A Negotiation Protocol to Improve Planning Coordination in Transport-driven Supply Chains

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 Journal of Manufacturing Systems 38 (2016) 13–26

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 Journal of Manufacturing of  Manufacturing Systems  j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / j m a n s y s

Technical Paper

A negotiation protocol to improve planning coordination in transport-driven supply chains Zhen-Zhen Jia Zhen-Zhen Jia a,b ,  Jean-Christophe Deschamps a,b , Rémy Dupas a,b,∗ a b

Univ. Univ. Bordea Bordeaux, ux, IMS, IMS, UMR5218, UMR 5218, F-33405 F-33405 Talence, Talence, France France CNRS, CNRS, IMS, IMS, UMR 5218, 5218, F-3340 F-33405 5 Talenc Talence, e, France France

a r t i c l e

i n f o

 Article history: Receiv Received ed 16 Januar January y 2015 2015 Receiv Received ed in revise revised d form form 14 Septem September ber 2015 2015 Accept Accepted ed 18 Octobe Octoberr 2015 2015 Keywords: Production Distribution Planning Coordination Negotiation

a b s t r a c t

This paper addresses the coordination problem of activities of activities between manufacturers and transport operators (third party of tactical planning. This critical problem is encountered encountered in many third party logistics) in the context of tactical Forecasting  and Replenishm Replenishment  ent  supply chains. Collaborative solutions, such as the the Collaborative Planning, Forecasting and (CPRF) model, are not fully automatized and remain poorly suited for enhancing the relation between manufacturers and transport operators. Furthermore, centralized planning isnot suitable in keeping confidential the objectives of each of  each partner of the of  the same supply chain. Therefore, this work aims to develop a decentralized planning approach based on a negoti negotiati ation on protocol. Our approach tries to reach a “win–w “win–win” in” planning solution and to give some decisional flexibility to transport operators. This protocol is founde founded d on an incentive mechanism that can be used by transport operators to progressively persuade manufacturers to accept a pick pickup up plan. This study study is focused on the case case of one of one manufacturer and one transport operator. The key determinant determinantss of the of the coordination protocol and a set of planning of  planning models based on linear programming are presented here, followed by the the design of  the experiments used to identify the factors affecting the overall performance of  each partner. The results demonstrate that it is possible to obtain plans that satisfy the manufacturer (i.e., the client of the of  the transport operator) while increasing profit for the transport operator. This is in favor of the of  the application of these of  these principles to the coordination of multiple of  multiple transport operators. © 2015 2015 The Society of Manufacturing of  Manufacturing Engineers. Published by Elsevier Elsevier Ltd. All rights rights reserved.

1. Intr Introd oduc ucti tion on

Thir Third d part party y logi logist stic icss prov provid ider erss (3PL (3PL)) are are firms firms in char charge ge of exeexecuti cuting ng a more more or less less sign signifi ifica cant nt part part of logi logist stic icss acti activi viti ties es.. Usin Using g their their servic services es genera generally lly provid provides es means means for compan companies ies to subcon subcon-tract tract storage storage and transpor transportt activiti activities es to third third parties. parties. Neverthele Nevertheless, ss, it raisesthe raisesthe issue issue of howthe relati relations onshipbetw hipbetweenthir eenthird d partie partiess and distribut distribution ion activiti activities es could could be improved improved when they are performed performed by indepe independ ndent ent indust industria riall partn partners ers,, who who usuall usually y aim to keep keep conconfiden fidenti tial al thei theirr own own data data and and know knowle ledg dge. e. The The sync synchr hron oniz izat atio ion n of  distribut distributed ed operation operationss primarilyoccursthroughaggreg primarilyoccursthroughaggregatedtactic atedtactical al informat information ion sharing,thus sharing,thus giving giving themaster planningfunctio planningfunction n great great import importanc ance e for insuri insuring ng an effect effective ive coord coordina inatio tion n of supply supply-ch -chain ain partners. The The pres presen entt work work focu focuse sess on the the coll collab abor orat ativ ive e rela relati tion onsh ship ip between between manufact manufacturersand urersand third third parties parties providin providing g transportactivtransportactiv-

∗ Corr Corres espo pond ndin ing g auth author or at: at: Univ. Univ. Bord Bordea eaux ux,, IMS, IMS, UMR  UMR  5218, 5218, F-3340 F-33405 5 Talenc Talence, e, France. France. Tel.: +33 553774057. 553774057. E-mail address: address: [email protected] (R. Dupas). Dupas).

itie ities, s, also also call called ed tran transp spor ortt oper operat ator ors. s. This This rela relati tion on has has two two main main singul singulari aritie tiess in compar compariso ison n with with those those that that link link produc productio tion n facilfaciliti ities in a supp supply ly netw etwork. rk. Fir First, st, the tran transp spo ort oper operat ator or’’s pro profit marg margin inss are are much much lowe lowerr than than the the reve revenu nue e of manu manufa fact ctur urer erss (i.e (i.e., ., clients1 of the the tran transp spor ortt oper operat ator or)) gene genera rate ted d by prod produc uctt sale sales. s. Tran Transp spor ortt oper operat ator orss also also have have diffi difficu cult ltie iess fore foreca cast stin ing g acti activi viti ties es because because their their various various clients clients (i.e., (i.e., transpor transportt orders) orders) require require multiple multiple and differ different ent transp transport ort servic services. es. In such such cases cases,, the the transp transport ortati ation on acti activi viti ties es of 3PLs 3PLs are are plan planne ned d by manu manufa fact ctur urer ers, s, base based d on the the use use of specifi specificc tools tools such such as DRP (dist (distrib ributi ution on requir requireme ement nt plann planning ing), ), when when they they intend intend to create create a longlong-ter term m clima climate te of confid confidenc ence e with with their their client clients. s. If these these tools tools provid provide e useful useful servic services es for compa companie niess in facilitati facilitating ng informati information on and materialmaterial-flow flow control, control, from consumer consumer dema demand nd to raw raw mate materi rial al supp supply ly,, thei theirr impl implem emen enta tati tion on requ requir ires es inform informati ation on sharin sharing. g. Howeve However, r, these these tools tools are rarely rarely implem implement ented ed by 3PLs 3PLs with with lowtranspo lowtransport rt capac capacity(i.e. ity(i.e.,, 3PLs 3PLs that that owna small small fleet fleet of vehi vehicl cles es:: less less than than 5). 5). Thei Theirr weak weak leve levell of comp comput uter eriz izat atio ion n and and

1

The follow following ing notati notations ons are adopte adopted: d: ‘ Client ’ refe refers rs to a custo custome merr of tran transp spor ortt servic services,and es,and ‘ customer ’ refe refers rs to a final final cust custom omer er..

http://dx.doi.org/10.1016/j.jmsy.2015.10.003 0278-6 0278-6125 125/© /© 2015 2015 TheSociety TheSociety of Manufa Manufactu cturin ring g Engine Engineers ers.. Publis Publishedby hedby Elsevi Elsevier er Ltd. Ltd. All rightsreser rightsreserved ved..

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 Z.-Z. Jia et al. / Journal of Manufacturing Systems 38 (2016) 13–26

the lack of finance to accessto theElectronicDataInterchange (EDI) usually reducethe usefulness of the DRP. Therefore, thedifficulty is the coordination of transport operations and the balance between transport resources and needs. The main objective of this work consists of developing an approach to coordinate transportation planning with production planning models. More precisely, this research aims to study the problem of production and transportation in the 3PL environment under a decentralized coordination mode [20]. This paper is organized as follows. Section 2 proposes a literature review, and Section 3 presents the problem studied. Section 4 proposes the description of mathematical models and the negotiationprotocol. Section 5 gives the numerical results for performance evaluation. Section 6 summarizes conclusions and future research directions. 2. Literature review 

Collaborative planning in supply chains has drawn strong interest for many years [1,27]. First, we present an overall view of  collaborative supply-chainplanning approaches. Then,we focus on the relation between distribution and production.  2.1. Supply chain collaborative planning 

Although an exhaustive literature survey of this field is beyond the scope ofthispaper, a classification ofthe mainparadigmsfor the planning coordination of partners is presented. The collaborative approaches are broadly composed of two main groups, presented below: - Centralized approaches are based on a full model of partners that supports the decision making for all supply-chain participants [4]. They rely on the hypothesis of complete information sharing. These models are then solved using either exact approaches, based on mathematical programming, such as decomposition approaches [5], or approximated approaches, such as heuristics or metaheuristics. Also included in this group are hierarchical planning methods, which aim to address the centralized problem throughits decompositioninto a hierarchy of interdependent sub-problems. These centralized approaches are often difficult to usein practice,primarily because companiesdo notwant to share their confidential data. - Decentralized or distributed approaches consider fully independent partners. A comprehensive classification of decentralized coordination methods in supply-chain planning can be found in Taghipour and Frayret [29]. These approaches can take various forms, such as information exchange, request for actions or more advanced cooperation. For instance, supply contracts that link customers with suppliers currently represent an important influence on the production and delivery of final products. Amrani et al. [3] showed that supply commitments, such as frozen horizon (i.e., ordered quantities are considered fixed during this time interval andcannotbe modified between two planningdecisions) or flexibility rate (i.e., customers can change the ordered quantities within a certain limit outside of the frozen horizon), as stipulated in this contract, can be a powerful way to manage and plan the product flow in a supply chain. - Among moreadvanced cooperation forms, negotiation is a central paradigm whose definition varies with authors. It can be defined as an exchange between two or more partners with a view to obtain an agreement[16]. Automated negotiationapproaches can be inexhaustively classified into three main following categories: o Heuristic approaches: Partners iteratively adjust their local initial plan according to the capabilities of other partners. One of 

the first approaches was proposed by Dudek [10], who developed a negotiation-based scheme. It combines mathematical programmingfor theoptimal planningof each party so that the two parties’ orders/supply plans can be synchronized for planning in the supply chain. Taghipour and Frayret [30] proposed an extension of this model to address the dynamic changes in the supply-chain environment that affect planning. In the same lineage, Albrecht and Stadtler [2] f o rmulated a theoretical scheme for coordinating decentralized parties that intends to encompass all functionalities of supply chains. Ben Yahia et al. [6] proposed a negotiation mechanism for collaborative planning within a supply chain that is based on fuzzy rules. Their approach is limited to cooperation between manufacturers, considering onlyproduction planningwithout distribution, supplier or retailers. These approaches are a practical and easy way to implement negotiations between partners, though they are not mathematicallyproven; for instance, theirconvergence toward an agreement is not guaranteed. o Game theory-based approaches: The best decision made by a given partner in a supply chain is found takinginto account the possible decisions of others. One of the first studies to apply coordination and negotiation inside a supply chain was proposed by Cachon and Netessine [8], who mentioned that two main types of games-cooperative and non-cooperative (i.e., a competitive game)-can be used. Game theory provides very powerful strategies. However, their implementation to solve a practical problem, such as planning coordination, remains a delicate topic due to their reliance on the hypothesis of perfect rationality. o Multi-agent system-based approaches: Developed in artificial intelligence problem solving, this paradigm has been intensively applied to supply-chain collaboration. It is particularly suited to automated negotiation due to the implementation of decision mechanisms such as auctions or biding. Hernández et al. [17] proposed a negotiation-based mechanism that is supported by a multi-agent system and focuses on the collaboration of demand, production and replenishment planning, combined with the use of standard planning methods, such as the material requirement system (MRP) method. Fischer et al. [15] proposed a methodology and a multi-agent tool for the simulation of the transportation domain. Their negotiation-based decentralized planning approach is applied to the scheduling of the transportation orders among an agent society consisting of shipping companies and their trucks. The multi-agent paradigm is a central and powerful paradigm. Its application for collaborative planning is limited only by the methodology used to build the model and the decision mechanisms integrated in the agents. This previous classification has a practical interestto give a simplified view of the domain. However, it must be noted that many approaches are developed at the cross between each category. For instance, the multi-agent paradigm can also be used to implement some game-theory principles.  2.2. Production and distribution planning 

Reviews[12,13,23] haveindicated thatmost studies focus on the formulationof an integratedproduction- and distribution-planning model. Barbarosoglu and Ozgur [5] developed a mixed-integer linear programming model solved by Lagrangian and heuristic relaxation techniques to transform the problem into a hierarchical two-stage model: one for production planning and another for transportation planning. Dhaenens-Flipo and Finke [9] developed a mixed-integer linear programming-based planning model in a multi-firm, multi-product and multi-period environment in

 Z.-Z. Jia et al. / Journal of Manufacturing Systems 38 (2016) 13–26

15

Fig. 1. Problem context.

which the supply chain is modeled as a flow network. Park [24] proposed an integrated transport and production planning model that uses mixed-integer linear programming in a multi-plant, multi-retailer, multi-productand multi-period environment.Selim et al. [25] proposed a fuzzy multi-objective linear programming model that incorporates uncertainty of the individual decision makers in charge of manufacturing plants or distribution centers. Song et al. [26] studied a problem of a third party logistics (3PL) provider that coordinates shipments between suppliers and customers through a consolidation center in a distribution network. The problem is formulated as a nonlinear optimization problem and solved with a Lagrangian method. Bonfill et al. [7] proposed a framework to address the interrelated production and transport scheduling problems that aims to support the coordination of production and transport activities to manage the inventory profiles and material flows between sites. Two approaches are compared in this study: an integrated model and a solving strategy using sequentially production and scheduling models. Jhaa and Shankerb [19] studied the coupling of an inventory problem with a vehicle-routing problem with transportation cost in a single-vendor multi-buyer supply chain. They proposed an iterative approach for solving the integrated problem to optimality. Zamarripa et al. [32] proposed an integrated multi-product and multi-echelon tactical planning model for the coordination of partnersinsidea supply chain. The linear programmingmodel proposed encompasses the production–distribution relation inside a supply chain of chemicalproducts. Theseauthorsalso comparedtheir integrated model with a competitive game theory-based approach, which enabled them to find the best scenario among several alternatives [31]. As far as full decentralized approaches are concerned, Jung et al. [21,22] proposed a negotiation process that aimed to find a contract for a distributor and a manufacturer in a distributordriven supply chain. Nevertheless, the negotiation principle used, which is based on the opportunity given to the manufacturer to report shortages, offers little flexibility because it does not take into account prices, auctions or the availability of extra resources. Taghipour and Frayret [28] proposed a decentralized coordination mechanism that is based on explicit negotiation using mathematical programming and involves two enterprises within the supply chains.

Indeed, the decentralized-based cooperation of independent production and distribution partners focused on mid-term tactical planning has received limited attention. In this paper, we propose a decentralized approach for distribution and production collaborationbased on negotiation. A heuristic decentralized approach is chosen due to the previously mentioned advantages. This approach is founded on the negotiation-based collaborative planning process, which was initially proposed by Dudek [10] and refined by Dudek and Stadtler [11]. Its principle consists of exchanging only non-confidential data between partners and searching for new compromise solutions through an iterative improvement process. In this process, each partner uses a so-called “preferred plan” as a target plan representing its own interest. This process also includes the possibility for customers to claim compensation associated with a compromise proposal. Note that the process proposed by Dudek et al. is dedicated to the relation between suppliers and customers. Our negotiation approach, detailed below, extends their collaborative planning process by considering explicitly the transport operator as a collaborative partner. 3. Problem definition

This work falls within the general objective of studying the complex relationships that link manufacturers with their multiple transport operators. Our contribution focuses on the study of the relationship between one manufacturer (i.e., a client of transport services) and one transport operator (Fig. 1). The manufacturer makes different products to satisfy the demands of various customers and has a limited production capacity and a limited finished-product storage capacity. The transport operator manages a fleet of trucks that have to pick up products from manufacturers and deliver them to customers before returning to their initial location. Each partner is in charge of planning its own activities and trying to maximize its profit while taking into account the limitations of others, which emerge from the plans exchanged during the negotiation. Inthis context, we aimto propose a negotiationprotocolto align the activities of two cooperating partners (manufacturerand transport operator) with the aim to give more flexibility to the transport

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operator. This requires that the planningactivities of both partners be simulated and that the protocol be proposed. The current study is indeed supported by a numerical simulation, basedon a linear programmingapproach, andan experimental approach, based on the design of experiments (DOE), to proceed in a structured way and to reduce the number of experiments. Thus, we aim to extract from this analysis the main dominant factors that affect the performance of both partners before extending the analysis to more complex situations. Our study is based on the following hypothesis regarding the three partners: Customers:

– Customers accept that the quantities of delivered products can have small deviations from the initial ordered quantities (late or early deliveries). Nonetheless, they negotiate penalty clauses when drafting the frame agreement between them and manufacturers. Manufacturer :

– The manufacturer produces different products to satisfy the demands of various customers. The demands of products from all of these customers are known over a given non-rolling planning horizon. The manufacturer knows the transportation prices and the delivery lead time required to serve the customers. – Inventory levels of rawmaterials are considered infinite because we focus only on the interaction between the manufacturer and the transport operator. The replenishment decisions of materials are not taken into account in this study. – If the manufacturer cannot supply the right product quantity at the right time, as requested by customers,  financial penalties arise from these deviations, as defined in the frame agreement, and reduce the partner’s profit. These deviations are due to limited capacity constraints in production or transport and lead to advanced delivery to customers or delayed transportation. Transport operator :

– This partner has a limited operational capacity but has recourse to subcontracting when customer demand requires a number of  trucks over its own capacity. The principle of a standard cost, whose value is independent of the use of subcontracting, is retained to cover all transport costs. Recourse to the outsourcing and negotiation of transport arrangements is the sole responsibility of the transport operator. – To try to maximize its profit, the transport operator has the opportunity to propose a pickup and transport plan with small deviations fromthe delivery planrequestedby the manufacturer. Any deviation causes the transport operator to pay penalties to the manufacturers affected by this change; those penalty clauses are also stipulated in a specific agreement negotiated between transport operators and manufacturers. These penalties, which are called  planning change penalties, differ from the  financial  penalties previously defined. – Theprovidedtransport service is addressedonly in a globalpoint of view; the warehouse storage problems that arise in distribution activities are not studied. The transportservice is considered a whole activity, including all service times related to the movementof freight, i.e.,the dispatching and consolidation of material flows, storage,handling andmoving. Thisactivity is characterized by a determined delivery lead time.

4. Negotiation framework and modeling 

We consider a manufacturer and a 3PL that agreed to negotiate to finda profit-maximizingsupply-chainplanning solutionwithout sharing any confidential information. The negotiation is based on the main following characteristics: – The partnership relation already exists. The producer and transport operator signed a global contract to define the framework of collaboration, which details all necessary information, such as price, global quantity for a long period, each partner’s responsibility and penalties. The demand quantities for more detailed time period (e.g., delivery plan, pickup plan) are not specified in the contract but are negotiated during the collaborative process. Therefore, negotiation takes place within the limits of this contract. – The negotiation between partners—manufacturer and logistic service provider—is not supported by a DRP but is based on the transmission of distribution plans so that the 3PL can have a forecast over several days of the load induced by the clients of  transport services (i.e., manufacturer). Moreover, this negotiation aims to be a “win–win” relationship for the two parties: The required solution must aid the 3PL in maximizing its own profit without significantlydecreasing the service rateof the final customers. The presentation of the negotiation framework is composed of  three sections. First, the overall description of the negotiation protocol is provided. The last three sections, respectively, focus on the planning models used inside the negotiation protocol, the key determinants and the flow-control logic of this protocol. 4.1. Overall description of the negotiation protocol

The negotiation protocol can be described as follows. The manufacturer is the first to plan its production under limited-capacity constraints and to attempt to generate a delivery plan according to the customer’s demands, which is sent to the 3PL (Fig. 2). Through the generation of two different plans (i.e., the best profit and the best service plans), the transport operator evaluates whether its own profit shouldbe increasedby proposinga pick-up plan distinct from the delivery plan requested by the manufacturer. According its own interest, the transport operator has to payplanningchange penalties in cases of late or early deliveries and canalso offer financial compensation to convince the manufacturer to accept the new plan. When a pickup plan received by the manufacturer completely satisfies the delivery constraints of the production–planning process, a converged solution is reached. Otherwise, the manufacturer rejects thepickup plan proposed by the transportoperator, considering that its own profit is too low or not all production constraints can be respected according to the received plan. The manufacturer refuses to modify its initial delivery plan, so the transport operator needs to make a new pickup plan, called the relaxed pickup plan, by relaxing some economic constraints. Itmay happen thatthe transportoperator cannot relaxanymore, and no proposed pickup plan has ever been considered acceptable by the manufacturer. In this case, the latter must adapt his production to the constraints expressed by the transport operator to generate a relaxed delivery plan. Consequently, a new round of  negotiation begins, based on the same process, until a compromise solution is found. The transport operator progressively reduces its economic standard in terms of profit, intending to send an acceptable pickup plan to the manufacturer. Note that our approach is based on the definition of an original negotiation protocol between the manufacturer and the transport

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 Z.-Z. Jia et al. / Journal of Manufacturing Systems 38 (2016) 13–26

operator.The main feature of this protocol is the degree of freedom given to the transport operator. The models presented below are standardbut aredevelopedto simulate thedecisionmakingprocess of each partner and the global negotiation protocol. 4.2. Planning models

to the customer, which provides the producer certain flexibility to supply products. Constraint (A.7) indicates that delivery quantities cannot exceed customer demand. Constraint (A.8) is a non-negativity constraint.

        

Max

(SP  p,j  · l p,j,t ) −

 p

The protocol definition is based on two sets of three linear programmingmodelsthat characterizethe planningprocessof thetwo partners. These two sets are successively presented below.



 p

 j

(CS  p  · i p,t ) −



 p

4.2.1. Models simulating the planning activities of the manufacturer  The planning activities of the manufacturer are carried out by the following models:

(CP  p  ·  f  p,t )





(CR p,j  · b p,j,t  + CE  p,j  · e p,j,t )

 p



 j

(TP  j  · v  p  · l p,j,t )



 p



 

(A.1)

 j

s.t. – The “best production profit” (BPP) model describes the planning process that leads to an initial production and delivery plan and maximizes the manufacturer’s profit. – The “Production Profit Evaluation” (PPE) model estimates the admissibility of the pickup plan sent by the 3PL and calculates the expected profit in cases of acceptance. – The “Relaxed Production Profit” (RPP) model proposes to adapt the production plan to pick up constraints imposed by the 3PL  to converge toward a consensual planning solution that limits decreases in the manufacturer’s profit.

i p,t  = i p,t −1  +  f  p,t −DP  p −

(A.2)

l p,j,t  ∀ p ∈ P, ∀t  ∈ T.

 j

l p,j,t  + b p,j,t  − e p,j,t  = d p,j,t +DT  + b p,j,t −1  − e p,j,t −1  j

∀ p ∈ P, ∀t  ∈ T, ∀ j ∈  J.

(A.3)

DP  p

   u p  ·

 f  p,t − +1

≤ Pcapt 

∀t  ∈ T.

 

(A.4)

 =1

 p

Below, we introduce the notations used before formulating the mathematical models. Sets T  P   J 

Set of periods Set of products Sets of customers

Indices t 

Index of planning period

Parameters DT i DP  p SP  p,i CS  p CP  p CR p, j  

 p

Index of products

CE  p, j

 j

Index of customers

TP  j   vu p v p   d pjt  Emax p, j Pcapt  Icapt  MinP 

Decision variables b p, j,t  e p, j,t   f  p,t  i p,t  l p, j,t  P  b p,j,t  P  e p,j,t 

   

P  b control p,j,t  P  e control p,j,t 

Late supplied quantity of product  p for customer j at period t Early supplied quantity of product  p for customer j at period t Production quantity of product  p launched in production at period t Inventory level of product  p at the end ofperiod t Delivery quantity of product  p to be launched in transportation to customer j at period t  Max(0, qq p, j,t  − l p, j,t ) Max(0, l p, j,t  − qq p, j,t )

 

Transportation lead time to customer  j Production lead time forproduct  p Selling price of product  p to customer j Unitary inventorycost of product  p per period Unitary production cost of product  p Unitarylate supply cost of product  p per period (financial penalty) Unitary early supply cost of product p per period (financial penalty) Transportation price/ton to customer  j Quantity of resource required to produce a product  p Weight or volumeof product  p Demand of product  p from customer j at period t  Upper bound forallowed early supplied quantity Production capacity at period t  Inventory capacity at period t  Relaxation lower profit bound of manufacturer Very large integer Pickup quantity of product  p that the transport operator decides to transport to customer  j at period t 

M  qq p, j,t 

P  Binary variable equal to1 if b p,j,t   > 0, otherwise 0 P   > 0, otherwise 0 Binary variable equal to1 if e p,j,t 

Best Production Profit model (BPP)



(v  p  · i p,t ) ≤ Icapt  ∀t  ∈ T.

(A.5)

 p

The BPP model formalizes the manufacturer decisions related to production, inventory and delivery. The objective function (A.1) maximizes the profit resultingfrom the revenue from selling products (SP), the production cost (CP), the inventory cost (CS) and the financial penalties for late and early deliveries (CR and CE). Constraint (A.2) is the inventory balance equation. Constraint (A.3) expresses the difference between the required and the supplied quantities, taking into account the transportation lead time and possible late and early deliveries. Constraints (A.4) and (A.5) guarantee production loads with respect to production and inventory capacities. Constraint (A.6) limits the early supplied quantities

e p,j,t  ≤ Emax p,j

  l p,j,t  ≤



∀ p ∈ P, ∀t  ∈ T, ∀ j ∈  J.

d p,j,t +DT  j

∀ p ∈ P, ∀ j ∈  J.

(A.6) (A.7)



i p,t , b p,j,t , e p,j,t , f  p,t , l p,j,t  ≥ 0 ∀ p ∈ P, ∀t  ∈ T, ∀ j ∈  J.

(A.8)

Production Profit Evaluation model (PPE)

The PPE model is a variant of the BPP model. The parameters and decision variables of EPP are identical to those of the BPP model. Constraints (A.2)–(A.8) f rom the BPP model are included

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 Z.-Z. Jia et al. / Journal of Manufacturing Systems 38 (2016) 13–26  Table A.1 Customer’s demands profile.

Product 1 required resource/unit

Demand (unit) d p, j,t 

Period

Customer 1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

0 0 130 150 170 130 170 179 200 170 150 200 230 201 150 160 130 121 150 169 100 151

0 0 150 130 170 200 170 120 150 170 190 200 150 170 100 130 170 150 150 170 150 120

Total

3211

3110

Customer 2

Product 2 required resource/unit

Demand (unit) d p, j,t 

Period

Customer 1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

L3

1.01

0.96

0.75

Pcapt  931

980

1254

 Table A.3 Selling prices. R SELLin

L1

L2

L3

0.5

1

2

SP  p,2

270 360

135 180

3643

88,000

 Appendix A. Input data and models parameters

SP  p,1

Product 1 Product 2

4000 4000 4000 4000 4000 4000 4000 4000 4000 4000 4000 4000 4000 4000 4000 4000 4000 4000 4000 4000 4000 4000

needs to study the problem of the splittingand the assignment of  a global delivery request to each individual transport operator. • Regarding the planning method related to the manufacturer and the transportoperator, it would be necessaryto integratea rolling planninghorizon, which is commonlyused in industrial practices. Indeed, the rolling planning mechanism is effective for coping with the uncertainty of the market, which causes customers to change their orders. • Finally, concerning the negotiation, it would be useful to take advantage of some of the principles from cooperative game theory to improve the efficiency of our protocol. Our ongoing research aims to test the relevance of using the Shapley value in defining a win–win relationship between a manufacturer and many transport operators.

R C APin  

L2

0 0 200 210 170 200 150 120 200 190 210 220 160 220 130 200 200 190 200 133 150 190

2605

 Table A.2 Production capacities.

L1

Customer 2

0 0 110 120 110 130 130 108 140 180 140 110 100 130 105 123 125 132 125 155 200 132

Total

Inventory Capacity (ton) Icapt 

 

270 360

540 720

See Tables A.1–A.6.

 Table A.4 Unitary late/early supply and pickup penalties costs. R L ATin  

L1

L2

L3

0.5

1

2

BC  p, j

Product 1 Product 2

CR p, j

Customer 1

Customer 2

Customer 1

Customer 2

Customer 1

Customer 2

40 50

45 55

20 25

22.5 27.5

40 50

45 55

Customer 1 80 100

Customer 2 90 110

R EARin

L1

L2

L3

0.5

1

2

EC  p, j

Product 1 Product 2

CE  p, j

Customer 1

Customer 2

Customer 1

Customer 2

Customer 1

Customer 2

Customer 1

Customer 2

20 30

25 35

10 15

12.5 17.5

20 30

25 35

40 60

50 70

26

 Z.-Z. Jia et al. / Journal of Manufacturing Systems 38 (2016) 13–26

 Table A.5 Destination-related transportation costs and using extra capacity costs. R E XTin  

L1

L2

L3

2

5

100

FC  j

Customer 1 Customer 2

FC extra j

600 800

1200 1600

3000 4000

60,000 80,000

 Table A.6 Inventory costs. R I NVi n

L1

L2

L3

0.5

1

2

CS  p, j Product 1 Customer 1 Customer 2

11.25 11.25

22.5 22.5

45 45

Product 2 Customer 1 Customer 2

16.25 16.25

32.5 32.5

65 65

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