PLANNING AND SCHEDULING OF PRODUCTION SYSTEM IN ...

Management and Production Engineering Review

Volume 10 • Number 4 • December 2019 • pp. 3–10DOI: 10.24425/mper.2019.131440

PLANNING AND SCHEDULING OF PRODUCTION SYSTEMIN CONDITIONING LINE: INDUSTRIAL APPLICATION,OPTIMIZATION AND SIMULATION APPROACHZineb Ibn Majdoub Hassani1, Abdellah El Barkany1, Ikram El Abbassi2, Abdelouahhab Jabri1,Abdel Moumen Darcherif2

1 Mechanical Engineering Laboratory, Faculty of Science and Techniques, Sidi Mohammed Ben Abdellah University,Morocco2 ECAM-EPMI, France

Corresponding author:Zineb Ibn Majdoub HassaniMechanical Engineering LaboratoryFaculty of Science and TechniquesSidi Mohammed Ben Abdellah UniversityB.P. 2202 – Route d’Imouzzer – FEZ, Moroccophone: +212 667639374e-mail: [email protected]

Received: 3 April 2019 AbstractAccepted: 30 October 2019 In this article we present an industrial application of our mathematical model that integrates

planning and scheduling. Our main objective is to concretize our model and compare thereel results with the theoretical ones. Our application is realized on a conditioning line ofpharmaceutical products at the ECAM EPMI production laboratory. For this reason and tosave time, we used Witness simulation tool. It gives an overall idea of how the line works,the Makespan of each simulation and it highlights areas for improvement. We looked forthe best resulting sequence which corresponds to the minest Makespan and total productioncost. Then this sequence is applied on the conditioning line of pharmaceutical products forsimulation. On the other hand, we program our mathematical model with the parameters ofthe conditioning line under python in version 3.6 and we adopt a simulation/optimizationcoupling approach to verify our model.

KeywordsProduction, planning, scheduling, MILP, optimization, simulation, conditioning line.

Introduction

Over the three last decades, industries are moreinterested in production system. A key aspect ofthe industries is the integration between planningand scheduling. Planning determine the resources,technical operations, the arrangement of operationsand processes needed to produce a job. The result-ing product plan is executed in the operational levelwhere operations of the jobs on machines are sched-uled [1, 2]. Despite, the strong link between plan-ning and scheduling, the integration between thesetwo functions in manufacturing system still a realchallenge for searchers [3].

Planning and scheduling are the most impor-tant key techniques of manufacturing [3, 4]. In an

integrated strategy, planning improves productivitywhile scheduling optimizes process series, expect thatit is not always the case [5].

For entities, compliance with deadlines is a re-al requirement, thus the obligation to ensure thatdeadlines are met at the lowest possible cost. So, wemust find the best compromise between constraintsof planning and scheduling [6]. For [7], there are threestrategies for solving the problem of planning andscheduling• hierarchical,• iterative,• integrated.

In our modulization we choose to follow the in-tegrated strategy of resolution because planning andscheduling are considered as one problem. This strat-

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egy allows to integrate the different operational con-straints at the tactical level. The principle of theintegrated approach aims to define an optimal pro-duction plan for a fixed sequence of the jobs at thetactical level, then yield this production plan to theoperational level where it is fixed, and then its bestcorresponding scheduling is established [6, 8]. Theseoperations are repeated several times to determinethe best compromise between production plan andscheduling. Among the main difficulties of integrat-ing planning and scheduling, is the consideration ofa resource always available and a capability thatdoesn’t reflect the reality. What makes the capaci-ty becomes aggregated and therefore nothing guar-antees that the proposed production plan is feasibleat the scheduling level. This represent the weakness-es of the base models of [9, 10]. Consequently, thiscauses delays and important work in progress in thecase of overestimation of the capacity and the un-derutilization of the capacity in the inverse case. Interms of cost, the production one increase. At theplanning level, it is question of determining the sizesof production batches, whereas in scheduling it is thedefinition of the sequencing of the production orderson the available resources. According to the integrat-ed strategy proposed by [10, 11], a compromise mustbe found between the proposed production plan atthe tactical level and the best sequencing of the jobsat the operational one. The scheduling problem isdefined as the location in time and space of a set oftasks, given the time constraints (a start date witha duration or an end date) and constraints on the useand availability of resources required by the tasks.

Proposed approach

Our model aims to guarantee a feasible produc-tion plan at the scheduling level and introduce moreoperational constraints. The main objective of ourmodel is to propose a feasible production plan atscheduling level, while taking into consideration themaximum of the operational constraints. We usuallyschedule a set of activities so that resource capacitiesare not exceeded and a certain criterion, or objec-tive function, is minimized. In our case, we minimizeproduction, inventory and setup costs without con-sidering the backlog one. One of the major sources ofthe incoherence between planning and scheduling isthe consideration of resources always available. So,we added to the initial model of [12] a constrainton resources availability. It expresses the nature andquantity of resources used by the activities. It alsoavoids the resources consumed to exceed the avail-able capacity of the workshop in each period l.

Nomenclature

The parameters usually used to model this MILPproblem are presented below:Xi,l – quantity to produce from product i in

period l,Yi,l – a setup variable that is equal to 1 if the

product i is made in period l (Xil > 0),0 otherwise,

I+il – positive inventory level of product i atthe end of the period l,

Cpi – production cost per unit of product i,Cinvi – inventory cost per unit of product i,Csi – setup cost per unit of product i,Dil – demand for product i at period l,capal – length of period l (capacity available),αik – resources k consumed by product unit

i (machines),βik – consumption of fixed resources k by

product unit i,capakl – available capacity of resource k at peri-

od l,Li – lead time of the product i,O – all operations,Oi,m,t – operation of the product i to be manu-

factured on the resource m at period t,i(o) – product associated with operation o,l(o) – period associated with operation o,Puo – operating time of the operation O per

unit of the product i(o),So – setup time of the operation O per prod-

uct unit i(o),r(o) – availability date of the operation O,d(o) – desired end date of operation O,A – set of operation pairs in the product

range (O,O′)εA means that operationO precedes operation O′ in the operat-ing range,

L – all the last operations in the operatingranges,

F – all the first operations in the operatingranges,

E – all the pairs of operations that must beproduced on the same resource,

S(y) – all operations associated with the se-quence y,

(o, o′) ∈ S(y) – the operation o precedes the opera-tion o′ in the sequence of a resource.

The integrated model is presented as follow:

MinimizeN∑i=1

T∑l=1

(Cpi Xil + Cinvi Iil + Csi Yil), (1)

Iil = Iil−1 +Xil −Dil ∀ i, l, (2)

4 Volume 10 • Number 4 • December 2019


r(ofc ) +∑oεc

(Puo Xi(o),l(o) + SoYi(o),l(o)

)

≤l(olc)∑l=1

capal ∀ c εC(y),(3)

N∑i=1

αikXil +

N∑i=1

βikYil ≤ capakl ∀ i, l, (4)

Xil ≤

(T∑k=1

Dik

)Yil ∀ i, l, (5)

Xi,l, Iil ≥ 0 ∀ i, l, (6)

Yilε {0, 1} ∀ i, l, (7)

to ≥ 0 ∀ o. (8)

The objective function (1) aims to optimize thecost of production, storage and setup but withoutadmitting the backlog cost. Constraint (2), is theequilibrium equation for the single-level case. Con-straint (3), indicates that the sum of the executionand start times of operations on a path must end be-fore the end date of the last operation of the path.Constraint (4), is the new resource availability con-straint which considers the available capacity of theresources and guaranties that the resources to beconsumed don’t exceed the real availability to avoidthe blocking that results from the unavailability ofresources. Constraint (5), represents a connection

between the decision variables. Constraint (6), en-sures non-negativity of batch size and stock invento-ry. Constraint (7), ensures that the setup variable isbinary. Constraint (8), checks the non-negativity ofthe start dates of the operations.

Experimental study

Conditioning line

Due to an industrial need of an entity locatedin Cergy-pontoise, the planning manager resortedECAM-EPMI to resolve the problem of planning andscheduling of the jobs in a job-shop system. Actual-ly, ECAM-EMPI is a french engineering school ac-credited, it has a production laboratory that pro-vides valuable support for the development of toolsand methods for the modelling, optimization, simu-lation and control of production systems in generaland pharmaceutical conditioning systems in particu-lar. It is a full-scale conditioning line that representsa complete and concrete pharmaceutical manufactur-ing and conditioning plant. This automated transferline is equipped with four flexible workshops con-trolled by a programmable logic controller, all mon-itored by a computerized supervision and manage-ment system.

The existing system presented in Fig. 1, consistsof 7 workstations that are linked together by accumu-lation conveyors and allows the packaging of 3 typesof products (A, B, C).

Fig. 1. Description of the packaging line for pharmaceutical products.

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Each workstation allows a different operation tobe performed. The first station allows the loadingand departure of the pallets, then the dosing andfilling of effervescent tablet of FER, B12 and thenvitamin C. Then there is capping, labelling, unload-ing and finally packaging. The stations are connectedto each other by closed-loop conveyors and anotherone used to package the vials. Push arms facilitatethe passage of pallets from one conveyor to anoth-er and also to do the tour of the stations. At theunloading station there are two cylinders with a suc-tion cup system that take the vials filled with effer-vescent tablet to pack them and then transfer theempty pallet to the conveyor to transmit it to thefirst station. The line is supervised by a computerwhere the production lines are programmed, produc-tion ranges are defined, and the production ordersare launched.

Our modeling is based on a job-shop systemwhere the different products (A, B, C) go through allthe workstations in a different order. Each productconsists of three types of effervescent round tablets,such as FER, B12 and vitamin C.

Each product has a specific order and percentageof each vitamin as shown in Table 1.

Table 1Percentages of each vitamin in the three products.

Product A Product B Product C

FER 20% 42% 30%

B12 50% 46% 5%

Vitamin C 30% 12% 65%

The conditioning line where we make our indus-trial application limits us to 3X7 job-shop types be-cause the order of labelling, capping, unloading andpackaging stations cannot change from one productto another. Therefore, in this application we workwith three production ranges defined according tooperating times. These are related to the dosages ofeach pill in the vials.

Objective

Our main objective is to make an industrial ap-plication of our mathematical model in order to val-idate it and verify its performance in concrete termsand also to satisfy the industrial need presentedby the company. The verification of our model isdone by comparing the results obtained in real op-eration of our system. We then propose a simula-tion/optimization approach that will be the subjectof a concrete study to verify the performance of ourapproach by alternating the two phases. We startby modeling and optimizing our own model in order

to define the optimal cost and the corresponding se-quence. Then, we simulate our system using Witnesscomputer tool to have the best sequence with the op-timal Makespan corresponding to conditioning line.Finally, we test the best sequence given by Witnesson the conditioning line and compare it to the result-ing best sequence according to it total productioncost given by Python using genetic algorithm. Wit-ness simulation is not an optimization procedure, itjust allows as to model many scenarios, save the timeand make comparison.

Simulation tool: WITNESS

Witness is a flow simulation software distribut-ed by Lanner Group, used to simulate productionprocess and provide information on the operation ofthe system. It avoids simulating production underan arbitrary time period and gives an overall ideaof how the production line might operate in realityaccording to [13]. It is also a computer simulationof the consequences of different decisions of produc-tion for [14]. Witness Software is a friendly user ina risk environment, it improves efficiency and pro-ductivity [15]. On the other hand, it is used for mod-eling real-life failures, retooling and preventive main-tenance. Witness is efficient in predicting and solv-ing inefficiencies that may happen in production linessuch as bottlenecks, overly-idle resources, storage ar-eas and any potential issues with respect to laborattending to the processing of parts. It is a simula-tion software performant for modeling discrete andcontinuous elements that can be in different stateslike: busy, waiting, in-setup, broken down, and wait-ing labor and blocked. The platform of the softwarehas a variety of machines as assembly, batch, pro-duction, multiple-station, multiple-cycle and finallysingle machines that can be defined with specific pa-rameters of setup and breakdown in [13].

During the optimization process, different aspectsof the model are varied, and the resulting value forthe objective function will be compared to previousvalues to see if any improvement has taken place.

Experimental modelling

Simulation: conditioning line

The production system presented above wasgradually modelled using Witness predefined ele-ments. We modelled a job-shop with 3 products(A, B, C), each one with its own scheduling anddifferent operating times. We simulated a 3× 7 job-shop, which means we have 3! sequences to simulateon 7 machines. To date, Witness horizon 21 is the



Fig. 2. Conditioning line before the launch of simulation.

Fig. 3. Conditioning line after 48 seconds of simulation.

only tool capable of simulating a job-shop withproducts whose operating times are different foreach product on each machine. Indeed, it representsa graphical and mathematical tool for the analyticalevaluation and simulation of the system in question.

Figure 2 shows the model of the conditioning linestudied before the simulation was launched. Thenthe following Fig. 3 shows the conditioning line afterthe 48-second of simulation.

Definition of production ranges

In this application, we simulate three differentproduction ranges defined by taking into considera-tion the workstations and associated operating times.Indeed, the operating times of each product on eachstation are related to the dosages of each vitaminfilled in the workstation. The Tables 2, 3 and 4 be-low show the operating times of the three productionranges on the items used.



Table 2Definition and operating times of the first range.

Post Operating time

Filling of Fer 6.82

Filling of B12 18.96

Filling of vitamin C 7.5

Capping 21.5

Labelling 5.21

Unloading 20.5

Conditioning 28.6

Table 3Definition and operating times of the second range.

Post Operating time

Filling of Fer 30.03

Filling of B12 3.10


Capping 21.5

Labelling 5.21

Unloading 20.5

Conditioning 28.5

Table 4Definition and operating times of the third range.

Poste Operating time

Filling of Fer 5.72

Filling of B12 6.10


Capping 21.5

Labelling 5.21

Unloading 20.5

Conditioning 28.6

Preliminary study

We started by performing 3! simulations, whichcorresponds to 6 schedules of the 3 product ranges onthe 7 workstations. Then we took for each schedulingthe Makespan and the corresponding production costin order to select the best scheduling whose perfor-mance criteria are the optimal ones. Then we com-pare the results obtained with those found by thereal functioning and those resulting from Python.Figure 4 presents the simulation/optimization ap-proach adopted for our problem.

In our case, the simulation block is representedby the model modeled under Witness, which allowseach scheduling of the three jobs on the 7 machines tocalculate the Makespan. On the other hand, the op-timization block represents our own algorithm thatallows us to find the optimal solution to the problemby using genetic algorithms as a method of resolu-tion programmed in Python 3.6. This optimizationgives the optimal production cost corresponding toa production plan and an optimal sequence of jobs.If the optimal sequence given from the simulation isthe same as the optimization one, then our modelis validated and meets the required constraints. Oth-erwise we must return to the optimization in orderto improve the solution.

Table 5 below represents the six sequences stud-ied with its corresponding Makespan and total pro-duction cost emerged from the programming of ge-netic algorithms under Python.

Fig. 4. Simulation/optimization approach.



Table 5The sequences evaluated with the Makespan and total

production costs.

Witness Python

SchedulingMakespanin seconds

Productioncost

in monetaryunits

Sequence 1 A, B, C 12.35 1127

Sequence 2 A, C, B 12.37 1243

Sequence 3 B, A, C 14.40 1051

Sequence 4 B, C, A 13.13 1068

Sequence 5 C, A, B 12.21 891

Sequence 6 C, B, A 14.13 1259

According to Table 5 and the results found bysimulation using Witness and the optimization usingPython we can conclude that the optimal sequenceis as follows: C, A, B. The simulation under Witnesshorizon 21 gives a Makespan of 12.21 seconds andcorresponding to the 5th sequence, it has the short-est time of resolution.

Also, for the optimization under Python using ge-netic algorithm, the 5th sequence gives the minest to-tal production cost 891 monetary units. Consequent-ly, as result, we confirm the validation of our modeldue to the compatibility of the results between sim-ulation and optimization and the performance of ourproposed approach is asserted.

Conclusion and perspectives

The need expressed by the industry attests to thegreat importance and the hard complexity of plan-ning and scheduling and the intricacy of ensuringconsistency between the production plan and thesequencing of jobs on resources. Hence the interestshown in our approach. This article represents an in-dustrial application of our mathematical model. Theindustrial need presented by the company coincidedwith our need to verify our approach. Indeed, theconditioning line available at ECAM EPMI consistsof a set of production stations, each of which hasan operation performed. In our case we were lim-ited to a 3× 7 job-shop where the different prod-ucts (A, B, C) go through all the workstations ina different order. To verify and validate our mathe-matical model we adopted a simulation/optimizationapproach using Witness 21 for simulation and ge-netic algorithms programmed under Python for op-timization. For so doing, we timed the operatingtimes of each operation on the different stations forthe three products and we simulate under Witness.We obtained for the 3! sequences the correspondingMakespans. The optimal one suits to the best se-

quence of jobs on resources. Then we programmedgenetic algorithms under Python, and we took outthe best sequence of jobs corresponding to the op-timal production cost. The comparison of the bestsequence resulting from the simulation and optimiza-tion is satisfactory, because the best sequence is iden-tical and it’s the optimal in terms of Makespan andtotal production cost. In this way we ensure the va-lidity and performance of our proposed approach andwe have satisfied the request presented to ECAM-EPMI by the industrial entity.

References

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