the order quantities with the output of solving the above model will be discussed again in Section 3.3. Note that the value of C^ ft is set based upon the shortage reported by PA, while all the others are the private information of DA. 3.2. A production planning model for PA PA plays a passive role in the proposed agentbased supply chain planning. Responding to the orders submitted by DA, PA will meet the demand only up to the point at which the profit is maximized, and then will report the shortage to DA. We propose a linear programming model for PA by which the manufacturer can maximize the profit for given order quantities. In addition to
k;f ;t
(15) s.t. I kft þ xkft Okft þ bkft ¼ I kftþ1 X vk I kft pH ft 8f ; t,
8k; f ; t,
(16) (17)
k
X
ckf xkft pC ft
8f ; t,
(18)
8k; f ; t.
(19)
k
xkft ; I kft ; bkft X0
The objective function (15) is to maximize the profit of the Pmanufacturer, which is the payment from DA k;f ;t ðwkft ðOkft bkft ÞÞ minus production costs combined P and inventory carrying k;f ;t ðrkft xkft þ hkft I kft Þ . Constraints (16) are inventory balance equations, and they ensure that PA may not supply more than requested, but may refuse to meet the full quantity. Constraints (17) and (18) are from constraints (6) and (7) of the CSCP model. In addition, the proposed planning model of PA can be decomposed into f separate linear programming models. 3.3. Information exchange between DA and PA The proposed negotiation process is designed to allow participating agents to reveal the minimum private business information to their negotiating partners. The minimum information that DA has to forward to PA includes order quantities, while the minimum information that PA has to provide to DA is supply quantities. As per common practice between any buyer and seller, the supply quantities may not exceed the order quantity but there is no practical mechanism to prevent the supplier (or seller) from untruthfully reporting its lack of
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capacity to meet the whole order quantities. Therefore, our negotiation process allows PA to report the shortage, not for the actual lack of production capacity, but for the profit maximization of the manufacturer. In each negotiation round, DA submits to PA order quantities for each product type from each production facility in each period. Such information is a result of solving the problem P given in Eqs. (9)–(14). In the linear program, d ykfdt is the order quantity for product k from production facility f in period t that is to be submitted to PA, and then to be used as Okft in PA. Upon DA’s submission of order quantities, PA builds the production planning problem shown in Eqs. (15)–(19) to find a profit maximizing production plan. The production plan specifies the production quantity of each product at each production facility in each period. The production quantity in the production plan can be less than the corresponding order quantity, and PA has to report the shortage amount (bkft), if any, to DA. With the reported shortage amount received from PA, DA will adjust its perceived aggregate production capacity at production facility f in period t. That is, the new distribution planning problemPof DA in the next negotiation round will assume k ðOkft bkft Þ as an upper bound of the aggregate order quantity ðC^ ft Þ at production facility f in period t. If no shortage is reported at production facility f in period t, DA maintains the same aggregate capacity limit as in the previous negotiation round. Note that the aggregate production capacity at production facility f in period t should remain unlimited as long as PA reports no shortages in all previous rounds at the location.
from PA to DA. Note that the production (distribution) planning problem is feasible for any given order quantities (reported shortages). A trivial feasible solution is to produce (order) 0 units of all products at all locations in all periods regardless of the given order quantities (reported shortages). Also note that the perceived production capacities are monotonically decreasing for all product at all locations in all periods due to the design of the negotiation process (once shortages are reported, DA never places orders requesting more units of any product than the perceived capacity of that particular product at all locations in all periods). When the perceived capacities are all 0, DA should place an order for 0 units of all products at all locations in all periods, in which case PA should report 0 shortages. The perceived capacities are monotonically decreasing as long as PA reports shortages. Otherwise, the negotiation terminates with a feasible supply chain plan that has none-zero production quantity and none-zero distribution quantity. The perceived capacities are monotonically decreasing, and are bounded below (the perceived capacities cannot be negative). In conclusion, the sequence of supply chain plans is guaranteed to be feasible and the sequence of perceived production capacities is monotonically decreasing and bounded below by zero componentwise. Therefore, the negotiation process is bound to terminate with a feasible supply chain plan eventually. Based on the above explanation, a more thorough proof is as follows.
3.4. Analysis
Proof. The feasible supply chain plan requires that both a distribution plan of DA and a production plan of PA are feasible, and that there is no conflict between the order quantity of DA and the supply P quantity of PA (i.e., k bkft ¼ 0 8f ; t ). First, ordering nothing in DA and producing nothing in PA are obvious feasible plans to both the production planning and distribution planning problems. Next, we should show the P proposed negotiation process is convergent in k bkft as zero 8f ; t, as negotiation rounds proceed. Since bkftpOkft is true from the property P of objective functionP(15) and Eq. (16), if k Okft converges then k bkft converges. Also, from
In this section, we will show that the proposed negotiation process should always be terminated with a feasible supply chain plan. Typically, when a centralized planning problem is decomposed into two sub-problems, which are locally optimized iteratively, convergence is often not guaranteed, and negotiation may continue indefinitely. However, the negotiation process proposed in the paper always terminates with feasible plans for DA and PA. A feasible supply chain plan is a collection of a feasible distribution plan for DA and a feasible production plan for PA with no shortage reported
Theorem 1. The proposed negotiation process is guaranteed to terminate with a feasible supply chain plan.
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P ^ Eq. k Okft (i.e., P P(13) if C ft converges then y ) converges. Thus, we can say that if k d kfdt P C^ ft converges then k bkft converges. For example, let us suppose that Oikft ; bikft ; i ^ C ft ; yikfdt indicate the value of each of the variables at the ith negotiation round, respectively. Each negotiation round is composed of DA running first and PA running next. P 1 ^1 From Eq. (13), k Okft pC ft is true after DA running. Also, after PA running, the supply shortage quantity, bkft1 8k; f ; t are delivered to DA, and P P P DA will use k O1kft k b1kft (when k b1kft 40) or P 1 2 C^ ft (when k b1kft ¼ 0) as C^ ft in the second negotiation round. Thus, in the second negotiation round, either P 1 P 2 ^2 P 1 P 1 ^1 k Okft pC ft ¼ k Okft k bkftoC ft (when k bkft 40) P 2 P 2 1 or k Okft pC^ ft ¼ C^ ft (when k b1kft ¼ 0) is true. i Consequently, C^ ft has a non-increasing sequence iþ1 i (i.e., C^ ft pC^ ft ) as negotiation rounds proceed, and i bounded from below. In other words, C^ ft will P i1 decrease whenever k bkft 40 (i.e., there exists at least one bi1 40). kft ^ PAs mentioned above, since C ft converges, also b converges. k kft Until the terminating condition of the negotiation P process (i.e., b ¼ 0 8f ; t ) is satisfied, the k kft negotiation process continues due to the design of i the negotiation process and it means that C^ ft can P i1 decrease continuously whenever k bkft 40. Also, P i the worstPcase, C^ ft ¼ 0 8f ; t makes k Oift ¼ 0, and leads to k bikft ¼ 0 8f ; t. & 4. Computational study In this section, experimental results are presented to demonstrate the performance of the proposed negotiation process in terms of solution quality and computational efficiency. To this end, the total profit of the supply chain at the end of the negotiation is compared with that of the CSCP model, and the number of iterations before the negotiation process converges is investigated for many randomly generated examples. 4.1. Experimental design We randomly generate 40 problem instances in four categories depending on tightness of PA’s capacity (Tm) and DA’s capacity (Td): (Tm,Td)A
{(High, High), (High, Low), (Low, High), (Low, Low)}. Production and distribution plans are heavily influenced by the capacity of PA and DA, and the information exchange between them. In this paper, production capacity is used for PA’s capacity, while the inventory capacity of the distribution center is considered for DA’s capacity. Because production capacity might directly affect whether products can be shipped in each production facility, we used production capacity as PA’s capacity rather than storage capacity. Also, we considered inventory capacity as DA’s capacity. For simplicity of experiments, the inventory carrying capacity at production facilities is set to unlimited. Tightness is defined as a ratio of the sum of demands to the sum of available capacity of all the planning period. Tightness of a problem instance is considered to be low if the ratio is 2/3 ¼ 0.67 (or the total demand is 67% of the total available capacity) and to be high if the ratio is 5/3 ¼ 1.67 (or the total demand is 167% of the total available capacity). It is expected that the number of negotiation rounds is larger as the capacity of DA and PA is more tightly constrained. As for the given parameters for experiments, we generated each of them as follows: demand is randomly generated from U(1500, 3500); two different ranges for the tightness factor are considered: low (0.6–0.8) or high (1.2–1.4). In addition, costs have been determined in the following way. The production cost is determined by rkft ¼ ckftk+ dkftf, where ckft is a random number chosen from U(45,55) to consider the effect of each product, dkft is a random number chosen from U(0,5) to consider the effect of each production facility, k is an index of products, and f is an index of production facilities. This is for generating the production cost in a systematic way: the product with a higher product index may have a higher production cost, while the production facility with a lower facility index may have a lower cost. Using this approach, we can make a distinction between products (e.g., a high valued product and a low valued product) and between facilities (e.g., high labor cost and low labor cost) in generating the production cost. The inventory carrying cost at production facilities is set to the half level of its production cost: hkft ¼ rkft/2. The sum of the inventory carrying cost at a distribution center and the transportation cost from a production facility to a customer zone might be expensive as the production cost of a product.
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category contains 10 problem instances and the profits shown in the table is the average of such 10 instances. As shown in Table 1, average percentile gap for all 40 problem sets is 5.8%. Profit loss due to negotiation process becomes smaller for both PA and DA when PA has shortage in capacity (category (High, High) and (High, Low)), while the profit loss becomes larger when PA has surplus in capacity (category (Low, High) and (Low, Low)). General trend is the loss in profit becomes smaller as PA has tighter capacity. If PA has tighter capacity, PA has no many alternative ways to generate a production plan and cannot help choosing a restricted solution of production part that may be equivalent to the production plan of the CSCP model. Such observation is confirmed by statistical analysis as summarized in Table 2. It is determined by statistical test that neither tightness of distributor’s capacity nor the product of tightness of manufacturer’s capacity and distributor’s capacity make any significant difference in the loss of profit due to the negotiation process. It is only tightness of manufacturer’s capacity that influences the quality of the final solution of the negotiation process as indicated in Table 2. Table 3 presents the average number of negotiation rounds in each category. The average number of rounds in all 40 problem instances is 21.45. It tends to take more rounds as manufacturer has tight capacity. This is again confirmed by statistical tests as shown in Table 4. If PA has enough capacity to generate a production plan with the requested order quantity by DA, then PA can make a proper production plan without reporting any shortage against the request of DA in a few negotiation rounds. Otherwise, DA
The inventory carrying cost at a distribution center is approximately set to P the half level of the production cost: h^kdt ¼ ð f rkft =2f Þ Uð0:8; 1:2Þ. The transportation cost between locations is approximately set to the quarter level P of the production cost as follows: T ¼ kfdt f rkft =4f P Uð0:8; 1:2Þ and T kdmt ¼ f rkft = 4f Uð0:8; 1:2Þ. Finally, the distributor’s sales price and the whole sale price of the manufacturer for one unit of product are set properly in consideration of the total production or distribution cost, respectively. For example, pkmt is chosen from U(800,850) and wkft is chosen from U(400,450). The gap between maximum profits from the CSCP model and from the final round of negotiation rounds will be compared to demonstrate the quality of solution, and the number of negotiation rounds will be used to show the computational performance of the negotiation process. In each of 40 problem instances, there are 4 product types, 10 production facilities, 5 distribution centers, 10 markets, and 12 planning periods. The negotiation process and the CSCP model are implemented using ILOG OPL Studio version 3.1 and MINITAB version 12.1 is used for statistical analysis. 4.2. Experimental results and analysis Table 1 shows profits achieved using the negotiation process and the CSCP model for 40 problem instances. The first column shows categories under which 40 problem instances are generated, and the rest of table shows (1) profits for the manufacturer and the distributor and (2) gap between profits for the manufacturer and the distributor from negotiation process and from the CSCP model. Each
Table 1 Solution quality comparison between centralized and decentralized problems Tm, Td
Profit of PA Ca
High, High High, Low Low, High Low, Low Average a
380, 382, 546, 543, 463,
Profit of DA Db
634 973 494 610 428
359, 360, 490, 495, 426,
643 763 426 623 614
The solution of centralized problem. The solution of the negotiation. c The % deviation. b
Gapc
C
5.5 5.8 10.3 8.8 7.6
346, 348, 516, 513, 431,
Total profit D
291 147 062 871 093
337, 337, 488, 489, 413,
465 182 240 704 148
Gap
C
D
2.5 3.1 5.4 4.7 3.9
726, 925 731, 121 1062, 556 1057, 481 894, 521
697, 697, 978, 985, 839,
Gap 108 944 666 327 761
4.1 4.5 7.9 6.8 5.8
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Table 2 The ANOVA results on the solution quality problem
Table 4 The ANOVA results on the computational burden problem
Source
DFa
SSb
AdjSSc
AdjMSd
Fe
Pf
Source
DFa
SSb
AdjSSc
AdjMSd
Fe
Pf
Tm Td Tm, Td Error
1 1 1 36
92.598 0.992 5.580 110.048
92.598 0.992 5.580 110.048
92.598 0.992 5.580 3.057
30.29 0.32 1.83
0.000g 0.572 0.185
Tm Td Tm, Td Error
1 1 1 36
435.60 0.10 25.60 314.60
435.60 0.10 25.60 314.60
435.60 0.10 25.60 8.74
49.85 0.01 2.93
0.000g 0.915 0.096
Total
39
209.219
Total
39
775.90
a
a
b
b
Degree of freedom. Sum of squares. c Adjusted sum of squares. d Adjusted means square. e Computed F-value. f Computed P-value. g The result is significant to a significant level of 0.05.
Degree of freedom. Sum of squares. c Adjusted sum of squares. d Adjusted means square. e Computed F-value. f Computed P-value. g The result is significant to a significant level of 0.05.
Table 3 The experimental results on the computational burden problem Tm
Td
No of iterations
High High Low Low
High Low High Low
23.9 25.6 18.9 17.4
may try to reduce its order quantity in order not to make any shortage in PA, and it requires more negotiation rounds. Tables 3 and 4 repeat the same observation that it took statistically less rounds of negotiation to reach the final plans for the manufacturer and the distributor as the manufacturer has surplus in capacity. To show the convergence of the proposed negotiation process, a graphical illustration of the negotiation process is given in Fig. 1, where unmet demands reported by PA, requested order quantities by DA, and profits of PA and DA in each negotiation round are plotted for one of the 10 problem instances of category (High, High). Fig. 1 is prepared using the following experimental result given in Table 5. As negotiation rounds proceed, both total order quantity and the profit of DA are decreasing, whereas the profit of PA is increasing as shown in Fig. 1(a). This is because the initial order quantity of DA has adjusted accordingly by the available supply quantity of PA throughout the negotiation rounds. In other words, the initial ideal distribution plan of DA, assuming the infinite product supply
Fig. 1. Example graphs on the convergence of the negotiation process, (a) convergence of the profits of DA and PA and (b) convergence of production and distribution plans through negotiation.
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Table 5 The experimental result for the example graphs Iteration
DA profit
PA profit
Supply shortage
Order from DA
Supply from PA
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
528,660 519,580 520,417 520,473 519,018 516,636 518,379 516,485 515,328 514,824 514,189 510,710 500,140 504,809 486,250 456,781 438,174 415,537 338,593
38,760 166,829 181,976 178,081 210,633 254,971 221,865 247,927 250,801 250,670 275,205 268,755 304,693 290,545 309,449 322,596 325,952 333,815 360,288
9080 6932 6560 6677 6075 5245 5925 5375 5252 4896 4843 4654 4266 4555 4280 3443 3050 2392 0
9656 9656 9656 9656 9656 9656 9656 9656 9656 9656 9656 9656 9656 9656 9656 9028 8683 8025 5633
576 2724 3096 2979 3581 4411 3731 4281 4404 4760 4813 5002 5390 5101 5376 5585 5633 5633 5633
from PA, has changed into a more realistic one as negotiation rounds proceed. In addition, as shown in Fig. 1(b), there exist no total unmet demands reported by PA at the end of the negotiation process, and it means that the total order quantity of DA is identical with the total possible supply quantity of PA properly.
For future research, the extended negotiation models considering vendors are needed. Also the implementation using real data in various distributor-driven supply chains should be followed to check the network traffic and extra cost problems.
5. Conclusions
Amid, A., Ghodsypour, S.H., O’Brien, C., 2006. Fuzzy multiobjective linear model for supplier selection in a supply chain. International Journal of Production Economics 104 (2), 394–407. Barbarosog˘lu, G., O¨zgu¨r, D., 1999. Hierarchical design of an integrated production and 2-echelon distribution system. European Journal of Operational Research 118, 464–484. Dhaenens-Flipo, C., Finke, G., 2001. An integrated model for an industrial production–distribution problem. IIE Transactions 33, 705–715. Erengu¨c- , S.S., Simpson, N.C., Vakharia, A.J., 1999. Integrated production/distribution planning in supply chains: An invited review. European Journal of Operational Research 115, 219–236. Ertogral, K., Wu, S.D., 2000. Auction-theoretic coordination of production planning in the supply chain. IIE Transactions 32, 931–940. Fisher, M.L., 1997. What is the right supply chain for your product? Harvard Business Review 75 (2), 105–116. Gattorna, J., 1998. Strategic Supply Chain Alignment: Best Practices in Supply Chain Management. Gower Pub Co. Goetschalckx, M., Vidal, C.J., Dogan, K., 2002. Modeling and design of global logistics systems: A review of integrated strategic and tactical models and design algorithms. European Journal of Operational Research 143, 1–18.
In this paper, we propose a negotiation process that can be easily implemented in an information system connecting a manufacturer and a distributor. Advantages of the proposed negotiation process include: (1) only minimum information is shared between a distributor and a manufacturer and (2) negotiation process is guaranteed to terminate with a feasible supply chain plan, which has been empirically shown to be close to optimal plan. Numerical studies show that the distribution and production plans at the end of negotiation are on average only 5.8% below the optimal solution of centralized planning based on full information sharing. The proposed mechanism can be used not only as a negotiation framework between companies who are reluctant to share their business information but also a decomposition scheme for a complex integrated planning problem.
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