S Gholizadeh-Tayyar
email: shadan.gholizadeh_tayya@mines-albi.fr

L Dupont

J Lamothe

M Falcon
email: mfalcon@tbcinnovation.fr

Modeling a Generalized Resource Constrained Multi Project Scheduling Problem Integrated with a Forward-Backward Supply Chain Planning

Keywords: Generalized Resource Constrained Multi Project Scheduling Problem, Supply Chain Planning, Mixed Integer Programming Generalized Resource Constrained Multi Project Scheduling Problem, Supply Chain Planning, Mixed Integer Programming Generalized Resource Constrained Multi Project Scheduling Problem, Supply Chain Planning, Mixed Integer Programming Generalized Resource Constrained Multi Project Scheduling Problem, Supply Chain Planning, Mixed Integer Programming Generalized Resource Constrained Multi Project Scheduling Problem, Supply Chain Planning, Mixed Integer Programming

Generalized Resource Constrained Multi Project Scheduling Problem, GRCMPSP, is issue of determining a scheduling plan for executing projects' acti ities under satisfaction of precedence relationship between activities and availability of resources. This paper focuses on the resources' availability. To deal with feeding nonrenewable recourses over periods they are demanded and to define a production-transportation plan for them, our proposed mixed integer programming model integrates GRCMPSP with Supply Chain Planning model. Also, to establish a plan for assigning required amounts of renewable resources, it supposes possibility of renting supplementary quantities. This assumption leads the model to define an optimum assignment under considering rent cost of additional resources and penalty cost may originate from lateness of the activities. The results are shown from applying the model on a project called CRIBA, which is defined to reduce energy consumption level of buildings in France.

INTRODUCTION

In this paper we deal with a Generalized Resource Constrained Multi Project Scheduling Problem, GRCMPSP. The model is an extension of Generalized Resource Constrained Project Scheduling Problem, GRCPSP, where it expands the GRCPSP from scheduling one single project to scheduling of multiple projects. The objective of the problem, as it is introduced for the first time in (Elmaghraby, S.E., et al ,1992) is to schedule a number of activities subject to (i) generalized precedence relation between the activities and (ii) availability of the required resources. In term of (i), four possible types of relation comprising Finish-To-Start, Start-To-Start, Start-To-Finish and Finish-To-Finish are determined. A minimum (maximum) lag, that defines a minimum (maximum) time interval to spend between start (finish) of source activity and finish (start) of the target activity in a supposed precedence relation, is considered. In term of (ii), the execution of an activity quietly depends on the availability of the resources. Generally, two types of the resources including renewable and non-renewable resources are regarded in project scheduling problems, (Shirzadeh Chaleshtarti, A. et al,2014).

Project scheduling with renewable resources has been widely studied in the literature, (Pritsker, A.A.B., et al, 1969) as the first research study, (Kellenbrink, C., et al, 2015) and (Ranjbar, M., et al, 2013) as the recent ones in single project scheduling and (Krüger, D., et al, 2009) in multi project scheduling. In most of the researches, it is assumed that the availability of the resources is a constant value over different planning periods, (Khoshjahan, Y., et al, 2013). A modified approach of this hypothesis is regarded in Time Constrained Project Scheduling Problem, TCPSP, where the availability of the renewable resources can increase temporarily by adding new capacities, to meet totally deadline that is defined for project completion, (Hurink, J.L., et al, 2011) and (Klein, R., 1999). In our model, we take the advantage of TCPSP. The aim is to avoid paying surplus cost for completion of the activities whose penalty cost is significantly greater than the rent cost of additional capacities of the resources.

Interning non-renewable resources in project scheduling is initially investigated in (Aquilano, N.J., et al,1980), where it considers time windows for ordering and acquisition of the resources in order to execution of the activities. (Dodin, B., et al, 2001) considers rewards (penalties) and order discounts for reception of the resources. (Smith-Daniels, D.E., et al, 1987) proposes a mixed integer programming model that deals with ordering quantity of the resources over the periods. (Fu, F., 2014). extends the previous work by considering the possibility of executing the activities in different manners (multi-mode problems). To the best of our knowledge, all the previous researches define only a transportation plan to order the non-renewable resources. Our study moves beyond while it is defining a production-transportation plan by considering supply chain network, which supplies the resources in the projects' sites.

Considering the state of art in scheduling of the project(s), we classify the objectives into five groups: (i) Time-based objectives, in which the problem minimizes objectives such as completion time, earliness, tardiness and lateness; (ii) Quality-based objectives that are presented to deal with maximizing the projects' execution ualit (iii) ost-based objectives which approach minimization of total cost of executing the project like as execution costs, material costs, inventory holding costs, costs related to tardiness or earliness of the project; (iv) Net present value, to maximize the present

INTRODUCTION

In this paper we deal with a Generalized Resource Constrained Multi Project Scheduling Problem, GRCMPSP. The model is an extension of Generalized Resource Constrained Project Scheduling Problem, GRCPSP, where it expands the GRCPSP from scheduling one single project to scheduling of multiple projects. The objective of the problem, as it is introduced for the first time in (Elmaghraby, S.E., et al ,1992) is to schedule a number of activities subject to (i) generalized precedence relation between the activities and (ii) availability of the required resources. In term of (i), four possible types of relation comprising Finish-To-Start, Start-To-Start, Start-To-Finish and Finish-To-Finish are determined. A minimum (maximum) lag, that defines a minimum (maximum) time interval to spend between start (finish) of source activity and finish (start) of the target activity in a supposed precedence relation, is considered. In term of (ii), the execution of an activity quietly depends on the availability of the resources. Generally, two types of the resources including renewable and non-renewable resources are regarded in project scheduling problems, (Shirzadeh Chaleshtarti, A. et al,2014).

Project scheduling with renewable resources has been widely studied in the literature, (Pritsker, A.A.B., et al, 1969) as the first research study, (Kellenbrink, C., et al, 2015) and (Ranjbar, M., et al, 2013) as the recent ones in single project scheduling and (Krüger, D., et al, 2009) in multi project scheduling. In most of the researches, it is assumed that the availability of the resources is a constant value over different planning periods, (Khoshjahan, Y., et al, 2013). A modified approach of this hypothesis is regarded in Time Constrained Project Scheduling Problem, TCPSP, where the availability of the renewable resources can increase temporarily by adding new capacities, to meet totally deadline that is defined for project completion, (Hurink, J.L., et al, 2011) and(Klein, R., 1999). In our model, we take the advantage of TCPSP. The aim is to avoid paying surplus cost for completion of the activities whose penalty cost is significantly greater than the rent cost of additional capacities of the resources.

Interning non-renewable resources in project scheduling is initially investigated in (Aquilano, N.J., et al,1980), where it considers time windows for ordering and acquisition of the resources in order to execution of the activities. (Dodin, B., et al, 2001) considers rewards (penalties) and order discounts for reception of the resources. (Smith-Daniels, D.E., et al, 1987) proposes a mixed integer programming model that deals with ordering quantity of the resources over the periods. (Fu, F., 2014). extends the previous work by considering the possibility of executing the activities in different manners (multi-mode problems). To the best of our knowledge, all the previous researches define only a transportation plan to order the non-renewable resources. Our study moves beyond while it is defining a production-transportation plan by considering supply chain network, which supplies the resources in the projects' sites.

Considering the state of art in scheduling of the project(s), we classify the objectives into five groups: (i) Time-based objectives, in which the problem minimizes objectives such as completion time, earliness, tardiness and lateness; (ii) Quality-based objectives that are presented to deal with maximizing the projects' execution ualit (iii) ost-based objectives which approach minimization of total cost of executing the project like as execution costs, material costs, inventory holding costs, costs related to tardiness or earliness of the project; (iv) Net present value, to maximize the present

INTRODUCTION

In this paper we deal with a Generalized Resource Constrained Multi Project Scheduling Problem, GRCMPSP. The model is an extension of Generalized Resource Constrained Project Scheduling Problem, GRCPSP, where it expands the GRCPSP from scheduling one single project to scheduling of multiple projects. The objective of the problem, as it is introduced for the first time in (Elmaghraby, S.E., et al ,1992) is to schedule a number of activities subject to (i) generalized precedence relation between the activities and (ii) availability of the required resources. In term of (i), four possible types of relation comprising Finish-To-Start, Start-To-Start, Start-To-Finish and Finish-To-Finish are determined. A minimum (maximum) lag, that defines a minimum (maximum) time interval to spend between start (finish) of source activity and finish (start) of the target activity in a supposed precedence relation, is considered. In term of (ii), the execution of an activity quietly depends on the availability of the resources. Generally, two types of the resources including renewable and non-renewable resources are regarded in project scheduling problems, (Shirzadeh Chaleshtarti, A. et al,2014).

Project scheduling with renewable resources has been widely studied in the literature, (Pritsker, A.A.B., et al, 1969) as the first research study, (Kellenbrink, C., et al, 2015) and (Ranjbar, M., et al, 2013) as the recent ones in single project scheduling and (Krüger, D., et al, 2009) in multi project scheduling. In most of the researches, it is assumed that the availability of the resources is a constant value over different planning periods, (Khoshjahan, Y., et al, 2013). A modified approach of this hypothesis is regarded in Time Constrained Project Scheduling Problem, TCPSP, where the availability of the renewable resources can increase temporarily by adding new capacities, to meet totally deadline that is defined for project completion, (Hurink, J.L., et al, 2011) and (Klein, R., 1999). In our model, we take the advantage of TCPSP. The aim is to avoid paying surplus cost for completion of the activities whose penalty cost is significantly greater than the rent cost of additional capacities of the resources.

Interning non-renewable resources in project scheduling is initially investigated in (Aquilano, N.J., et al,1980), where it considers time windows for ordering and acquisition of the resources in order to execution of the activities. (Dodin, B., et al, 2001) considers rewards (penalties) and order discounts for reception of the resources. (Smith-Daniels, D.E., et al, 1987) proposes a mixed integer programming model that deals with ordering quantity of the resources over the periods. (Fu, F., 2014). extends the previous work by considering the possibility of executing the activities in different manners (multi-mode problems). To the best of our knowledge, all the previous researches define only a transportation plan to order the non-renewable resources. Our study moves beyond while it is defining a production-transportation plan by considering supply chain network, which supplies the resources in the projects' sites.

Considering the state of art in scheduling of the project(s), we classify the objectives into five groups: (i) Time-based objectives, in which the problem minimizes objectives such as completion time, earliness, tardiness and lateness; (ii) Quality-based objectives that are presented to deal with maximizing the projects' execution ualit (iii) ost-based objectives which approach minimization of total cost of executing the project like as execution costs, material costs, inventory holding costs, costs related to tardiness or earliness of the project; (iv) Net present value, to maximize the present

INTRODUCTION

In this paper we deal with a Generalized Resource Constrained Multi Project Scheduling Problem, GRCMPSP. The model is an extension of Generalized Resource Constrained Project Scheduling Problem, GRCPSP, where it expands the GRCPSP from scheduling one single project to scheduling of multiple projects. The objective of the problem, as it is introduced for the first time in (Elmaghraby, S.E., et al ,1992) is to schedule a number of activities subject to (i) generalized precedence relation between the activities and (ii) availability of the required resources. In term of (i), four possible types of relation comprising Finish-To-Start, Start-To-Start, Start-To-Finish and Finish-To-Finish are determined. A minimum (maximum) lag, that defines a minimum (maximum) time interval to spend between start (finish) of source activity and finish (start) of the target activity in a supposed precedence relation, is considered. In term of (ii), the execution of an activity quietly depends on the availability of the resources. Generally, two types of the resources including renewable and non-renewable resources are regarded in project scheduling problems, (Shirzadeh Chaleshtarti, A. et al,2014).

Project scheduling with renewable resources has been widely studied in the literature, (Pritsker, A.A.B., et al, 1969) as the first research study, (Kellenbrink, C., et al, 2015) and (Ranjbar, M., et al, 2013) as the recent ones in single project scheduling and (Krüger, D., et al, 2009) in multi project scheduling. In most of the researches, it is assumed that the availability of the resources is a constant value over different planning periods, (Khoshjahan, Y., et al, 2013). A modified approach of this hypothesis is regarded in Time Constrained Project Scheduling Problem, TCPSP, where the availability of the renewable resources can increase temporarily by adding new capacities, to meet totally deadline that is defined for project completion, (Hurink, J.L., et al, 2011) and (Klein, R., 1999). In our model, we take the advantage of TCPSP. The aim is to avoid paying surplus cost for completion of the activities whose penalty cost is significantly greater than the rent cost of additional capacities of the resources.

Interning non-renewable resources in project scheduling is initially investigated in (Aquilano, N.J., et al,1980), where it considers time windows for ordering and acquisition of the resources in order to execution of the activities. (Dodin, B., et al, 2001) considers rewards (penalties) and order discounts for reception of the resources. (Smith-Daniels, D.E., et al, 1987) proposes a mixed integer programming model that deals with ordering quantity of the resources over the periods. (Fu, F., 2014). extends the previous work by considering the possibility of executing the activities in different manners (multi-mode problems). To the best of our knowledge, all the previous researches define only a transportation plan to order the non-renewable resources. Our study moves beyond while it is defining a production-transportation plan by considering supply chain network, which supplies the resources in the projects' sites.

Considering the state of art in scheduling of the project(s), we classify the objectives into five groups: (i) Time-based objectives, in which the problem minimizes objectives such as completion time, earliness, tardiness and lateness; (ii) Quality-based objectives that are presented to deal with maximizing the projects' execution ualit (iii) ost-based objectives which approach minimization of total cost of executing the project like as execution costs, material costs, inventory holding costs, costs related to tardiness or earliness of the project; (iv) Net present value, to maximize the present

INTRODUCTION

In this paper we deal with a Generalized Resource Constrained Multi Project Scheduling Problem, GRCMPSP. The model is an extension of Generalized Resource Constrained Project Scheduling Problem, GRCPSP, where it expands the GRCPSP from scheduling one single project to scheduling of multiple projects. The objective of the problem, as it is introduced for the first time in (Elmaghraby, S.E., et al ,1992) is to schedule a number of activities subject to (i) generalized precedence relation between the activities and (ii) availability of the required resources. In term of (i), four possible types of relation comprising Finish-To-Start, Start-To-Start, Start-To-Finish and Finish-To-Finish are determined. A minimum (maximum) lag, that defines a minimum (maximum) time interval to spend between start (finish) of source activity and finish (start) of the target activity in a supposed precedence relation, is considered. In term of (ii), the execution of an activity quietly depends on the availability of the resources. Generally, two types of the resources including renewable and non-renewable resources are regarded in project scheduling problems, (Shirzadeh Chaleshtarti, A. et al,2014).

Project scheduling with renewable resources has been widely studied in the literature, (Pritsker, A.A.B., et al, 1969) as the first research study, (Kellenbrink, C., et al, 2015) and (Ranjbar, M., et al, 2013) as the recent ones in single project scheduling and (Krüger, D., et al, 2009) in multi project scheduling. In most of the researches, it is assumed that the availability of the resources is a constant value over different planning periods, (Khoshjahan, Y., et al, 2013). A modified approach of this hypothesis is regarded in Time Constrained Project Scheduling Problem, TCPSP, where the availability of the renewable resources can increase temporarily by adding new capacities, to meet totally deadline that is defined for project completion, (Hurink, J.L., et al, 2011) and(Klein, R., 1999). In our model, we take the advantage of TCPSP. The aim is to avoid paying surplus cost for completion of the activities whose penalty cost is significantly greater than the rent cost of additional capacities of the resources.

Interning non-renewable resources in project scheduling is initially investigated in (Aquilano, N.J., et al,1980), where it considers time windows for ordering and acquisition of the resources in order to execution of the activities. (Dodin, B., et al, 2001) considers rewards (penalties) and order discounts for reception of the resources. (Smith-Daniels, D.E., et al, 1987) proposes a mixed integer programming model that deals with ordering quantity of the resources over the periods. (Fu, F., 2014). extends the previous work by considering the possibility of executing the activities in different manners (multi-mode problems). To the best of our knowledge, all the previous researches define only a transportation plan to order the non-renewable resources. Our study moves beyond while it is defining a production-transportation plan by considering supply chain network, which supplies the resources in the projects' sites.

Considering the state of art in scheduling of the project(s), we classify the objectives into five groups: (i) Time-based objectives, in which the problem minimizes objectives such as completion time, earliness, tardiness and lateness; (ii) Quality-based objectives that are presented to deal with maximizing the projects' execution ualit (iii) ost-based objectives which approach minimization of total cost of executing the project like as execution costs, material costs, inventory holding costs, costs related to tardiness or earliness of the project; (iv) Net present value, to maximize the present IFAC Conference on Manufacturing Modelling, Management and Control June 28-30, 2016. Troyes, France value of money in project scheduling; and, (v) multi objective models that consider simultaneously two or more of the conflicting objectives mentioned above. In this study, our objective is to minimize the total cost.

It is notable to mention that two main approaches are regarded in network modeling of the project scheduling problems: 1-Single project approach, wherein all the multiple projects are joined together to make a single superproject. Herein, a single critical path is regarded in the scheduling of the projects. For the research works and their different extension we refer the reader to following references, (Węglarz, J., et al, 2011),( Hartmann, S., et al 2010) and (Klein, R., 1999). 2-Multi projects approach, in which the parallel separated projects are treated simultaneously while they use a common pool of renewable resources. In this approach each of the project networks can maintain their own critical path to make shorten, (Browning, T.R., et al, 2010) chooses this approach while they are justifying this approach is more realistic and it has a great opportunity for improving. In our modelling framework, we employ the multi project approach.

Dealing with projects planning in both of single-project and multi-project engages the researchers with NP-hard problems (Blazewicz, J., et al, 1983). In term of computation time of the models, treating with small size of these problems is reasonable by the commercial soft-wares in the condition that the number of activities is less than 50 activities (Fatemi Ghomi, S.M. T. et al ,2002) For large size problems implementation of the heuristics and meta-heuristics is proposed in the literature.

Regarding to the supply chain network, the model defines production-transportation plan of the stakeholders of the supply chain network. It also takes into consideration the sustainability deals by adding backward flows of produced wastes from the projects worksites to the recycling units, which are located either in manufacturing centers or in individual recycling centers.

PROBLEM DEFINITION

Mathematical Formulation

The following notation is used for presentation of the mathematical model.

Stin in(d,g),t-1 + ∑ TQ f (o,d,p| d,p є In(d,g)

Constraints ( 2)-( 13) define start time of the activities, regarding to earliest, latest start time, latest finish time and precedence relationships. Constraint ( 14) deals with the lateness may occur in executing the activities. Constraint (15) presents that the demand of activities for renewable resources can be satisfied by the initial available quantity and quantity could be added over time periods. Constraint ( 16) limits the quantity that can be added into the initial availability of renewable resources. Equations ( 17), ( 18) and ( 19) deal with balance of flows for stock of the products that are used at the destinations. Constraints ( 20) and ( 21) present the same concept for stock of the products that are sent from an origin. Constraint (22) imposes that the production/recycling of the products cannot exceed the available capacities plus the capacities could be added. Constraint (23) defines a limit for added capacities. Constraints ( 24) and (25) present the limited stock capacity respectively for the used products in a destination and sent products from an origin. Constraint (26) deals with limited supply capacity. Equations ( 27) and ( 28) present initial and final states of the stocked products. Constraints ( 29) and ( 30) present the variable types of the model.

Use Case and Numerical Results

The use case of the study relies on CRIBA ( Construction Industrialisée Bois et Acier) project, which is defined to reduce energy consumption level of buildings in France. For that purpose, insulating panels integrated with insulating carpentries are shipped to the projects' worksites to e installed on external facades of the buildings. Besides the insulating carpentries, the other composing elements of the panels are wooden frames, insulation material types and external coating product types. Each of the elements is procured by corresponding suppliers/ manufacturers. For performing the installation activities, several renewable resources such as labor-works, trucks and cranes should be present at the worksites. After posing the panels, former carpentries of buildings should be removed. In order to respect the sustainability concerns regarded in the environmental engagements, the produced wastes in the worksites should be shipped to recycling centers.

Fig. 1 and Fig. 2 present the dimension of the applied use case. It encompasses a supply chain network followed by two identical projects running in worksite1 and worksite2. The results are obtained by using CPLEX-Studio IBM on a notebook with 2.20 GHz processor, Intel® Core i7 and 64-bit of exploiting system. It is worth noting that the solution time was 12 seconds and 24 hundredth of a second.

Figure 1-Presentation of the system framework dedicated to use case.

IFAC MIM 2016June 28-30, 2016. Troyes, France Considering the results, one could stand out some points.

Both of the projects have the same structure and data setting nevertheless staring date of dummy activities of the projects as well as non-dummy activities are not the same. This matter originates from feeding up the non-renewable resources by the supply chain for starting the activities and also by the issue of assigning the renewable resources to activities to make them able to be started on a time between their earliest and latest start time. From the view point of feeding up the non-renewable resources, the supply chain attempts to supply the resources to the projects' worksites ased on its limited capacit of

  (25) TQ f(o,d,p)|oєu,t ≤ SupCap u ∀u є U, f(o,d,p) єF(o,d,p), tєT (26) Stin in(d,p),t = 0 ∀in(d, p) є IN(d,p), t=0,T (27) Stout out(o,p),t = 0 ∀out(o, p) є OUT(o,p), t =0,T (28) Z it , U it є {0,1} ∀i є I , t є T (29) Ltns i , S i , R rt , TQ f(o,d,p),t , Stin in(d,p),t , Stout out(o,p),t , ProdQ pro(l,u,p),t , AddL lt ≥ 0 ∀f(o, d, p)є F(o, d, p), in(d, p) є In(d, p), out(o, p)є OUT(o, p), pro(l, u, p)є PRO(l, u, p), l єL, i є I,r є R, tє T

Figure 2 -

 2 Figure 2-Activity-on-Node presentation for projects dedicated to the use case.

Figure 3 -

 3 Figure 3-Results for transported, produced/recycled quantities and starting date of activities.

  ),t-Tl f(o,d,p|d,p є In(d,g)) Stin in(d,g), t +∑ ProdQ pro(lc,u,p)|u,pє In(d,g), t ProdQ pro(l,m,p),t Wl p ≤ LAvCap lt +AddL lt ∀pro(l, u, p)є PR (l,m,p),tєT

				pro	∀in(d,p) є
	IN(d,g) ,t є T	(18)
	Stin in(w,nr),t-1 +∑ TQ f(o,d,p|p є In(w,nr)), t-Tl f(o,d,p|d,p є In(w,nr)) f	=
	∑	iє I w	Z it	Dnr i,nr|nr є In(w,nr) + Stin in(w,nr), t
	∀in(d,p) є (w, nr) ,tєT, nr є R	(19)
	Stout out(m,p), t-1 +
	∑ ProdQ pro(lp,u,p|u,p є OUT(m,p)), t-Pl pro(lp,u,p|u,p є OUT(m,p)) pro	=
	∑ TQ f(o,d,p|o,p є OUT(m,p)),t f	+ Stout out(m,p), t
	∀out(o,p) є U (m,p) ,t єT	(20)
	Stout out(w,p), t-1 + ∑	i є I w	Z it	Gp g|g є OUT(w,p), i =
	∑ TQ f(o,d,p|o,p є OUT(w,p)), t f	+ Stout out(w,p), t
	∀out(o,p) є U (w,p) ,pєG,tєT	(21)
					(22)
	∀lє L, t єT ≤ StinCap u ∀uє U, t єT AddL lt ≤ MaxAdd l ∑ Stin in(d,p)|dєu,t p	(23) (24)
	∑ Stout out(o,p)|oєu,t p	≤ StoutCap

f = u ∀u є U, t єT

  IFACMIM 2016 June 28-30, 2016. Troyes, France

Indices

i : index of activities. t: index of time periods. w: index of projects' worksites.

: index of manufacturing centers. : index of recycling centers. u: index to show all units of the network, including the worksites, w, manufacturing centers, m, collection-recycling centers, c, and suppliers of raw materials. nr: index of products used at the worksites (projects' nonrenewable resources). g: index of wastes types generated at the worksites. p : index of network's product items, including of the products used at the worksites, nr, wastes generated at the worksites, g, composing elements/ raw materials used at the manufacturing centers and products produced at the manufacturing centers . r: index of renewable resources used at the worksites. r : index of renewable resources used at the worksites with high rent costs, r є R. f (o,d,p) : index of flows which present the shipment of product p from origin o to destination d, o є U, d є U, p є P. in(d,p): index of pairs which show reception of product p at destination d, d є U, p є P. out(o,p) : index of pairs which show shipment of product p from origin o, o є U, p є P. l: index of lines, including lp as production lines and lc as recycling lines. pro(l,u,p) : index which identifies line type l at unit u which is dedicated to produce/recycle product p.

(p, p ) : index to present linkage between composing element p and made product p . , t, w, m, c, u, nr, g, p, r, r , f(o,d,p), in(d,p), out(o,p), l, pro(l,u,p) and (p, p ) are used to present related set notation. I w : set of activities that belong to worksite, (I w I). SSpr : start to start precedence of activity j by pairs (i, j). SFpr : start to finish precedence of activity j by pairs (i, j). FSpr : finish to start precedence of activity j by pairs (i, j). FFpr : finish to finish precedence of activity j by pairs (i, j).

Sets

Capital letters of following indices i

owait pr : 1 if activity j of precedence SSpr starts immediately after activity i has started, 0 otherwise. owait pr : 1 if activity j of precedence SFpr finishes immediately after activity i has started, 0 otherwise. owait pr : 1 if successor activity j of precedence pre starts immediately after finishing the predecessor activity i, 0 otherwise. owait pr : 1 if successor activity j of precedence pre finishes immediately after finishing the predecessor activity i, 0 otherwise.

w : linkage (i, j) presents beginning activity of worksite w by i and ending one by j. r w : linkage (i, j) presents beginning activity of worksite w which uses renewable resource r by i and the ending activity by j.

Parameters

i : earliest start of activity i . l i : latest start of activity i . DD i : due date of activity i. Du i : duration of activity i. Dnr i,nr : demand of activity i for nonrenewable resource nr. Dr ir : demand of activity i for renewable resource r. FS i : minimum time lag between the finish of activity i and the start of activity j.

IFAC MIM 2016 June 28-30, 2016. Troyes, France SS i : minimum time lag between the start of activity i and the start of activity j. SF i : minimum time lag between the start of activity i and the finish of activity j. FF i : minimum time lag between the finish of activity i and the finish of activity j. Ar r : availability of renewable resource r. Max r : maximum add value for resource r. P w per period cost of running worksite w.

C r w per period cost of using renewable resource r at worksite w . R rt : rent cost of renewable resource r at time period t. P n i : penalty cost for one-period delay of activity i. StinCap u : capacity for stocking the products which are using at unit u. StoutCap u : capacity for stocking the products which are produced at unit u. SupCap u : supply capacity of raw material supplier u. LAvCap lt : production capacity of line l at time period t. MaxAdd l : maximum add capacity in line l. AddCost l : cost for adding one unit of production/recycling capacity to line l. (1)

The objective of the model is to minimize total cost of the system. Generally, it includes two major types of the cost: -Project planning costs (terms including in the first bracket), which are respectively total periodic cost of running the projects, costs related to the renewable resources whose rent cost is high( The aim is to minimize the period that these resources are maintained at the worksites.), total penalty cost and total cost of adding supplementary renewable resources.-Supply chain planning cost (terms in the second bracket), including the total transportation cost for shipping products, stock cost of the products that are received at the destinations, stock cost of the products that are sent from an origin, production/recycling cost and the cost related to add of new production/recycling capacities in the related lines. From the view point of assigning the renewable resources, the model associates the start dates to the activities based on the initial availability of the resources and probable rented quantities. In this context, for defining the rent of the renewable resources, it regards the rent cost of the resources as well as the penalty cost for lateness of the activities. The optimality defines, either to rent additional resources and avoid paying high penalty costs, or to pay low penalty cost in order to not to pay for high additional renewable resources.

Subject to

CONCLUSIONS

An integrated mixed integer programming model of scheduling GRCMPSP with forward-backward SCP model is proposed in this work. The model defines a transportationproduction plan for supplying the non-renewable resources at the projects' worksites and for shipping the wastes to the recycling centers. Also it defines a plan for assignment of the renewable resources to the activities. Possibility of renting additional capacity of renewable resources makes the model able to propose results that are optimum in term of either paying for penalty cost or paying for rent costs. For the future work, the authors are interested in applying a proper metaheuristic algorithm to treat with problems in large sizes. It will be interested to reduce the total number of the binary variables Z it , that is equal to ∑ f (l i i ), by a heuristics which limits l i and i to make tighten [ i l i ].

ACKNOWLEDGMENT

The authors gratefully acknowledge Agence d' n irronnement et a trise de l' nergie for founding this research study and IBM for its support in providing CPLEX solver. REFERENCES Aquilano, N.J., Smith, D.E., (1980). A formal set of algorithms for project scheduling with critical path scheduling/material requirements planning. Journal of Operations Management 1, 57 67. Blazewicz, J., Lenstra, J.K., Kan, A.H.G.R., (1983).

Scheduling subject to resource constraints: classification and complexity. Discrete Applied Mathematics 5, 11 24. Browning, T.R., Yassine, A.A., (2010)


Aurelie Charles

Matthieu Lauras

Luk Van Wassenhove

A

Keywords: Supply chain management, Aid agencies, Flexible organizations, Modelling Paper type Research

published or not. The documents may come   L'archive ouverte pluridisciplinaire

Introduction and research questions

One of the particularities of humanitarian logistics is the level of uncertainty they have to cope with. Every day, in many parts of the world, humanitarian workers are confronted with various forms of uncertainty. Given that beneficiaries' needs evolve over time and are really difficult to forecast, demand and supply vary on a daily basis. Also, there are many cause-and-effect interactions that affect operations. For example, an earthquake can provoke a flood if a brimming lake is formed by landslides from the earthquake. Local infrastructure may also be damaged to the extent that the supply chain network has to be continuously rethought, along with the reconstruction of roads, airports and other key elements of the network. Humanitarian logisticians have, therefore developed tools and methods to respond quickly to short-term changes, thereby improving the agility of their supply chain.

This high level of agility is more and more required in the private sector [START_REF] Kleindorfer | Managing risk in the global supply chain[END_REF]. Many examples can be used to illustrate the low responsiveness of most commercial supply chains. After the earthquake in Taiwan in 1999, the prices of global semiconductor were almost doubled, and of the 62 companies based in Asia, only 21 percent had full business contingency plans to protect themselves against business interruption (World Economic Forum, 2008). Demand volatility is also becoming higher in the private sector. Owing to market turbulence, demand in almost every industrial sector seems to be more volatile than it used to be in the past [START_REF] Christopher | Mitigating supply chain risk through improved confidence[END_REF]. Consequently, being able to react quickly to changes is an essential capability for commercial supply chains (Kisperska-Moron and Swierczek, 2009).

Cross-learning opportunities between business and humanitarian sectors have been listed by many authors (Van Wassenhove, 2006; [START_REF] Oloruntoba | Humanitarian aid: an agile supply chain?[END_REF]. Recently, disaster relief is becoming a testing ground for many researchers in logistics. More often, they propose methods for implementing in the humanitarian sector the tools that they initially designed for the business sector. Yet, to date, no work seems to have been done the other way round. In other words, no one has explicitly identified the best practices that the business sector can borrow and adapt from humanitarian experts. This paper aims to fill this gap in line with our belief that the business and humanitarian sectors can both learn from each other.

From an academic point of view, supply chain agility is becoming a major field of research. It is highlighted as one of the fundamental characteristics of the best supply chains [START_REF] Lee | The triple -a supply chain[END_REF]. Given the complexity that is linked to a high level of constraints and uncertainty, the humanitarian sector is an interesting field to study. Moreover, they present a potential added value for both the humanitarian and the private sectors. It is very important for humanitarian organizations to explicitly establish the best practices found in relief chains, and by so doing, they clarify their achievements and facilitate the ramification of these best practices. The business sector could then learn from them in order to improve the agility level of their supply chain. It would enable them to deal with supply, demand and environment uncertainties, and this capability is becoming an order winner for many commercial supply chains.

Many supply chain managers are, therefore in search of methods that would enable them to better assess the level of agility of their supply chain. Unfortunately, in the literature, there is no unanimously accepted framework and consistent system for defining and measuring supply chain agility.

We can therefore formulate two research questions (RQ) as follows:

RQ1. How should supply chain agility be defined?

RQ2. How should supply chain agility be assessed?

Based on the review of literature, we will, in Section 2, address the RQ1 and present our framework in the form of a house that we will refer to as the "house of supply chain agility". The RQ2 will be studied in Section 3. By analyzing the capabilities of the major existing approaches, this study evaluates the different ways of assessing supply chain agility. A comparative analysis of the main features of both the humanitarian and the commercial supply chains is done in order to ensure that our assessment is valid for both sectors. An application of the model in the humanitarian sector is used to illustrate the logic of our approach. Finally, in Section 4, we will present our analysis, conclusions, limitations and perspectives for further research. Figure 1 shows a step by step view of our approach.

2. How should supply chain agility be defined?

In the last decade, agility has been one of the key concepts discussed by many authors.

We have, therefore reviewed the literature in order to gather its various definitions and dimensions as it applies to supply chains. In this paper, we do not intend to provide an exhaustive literature review but simply a quick scan that is elaborate enough to enable clarify the notion of supply chain agility and to build a consistent assessment model. The conclusions of our literature review are presented in the following paragraph. Supply chain agility is usually defined as the ability to respond to unanticipated changes [START_REF] Sheffi | Demand variability and supply chain flexibility[END_REF]. The focus on agility from the supply chain perspective emerged in the year 2001 and was first initiated by [START_REF] Van Hoek | Measuring agile capabilities in the supply chain[END_REF]. According to [START_REF] Lee | The triple -a supply chain[END_REF], the main objectives of an agile supply chain are responding quickly to short-term changes in demand (or supply) and handling external disruptions smoothly. Sometimes agility could be mistaken for other similar but different concepts such as adaptability and resilience. While agility is being able to deal with and take advantage of uncertainty and volatility, adaptability is rather used for more profound medium-term changes. Adaptable supply chains adjust their design to meet structural shifts in markets and, modify and adapt the supply network to strategies, products and technologies [START_REF] Lee | The triple -a supply chain[END_REF]. Figure 2 shows an illustrated difference between agility and adaptability. As for resilience, it aims to mitigate identifiable risks and ensure continuity in the firm's business. [START_REF] Christopher | Building the resilient supply chain[END_REF] defined resilience as the ability of a system to return to its original state or move to a new and more desirable state after being disturbed. Differences between agility and resilience are depicted in Table I. To achieve a high level of agility, a supply chain has to acquire some key capabilities. Many authors have already listed one or more elements associated with agility. Table II shows the definitions and details of these capabilities. The aim of this section is to illustrate all the facets of agility that have to be worked on. The house of supply chain agility (Figure 3) summarizes the main components, which enable the supply chain to be agile. We developed it based on a thorough literature review on agility.

Our approach step by step

According to [START_REF] Christopher | Supply chain migration from lean and functional to agile and customised[END_REF], a key characteristic of an agile organization is flexibility. In other words, supply chain agility is an externally focused capability that is derived from flexibilities in the supply chain processes [START_REF] Swafford | The antecedents of supply chain agility of a firm: scale development and model testing[END_REF]. They thus assert that "procurement/sourcing flexibility", "manufacturing flexibility" and "distribution/logistics flexibility positively impact supply chain agility". Manufacturing flexibility is broken down into four competences (machine, labor, material handling and routing flexibilities) and two capabilities (volume and mix flexibility) [START_REF] Zhang | Manufacturing flexibility: defining and analyzing relationships among competence, capability, and customer satisfaction[END_REF]. Knowing that internal manufacturing flexibility competencies are neither relevant to our focus on supply chains nor appropriate for service providers such as humanitarians, we will restrict our study to capabilities as pertained to flexibility. We will, therefore adopt and study four flexibility capabilities (product, mix, volume and delivery flexibility) as they are defined and classified by [START_REF] Slack | The flexibility of manufacturing systems[END_REF], and summarized in Table II. There is abundant literature on the notion of agile manufacturing [START_REF] Yusuf | Agile manufacturing: the drivers, concepts and attributes[END_REF][START_REF] Sharifi | A methodology for achieving agility in manufacturing organisations: an introduction[END_REF][START_REF] Giachetti | Analysis of the structural measures of flexibility and agility using a measurement theoretical framework[END_REF].

Consequently, flexibility is a requirement that is necessary to achieve supply chain agility. It is, therefore represented as the foundation of the house of agility. Though a key component, it is not the only capability needed to achieve supply chain agility. Enhanced responsiveness is also a major capability of an agile supply chain [START_REF] Stevenson | Flexibility from a supply chain perspective: definition and review[END_REF]. Two other key ingredients of agility are visibility and velocity [START_REF] Christopher | Building the resilient supply chain[END_REF]. A complementary capability is mentioned by [START_REF] Okongwu | Trade-offs in order management: a multi-criteria advanced ATP approach[END_REF], for whom agility in a supply chain is the combination of effectiveness and responsiveness in a flexible environment. As shown in Table II, our framework will be organized in the following order and manner: flexibility is broken down into four capabilities II. Supply chain agility capabilities: definitions and assessments (volume, delivery, mix and product flexibilities), responsiveness into three capabilities (reactivity, velocity and visibility) and effectiveness is composed of completeness and reliability. All these enable to provide a quick and adequate response to short-term changes. The definitions of these capabilities are given in Table II.

Based on this discussion, we can define supply chain agility as the ability to respond quickly and adequately to short-term changes in demand, supply or the environment. It is derived from the flexibility, responsiveness and effectiveness of the supply chain.

How should supply chain agility be assessed?

If we presume that agility is the future business system that will replace the mass production businesses of today [START_REF] Kidd | Agile manufacturing: a strategy for the 21st century[END_REF], then it will be of prime importance to have a logical, consistent, robust and reproducible model that will be used to assess supply chain agility. This is true for the business, as well as for the humanitarian sector where a high level of agility is needed. The use of a model to assess supply chain agility should:

. emphasize the vital need of humanitarians for preparedness, and this would constitute an additional argument to motivate their donors to increase funds for disaster preparedness actions;

. provide supply chain managers with effective ways of collaborating with other stakeholders in order not only to enhance benchmarking and cross-organizational learning, but also to mutually improve the agility capabilities of their supply chains; and enable to measure performance, better manage skills and abilities and facilitate knowledge management, which constitutes a path toward self-improvement.

In this section, we will start by studying existing methods of assessing agility capabilities. Then, we will explain the reasons why we propose a benchmark for humanitarian supply chains and also discuss the consequences of this study of cross-organizational learning on the scope of our work. To carry out this benchmark, we have designed a case study. Indeed:

[. . .] the case study method allows investigators to retain the holistic and meaningful characteristics of real life events such as individual life cycles, organizational and managerial processes, changes in the neighborhood, international relations and the maturation of industries [START_REF] Yin | Case Study Research: Design and Methods[END_REF]. This fits our purpose to assess the agility of supply chains. For this study, we gathered documents, archival records and 12 semi-directive interviews of practitioners working in various regions (Europe, Middle-East or Africa) and at different organizational levels (headquarters, regional logistics centers or field workers). This paper summarizes the evidence collected from the International Federation of the Red Cross (IFRC) and Red Crescent Societies, "Medecins Sans Frontie `res" (MSF) and the French Red Cross. Other organizations such as Oxfam and the World Food Program (WFP) were also approached but with more informal interviews.

Finally, we will present our model for assessing supply chain agility, its construction and its implementation using a real-life case study. To build the assessment model, we used a symbolic modeling approach. A symbolic model is a representation of the performance measure of a system in terms of its variables. This means that the attributes of the system are linked by an equation [START_REF] Panneerselvam | Research Methodology, PHI Learning[END_REF]. In Section 2, we presented a list of attributes of supply chain agility and in Sections 3.3 we will present a list of metrics associated to these capabilities, as well as a consistent method to evaluate and aggregate them.

Existing approaches for assessing the capability level of a system

There are two main approaches for assessing the capability level of a system: maturity assessment and performance evaluation. We have looked at the capability maturity model (CMMI w ) used for assessing the maturity level of organizations, the European Quality Award of the European Foundation for Quality Management (EFQM) used for auditing the quality competencies of companies and the supply chain operations reference (SCOR) model used for measuring the performance of supply chains. The EFQM model is not suitable for humanitarian organizations or for industrial sectors that are faced with frequent short-term changes. In both cases, the emphasis on strict procedures and their documentation may particularly go against agility. For these reasons, EFQM cannot be used in our specific case.

CMMI w cannot readily be used either. The design of a specific model for agility capabilities is necessary as CMMI w has more than 500 pages. This leaves little room for interpretation and makes it a time-consuming process, and therefore not usable in humanitarian organizations. Moreover, the emphasis on strict procedures and their documentation could lead to a bureaucratic behaviour. It also aims to have stabilized processes, which is not a fundamental characteristic of agile processes. Supply chain performance measurement systems, such as the SCOR model, use a language of common metrics with associated benchmarks and provide a platform for best-in-class comparison and inspiration [START_REF] Huan | A review and analysis of supply chain operations reference (SCOR) model[END_REF]. Some of the performance dimensions in the SCOR model are required to achieve supply chain agility but the model cannot be used to assess agility either, for it focuses on transactional efficiency rather than on the relationship with customers and suppliers [START_REF] Lambert | An evaluation of process-oriented supply chain management frameworks[END_REF].

Finally, we believe that our quest to define a specific model for assessing agility represents a real need that neither quality awards nor actual maturity models (or performance measurement systems) can satisfy. Our proposition follows a similar approach as maturity models but the assessment is done on performance dimensions rather than on the completeness of the process implementation. This is because first, stabilized processes are not a fundamental characteristic of agile processes and second, processes are only one of the various areas to work on. People, products and partners are also elements that impact the capability levels (Figure 4). Actually, to be able to react quickly and adequately to short-term changes, specific processes are needed, but these processes should be able to move quickly from one stabilized state to another. Having them stabilized may help, for example, in terms of visibility, but it is not enough to achieve agility.

Humanitarian supply chains: the experience of uncertainties

The notions of change and uncertainty that we have previously discussed are closely connected to that of agility. There are four sources of uncertainty: foreseeable uncertainties, residual risks ("what is left over after planning for foreseeable uncertainty"), complexities and unknown unknowns: [. . .] those that do not have a definite formulation, have no stopping rule that allows one to determine when the problem is solved, where solutions cannot be fully tested and the problem cannot be generalized, and where there is ambiguity on the causes of the problem [START_REF] Loch | Managing the Unknown: A New Approach to Managing High Uncertainty and Risk in Projects[END_REF].

Agility would then mean to be able to respond quickly when confronted with any of these uncertainties. All these sources exist in the humanitarian world. There are many occasions where humanitarian supply chains have to develop their agility capabilities and they often do that successfully. One has to pay close attention to the elements that distinguish humanitarian supply chains from commercial supply chains in order to transfer the best practices of the former to the latter. Because of the differences, studies of the agility capabilities of humanitarian supply chains need to be filtered and adapted before they can be used in the business sector (Table III). First, our study will focus on the whole supply chain, except the manufacturing part, since it is irrelevant both from a humanitarian point of view and from an academic perspective (see Section 2).

The choice of adequate semantics also needs to be considered. Within humanitarian organizations, there is actually no consensus on the acceptance and the definition of the notion of customer. In a commercial supply chain, a customer pays for the product or service he uses. In the humanitarian world, the end-user (or beneficiary) is an entity different from the buyer or donor. Similar comments can be made upstream of the supply chain, where there are two kinds of suppliers: those who give products or money (donors), and those who are paid by the organization for the supply of the necessary items. Given these elements, we can, therefore say that the notion of supply chain (and hence the notion of supply chain agility) varies slightly from one sector to another. As a result, a clear statement on the scope of the study is required in order to clarify the other areas. In this paper, we focused on suppliers and end-users, but not on donors. We also did not consider the manufacturing part, thereby focusing on the elements that are common to most supply chains.

Another major difference lies in the lifecycle of each supply chain. Relief chains are project oriented. They have a short lifecycle and are set up in specific conditions, thus facing more uncertainties. They, therefore require a high level of agility. Not all commercial supply chains require such agility capabilities. Consequently, a preliminary assessment of the most appropriate level of agility for a given commercial supply chain is needed prior to any cross-learning implementation. Such a study may be inspired from Weber, who proposes a tool for measuring an organization's need for agility [START_REF] Weber | Measuring supply chain agility in the virtual organization[END_REF].

A last comparative element is the nature and size of flows in each supply chain. Regarding information flows, the role played by the media is incredibly high in humanitarian supply chains. It directly impacts the size and the complexity of the relief operations. With no media coverage, the number and commitment of donors, and, therefore the number of items transiting the supply chain, tends to diminish. On the contrary, over exposition leads to over reaction of donors and this creates some imbalance between the amount of items received and the amount of resources available to manage them. Also, it often leads to a higher number of unsolicited items that get in the way of relief operations and hinder the actual delivery of aid. Moreover, local means of communication are often reduced at the end of a disaster; scarce internet access is an example. Visibility is, therefore much more difficult to achieve for humanitarian supply chains. The next step in the development of our assessment model entails creating explicit humanitarian methods that enable to achieve supply chain agility. David Kaatrud, former Chief of Logistics for the United Nations WFP, explains that in comparison to the business sector, their: [. . .] operational settings are typically very different and difficult, and to get supplies to the most remote areas, we may have to resort to a range of imaginative and unconventional delivery systems, from air-dropping to using elephants for transport [START_REF] Tomasini | Humanitarian Logistics[END_REF].

They also developed specific tools to better monitor their supply chains and enable a quicker response to changes. The humanitarian logistics software (HLS), for example, enables the IFRC to increase its supply chain visibility. Similar logistics software, such as HELIOS, the second generation of HLS or SUpply MAnagement (SUMA) is in use or under deployment in other agencies, namely Oxfam and World Vision International for HELIOS and the World Health Organization for SUMA. Specific platforms for sharing information have also been developed. ReliefWeb, the web site of United Nations Joint Logistics Center or Humanitarian Information Centers allow various stakeholders to use the information given to build their knowledge of the situation and, with it, take effective action in the field [START_REF] Tomasini | Managing Information in Humanitarian Crises: the UNJLC Website[END_REF].

Short-term changes are thus humanitarians' daily routine. To cope with uncertainties, they have developed quite a good number of methods. Whereas most of them are widespread in many organizations, others are not so commonly used. To help humanitarians formalize those practices and enable the business sector to draw from them, we have designed and conducted a case study research as earlier explained. The methods used by the IFRC to quickly respond to changes are shown in the Appendix. A reference to the corresponding methods that are listed in the literature is added. It is inspired from [START_REF] Lee | The triple -a supply chain[END_REF] Surprisingly (or perhaps not), majority of the methods found in the literature are applied in the humanitarian sector. Those that cannot be found have no application for humanitarian supply chains since they concern agile manufacturing.

Supply chain agility assessment model

As we mentioned earlier, humanitarian and commercial supply chains differ on many points. Therefore, for the transfer of best practices to be relevant, we need to focus on the agility metrics that are relevant for both supply chains. This leads to a fundamental question: how can agility capabilities be assessed in a consistent manner?

With reference to Section 2, the agility capability of a supply chain is measured by its reactivity to changes. Some agility metrics can be found in the literature ( [START_REF] Sethi | Flexibility in manufacturing: a survey[END_REF]; Kisperska-Moron and Swierczek, 2009). Unfortunately, most of the metrics listed are not relevant for humanitarians since they usually deal with the production of goods. We have thus refined the tables such as to list only agility indicators that are relevant for both sectors, hence dropping the metrics that are used to assess manufacturing agility (Figure 4).

From these metrics, an assessment of the agility capabilities of the supply chain has to be deduced. For this specific purpose, we used a symbolic modeling approach. The idea is to use the above metrics to measure each capability. They will enable to qualify the supply chain to a given level for each capability, using evaluation grids such as the one shown in Figure 5. As we can see in figure, supply chain agility metrics are linked by equations in order to enable a consistent assessment of each capability. Supply chain agility can then be deduced from the previous scores on the basis of the model shown in Figure 6. The method used to build these equations is similar to the one used to build the CMMI w maturity model: brainstorming and validation by practitioners. To conduct an overall assessment of supply chain agility, each capability (flexibility, responsiveness and effectiveness) has to be evaluated through its evaluation grid. Special care has been taken to keep it as robust and reproducible as possible.

To illustrate how to use the model, we conducted an assessment of the agility of IFRC's relief chain during its response to the 2006 Yogyakarta earthquake. The detailed scores of the responsiveness of IFRC's supply chain correspond to the darker cells in Figure 5. The overall assessment is summarized in the radar graph, as shown in Figure 7. On the 0-3 scale for the capability levels, we can see that IFRC scored 3 on velocity, 2 on reactivity and 1 on visibility. Indonesia being used to natural disasters, its National Society has developed contingency plans and the local delegation fosters a Regional Disaster Response Team, a trained team of experts with pre-prepared field equipment, including computers and telecommunications. These teams are deployed from the region and are, therefore more likely to point out local specificities and adequately evaluate the needs of beneficiaries. They helped increase reactivity. IFRC has also developed units to respond to specific needs, for example, IT and telecommunications, and referral hospital or logistics. Dispatching these units definitively contributed to increasing velocity and reactivity levels. Consequently, IFRC's velocity and reactivity levels are quite high. Regarding visibility, IFRC scored only 1 for this specific operation. Actually, following their decentralization process, they had a system in place to track the location and status of goods at the regional level. Since it was their first operation with such an organization, the information flow was not optimal. During the first days of the operation, there was no tracking system in place. They had parallel pipelines, which hindered visibility and reporting lines were not clearly defined.

Proceeding method of our model for assessing supply chain agility

The aim of the evaluation grid shown in Figure 5 is to assess the responsiveness of supply chains. Other similar tables have been built to assess the overall agility level. To make the best out of it, it should not be used without a method that should provide organizations with instructions on how to use it, as well as improvement paths that would enable to achieve higher levels in the grid. The assessment of supply chain agility starts with the preparation phase, where the person in charge of the audit selects the participants to be interviewed, selects and prepares the assessment team and develops the assessment plan. The second phase consists in conducting the assessment. To do this, interviews, records and documentation are used to gather relevant information and generate results. Once the results are validated, the final report can be delivered and documented. The final step consists then in developing the improvement plan, with the aim of achieving the desired levels for all capabilities.

To design the improvement plan, two options are open to the organization. Either it focuses on the capabilities with the lowest score or it focuses on sets of pre-defined capabilities depending on its current and desired agility level. The first option enables an organization to implement process improvement in different process areas at different rates. The capabilities that the organization want to focus on are evaluated independently using their specific evaluation grid, for example, Figure 5 for the assessment of responsiveness. The second option is shown in Figure 6. To use it, each capability has to be assessed with its evaluation grid. The results are then aggregated to qualify the supply chain to a given level of agility. There are five levels of overall agility (ad hoc, repeatable, defined, managed and optimized) and four levels for each capability that can be assessed thanks to the metrics defined in the previous section. A rough correspondence between agility maturity and capability levels is shown in Figure 6. The improvement path may be either increasing a given capability (depending on the organization's strategy) or increasing the overall agility level by targeting a given profile. For example, an organization that has achieved a capability level of 2 on all dimensions (flexibility, reactivity and velocity) may want to increase its agility level by working on its reliability and completeness.

Let us now go back to our previous application -the IFRC solution to the 2006 Yogyakarta earthquake. Figure 7 shows the summarized results of this example.

As we can see in the figure, IFRC achieved capability levels of 2 for flexibility, reactivity and reliability, 3 for velocity and completeness and 1 for visibility. Consequently, its agility level is ranked 4 (managed) for this relief operation. A realistic improvement plan should first be discussed with the IFRC management team in order to validate the desired level. One recommendation that ensues from these results could be to start by improving the flexibility of the supply chain before improving reliability and finally visibility. This is the first application of our model. Further research is underway to use this tool in other situations. In the case of project-oriented supply chains, as is the case for the humanitarian and some industrial sectors, the study can be carried out in two ways:

(1) For a single organization, assess the agility of the supply chain in multiple projects in order to evaluate the consistency, evolution, min, max and average level of their supply chain agility. (2) For a given type of project, assess the agility of the supply chain of various organizations. For example, how well did various organizations perform during the 2009 hurricane season in the Caribbean?

Such a study will enable to identify best practices and gaps, first steps toward self-improvement and opportunities for the transfer of best practices.

Conclusion and perspectives

As we have shown is this paper, humanitarians have developed tools and methods to quickly respond to changes. Yet, especially in the humanitarian context, it is hard, if not impossible, to extensively develop some of the agility capabilities enumerated in Section 2. Total visibility, for example, is not easily achievable by humanitarians, for not only there is usually no single entity responsible for the whole supply chain, but also there are few systems in place to share information between all the actors of the end-to-end supply chain. On the other side, given the highly competitive and uncertain business environments in which they operate, commercial supply chains constantly search for new ways of developing their agility capabilities in order to improve their competitiveness and profitability. Thus, supply chain agility is a strategically important capability in many sectors, including the humanitarian. The contributions of this paper are twofold. First, it provides a framework (represented in the form of a house of supply chain agility) that enables to understand the notion of supply chain agility. Second, it develops a model for assessing the agility of a supply chain. The expertise of humanitarians in the field of supply chain agility is used to suggest some systematic methods used to achieve a high level of agility. We also propose some metrics and a proceeding method that can be used to evaluate supply chain agility. All this will constitute a basis for future field research, with the aim of identifying and transferring best practices in supply chain agility. Further work to finalize the maturity model is in progress. This will be followed by field applications for various humanitarian relief operations as well as for some commercial supply chains.

Figure 1 .

 1 Figure 1. Our approach step by step

Figure 2 .Flexibility

 2 Figure 2. Agility vs adaptability

Figure 3 .

 3 Figure 3. House of supply chain agility

Figure 4 .

 4 Figure 4. List of metrics

  , Van Hoek et al. (2001), Swafford et al. (2006) and Lin et al. (2006).

Figure

  Figure 5. Utilization of the metrics to assess capabilitiessupply chain responsiveness evaluation grid

Figure

  Figure 7. Summarized results for IFRC supply chain in Yogyakarta in 2006

  Van Hoek et al., 2001; Slack, 2005; Okongwu et al., 2008; Kekre et al., 1995; Narasimhan and Das, 1999; Sethi and

  7.

			Agility level 5
			Flexibility = 3
			Reactivity = 3
			Velocity = 3
			Effectiveness = 3
			Visibility ≥ 2			Key improvement		Capability level
			Agility level 4			area	0	1	2	3
			Flexibility ≥ 2 Reactivity ≥ 2 Velocity ≥ 2 Visibility ≥ 1 Effectiveness ≥ 2			Velocity Reactivity Volume flexibility Delivery flexibility Mix flexibility Product flexibility	maturity1 Agility	Agility maturity 2 Agility maturity 3
			Agility level 3 Flexibility ≥ 2 Reactivity ≥ 1			Reliability Completeness Visibility		Agility maturity 4	Agility maturity 5
			Velocity ≥ 1
			Agility level 2 Flexibility ≥ 1 Agility level 1 Flexibility <1						Figure 6. Proceeding method and evaluation grid for supply chain agility
										IFRC
	Key improvement area	0	1	Capability level 2	3		Flexibility 3		results Agility maturity 1
	Volume flexibility Delivery flexibility Mix flexibility Product flexibility Reactivity Velocity Reliability Completeness Visibility		X	X X X X X X	X X	Effectiveness Visibility	2 1 0	Velocity Reactivity	Agility maturity 2 Agility maturity 3 Agility maturity 4 Agility maturity 5	Summarized results for IFRC supply chain in Yogyakarta in 2006

This article has been cited by:

Toulouse -Mines Albi, as an Associate Professor and the Toulouse Business School as an Affiliate Professor. His works mostly focus on supply chain management and performance management for project and business process. All his researches concern as well the industrial sector as the humanitarian sector. He has published several papers in journals and international conferences in the area of performance assessment and supply chain management.

Luk Van Wassenhove holds the Henry Ford Chair in Manufacturing at INSEAD while serving as the Academic Director of INSEAD's Social Innovation Centre. His research focus is on closed-loop supply chains and disaster management, producing several award-winning case studied and articles on both subjects. He regularly consults for international organizations in the profit as well as not-for-profit sectors.

Appendix