Felicetto ; Ferrara
email: felicettoferrara@katamail.com

Tiziana Izzo

Clelia Criscuolo

Cira Riccardi

Maria Celentano

Giuseppina Mele

Tiziana Criscuolo

Cira Celentano

Maria Mele

Day 15 bone marrow

Keywords: Acute myeloid leukemia, early blast clearance, double induction

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

For longer than 20 years, the combination of daunorubicin, given for 3 days, with continuous infusion of cytarabine for 7 days (3+7) has been the standard of induction therapy for acute myeloid leukemia (AML). Use of this regimen results in a complete remission (CR) rate of 60-70% in patients up to the age of 60 years [START_REF] Ferrara | Unanswered questions in acute myeloid leukaemia[END_REF][START_REF] Shipley | Acute myelogenous leukemia[END_REF][START_REF] Heerema-Mckenney | Acute myeloid leukemia[END_REF]. Because achievement of a complete response is an absolute prerequisite for long-term survival and cure, several attempts have been made to improve the effectiveness of this regimen in terms of both the rate and quality of remission. These investigations have included use of higher those of daunorubicin or alternative anthracyclines, high-dose cytarabine, regimens that contain fludarabine, a third drug alongside daunorubicin and cytarabine (etoposide or tioguanine), haemopoietic growth factors, and, more recently, addition of monoclonal antibodies or other new agents [START_REF] Mandelli | Daunorubicin versus mitoxantrone versus idarubicin as induction and consolidation chemotherapy for adults with acute myeloid leukemia: the EORTC and GIMEMA Groups Study AML-10[END_REF][START_REF] Fernandez | Anthracycline dose intensification in acute myeloid leukemia[END_REF][START_REF] Löwenberg | High-dose daunorubicin in older patients with acute myeloid leukemia[END_REF][START_REF] Stock | Clinical trials in adult AML[END_REF][START_REF] Fathi | New agents in acute myeloid leukemia: beyond cytarabine and anthracyclines[END_REF][START_REF] Estey | Incorporating novel treatment strategies into conventional therapy[END_REF]. Following conventional induction therapy with 3 days of an anthracycline and 7 days of cytarabine ("3 + 7") or therapies of comparable intensity, response assessment is commonly performed between day 21 and 28 after start of therapy [START_REF] Döhner | Diagnosis and management of acute myeloid leukemia in adults: recommendations from an international expert panel, on behalf of the European LeukemiaNet[END_REF]. However, the exact timing may vary among protocols and should meet the specific objectives of the study. In an further attempt to improve the long-term prognosis of patients with AML, in the nineties the German AML Cooperative Group (AMLCG) introduced the concept of "double induction" (DI). This strategy is focused primarily on patients younger than 60 years and consists of 2 courses of chemotherapy irrespective of the degree of cytoreduction in the bone marrow after the first course, with the second course starting on day 21 unless severe complications prohibit its application [START_REF] Büchner | Double induction strategy for acute myeloid leukemia: the effect of high-dose cytarabine with mitoxantrone instead of standard-dose cytarabine with daunorubicin and 6-thioguanine: a randomized trial by the German AML Cooperative Group[END_REF]. This approach resulted in a significantly longer remission duration and overall survival compared with standard induction in patients with unfavorable features at presentation [START_REF] Büchner | Double induction containing either two courses or one course of high-dose cytarabine plus mitoxantrone and postremission therapy by either autologous stem-cell transplantation or by prolonged maintenance for acute myeloid leukemia[END_REF].

An important factor of potential utility into clinical practice is the early assessment of marrow blasts after administration of induction chemotherapy [START_REF] Elliott | Early peripheral blood blast clearance during induction chemotherapy for acute myeloid leukemia predicts superior relapse-free survival[END_REF][START_REF] Ferrara | Clinically useful prognostic factors in acute myeloid leukemia[END_REF][START_REF] Schneider | NPM1 but not FLT3-ITD mutations predict early blast cell clearance and CR rate in patients with normal karyotype AML (NK-AML) or highrisk myelodysplastic syndrome (MDS)[END_REF]. A threshold value of 10% at day 14-15 from the beginning of chemotherapy is highly prognostically relevant, in that the degree to which the blasts are cleared from the marrow in response to the first course of chemotherapy represents a surrogate for chemoresistance [START_REF] Kern | Early blast clearance by remission induction therapy is a major independent prognostic factor for both achievement of complete remission and long-term outcome in acute myeloid leukemia: data from the German AML Cooperative Group (AMLCG) 1992 Trial[END_REF][START_REF] Gianfaldoni | Clearance of leukaemic blasts from peripheral blood during standard induction treatment predicts the bone marrow response in acute myeloid leukaemia: a pilot study[END_REF]. In order to achieve better therapeutic to WHO classification, by using > 20 % bone marrow blasts as threshold for the diagnosis of AML [START_REF] Vardiman | The 2008 revision of the World Health Organization (WHO) classification of myeloid neoplasms and acute leukemia: rationale and important changes[END_REF]. In all cases, diagnosis was confirmed by immunophenotypic study, as previously described [START_REF] Ferrara | CD56 expression is an indicator of poor clinical outcome in patients with acute promyelocytic leukemia treated with simultaneous alltrans-retinoic acid and chemotherapy[END_REF]. The analysis of FLT3 mutation was performed as previously described [START_REF] Ferrara | Presence of FLT3 mutations does not impair stem cell mobilization and feasibility of autologous peripheral blood stem cell transplantation in acute myeloid leukemia[END_REF]. Analysis of NPM1 mutations in AML cells was performed by fragment analysis according to molecular assay as previously published [START_REF] Ferrara | Favorable outcome in patients with acute myeloid leukemia with NPM1 mutation autografted after conditioning with high dose continuous infusion idarubicin and busulphan[END_REF] to induction death (ID), that is death related to treatment and/or hypoplasia, or as resistant disease (RD), i.e. related to the failure of therapy to eliminate the disease (including partial remission with 5 to 15 % bone marrow blasts after FLAG) [START_REF] Cheson | Revised recommendations of the international working group for diagnosis, standardization of response criteria, treatment outcomes, and reporting standards for therapeutic trials in acute myeloid leukemia[END_REF]. A population of cells with leukaemia-associated aberrant immunophenotype (LAIP) was identified in each patient from the initial BM aspirate. At day 14, FC analysis was performed on BM in order to identify LAIP-positive residual blasts. The degree of BM clearance was expressed as the ratio, converted to logarithmic scale, between the percentage of LAIP positive blasts determined at diagnosis and day 15 [START_REF] Gianfaldoni | Clearance of leukaemic blasts from peripheral blood during standard induction treatment predicts the bone marrow response in acute myeloid leukaemia: a pilot study[END_REF].

Disease-free survival (DFS) was defined as the time from CR achievement until the month of relapse, death from any cause or the date of last follow-up. Overall survival (OS) was defined as the time from diagnosis to death or last follow-up. Either DFS or OS were calculated by Kaplan-Meier method [START_REF] Kaplan | Non-parametric estimation from incomplete observations[END_REF]. All statistical comparisons used two-tailed p-value. The p-value used to define statistical significance was 0.05.

Results

Among 33 consecutive patients found with more than 10 % blast cells at morphological and or immunophenotypic evaluation, 30 Either WBC or platelet recovery from the start of induction chemotherapy was significantly longer for the group managed with double induction than controls (38 days vs. 21 days for neutrophils and 43 days vs. 23 for platelets, p.=.001 and 0.003, respectively). In addition, the need for RBC and platelet support was significantly higher for DI patients as opposed to controls (median RBC Units:

15 vs 9, p 0.01; median platelet units: 16 vs. 8, p:0.006, respectively); finally, the duration of hospitalization was significantly longer for DI patients as opposed to those in the control group 44 days (39-65) vs. 30 days (22-44), p: 0.005. Notwithstanding, there was neither difference in induction death rate, nor in the overall incidence of FUO and documented infections (see table 3).

Finally, the incidence of grade 3 or 4 non hematologic toxicity, consisting of diarrhea, liver enzyme elevation and stomatitis was comparable. All remitters were consolidated with an additional course of FLAG and were programmed to receive allogeneic stem cell transplantation, given that all of them were considered at high risk because of persistent leukemia at day 15 BM examination [START_REF] Morra | Clinical management of primary non-acute promyelocytic leukemia acute myeloid leukemia: Practice Guidelines by the Italian Society of Hematology, the Italian Society of Experimental Hematology, and the Italian Group for Bone Marrow Transplantation[END_REF]. Overall, 11 out of 20 patients (55%) received allogeneic BMT; of these, 7 are alive in

Discussion

Double induction treatment is based on early administration of a second course of induction, which is usually given independently of bone marrow status [START_REF] Döhner | Diagnosis and management of acute myeloid leukemia in adults: recommendations from an international expert panel, on behalf of the European LeukemiaNet[END_REF]. In a randomized study, Buchner and coworkers administered either conventional or more aggressive therapy based on high-dose cytarabine as second induction on day 21 after therapy was started [START_REF] Büchner | Double induction strategy for acute myeloid leukemia: the effect of high-dose cytarabine with mitoxantrone instead of standard-dose cytarabine with daunorubicin and 6-thioguanine: a randomized trial by the German AML Cooperative Group[END_REF]. Toxic effects were substantial, and a survival advantage from receiving the more aggressive treatment was limited to poor-risk patients. More recently, the AMLCG has piloted a dose-dense induction regimen sequential high-dose AraC and mitoxantrone followed by pegfilgrastim (S-HAM) in which two induction cycles are applied over 11 to 12 days instead of 25 to 29 days as used in conventional double induction, thereby increasing dose density two-fold [START_REF] Braess | Dose-dense induction with sequential high-dose cytarabine and mitoxantone (S-HAM) and pegfilgrastim results in a high efficacy and a short duration of critical neutropenia in de novo acute myeloid leukemia: a pilot study of the AMLCG[END_REF]. Importantly, the compression of the 2 induction cycles into the first 11 to 12 days of treatment was beneficial for normal hematopoiesis as demonstrated by a significantly shortened duration of critical neutropenia of 31 days compared with 46 days after conventionally timed double induction [START_REF] Braess | Dose-dense induction with sequential high-dose cytarabine and mitoxantone (S-HAM) and pegfilgrastim results in a high efficacy and a short duration of critical neutropenia in de novo acute myeloid leukemia: a pilot study of the AMLCG[END_REF].

The main difficulty of double induction is that it relies on the judgment of the attending physician as to the eligibility of patients for the second induction. Although eligibility by itself can be an important outcome to determine, it is conceivable that the physician's personal attitude will significantly affect the results-especially given the variety of the clinical status of patients, mainly in terms of suspected or documented infections [START_REF] Ferrara | Unanswered questions in acute myeloid leukaemia[END_REF]. Because the data from the German trials suggested that the survival advantage of double induction was limited to the poor-risk category, phase, was not significantly higher for the more intensive arms; notwithstanding, event-free survival and overall survival were similar in the 3 randomization arms [START_REF] Castaigne | Randomized comparison of double induction and timed-sequential induction to a "3 + 7" induction in adults with AML: long-term analysis of the Acute Leukemia French Association (ALFA) 9000 study[END_REF].

Our approach was unique in that administration of DI was based on bone marrow status at day 15.

The timing was established on the basis of previous observations, which did clearly demonstrate that patients with absence or low blast count day 15 BM, which reflects major sensitivity to induction therapy, had a significantly better clinical outcome as compared to those with persistent leukemia [START_REF] Elliott | Early peripheral blood blast clearance during induction chemotherapy for acute myeloid leukemia predicts superior relapse-free survival[END_REF][START_REF] Ferrara | Clinically useful prognostic factors in acute myeloid leukemia[END_REF][START_REF] Schneider | NPM1 but not FLT3-ITD mutations predict early blast cell clearance and CR rate in patients with normal karyotype AML (NK-AML) or highrisk myelodysplastic syndrome (MDS)[END_REF][START_REF] Kern | Early blast clearance by remission induction therapy is a major independent prognostic factor for both achievement of complete remission and long-term outcome in acute myeloid leukemia: data from the German AML Cooperative Group (AMLCG) 1992 Trial[END_REF]. As DI, we decided to employ the FLAG regimen, which has been proven as useful and safe for poor prognosis AML as well as for high risk MDS. In addition, FLAG regimen delivers high-dose treatment without increasing overall toxicity, an approach which is of particular interest in patients potentially candidate to receive further chemotherapy, while being severely pancytopenic from previous conventional induction [START_REF] Martin | Salvage therapy for acute myeloid leukemia with fludarabine, cytarabine, and idarubicin with or without gemtuzumab ozogamicin and with concurrent or sequential G-CSF[END_REF][START_REF] Borthakur | Treatment of core-binding-factor in acute myelogenous leukemia with fludarabine, cytarabine, and granulocyte colony-stimulating factor results in improved event-free survival[END_REF][START_REF] Ossenkoppele | The value of fludarabine in addition to ARA-C and G-CSF in the treatment of patients with high-risk myelodysplastic syndromes and AML in elderly patients[END_REF][START_REF] Ferrara | De novo acute myeloid leukemia with multilineage dysplasia: treatment results and prognostic evaluation from a series of 44 patients treated with fludarabine, cytarabine and G-CSF (FLAG)[END_REF][START_REF] Ferrara | Fludarabine, cytarabine, and G-CSF (FLAG) for the treatment of acute myeloid leukemia relapsing after autologous stem cell transplantation[END_REF]. Of note, 30 out of 33 patients (91 %) of patients were considered as clinical eligible to receive a second induction therapy, causes of non eligibility being in all cases severe active infections. In spite of severe pancytopenia at the start of DI, toxic death rate was low and comparable to that we observed after conventional induction, confirming the tolerability of the FLAG regimen. The absence of anthracyclines could account for the favorable results we observed in terms of treatment related mortality (TRM) and eligibility to the programmed allo-SCT. In this regard, it is noteworthy that the only reason for exclusion from allo-SCT was early relapse while patients were in the waiting list.

Even though we cannot exclude that some patients would achieve CR without receiving DI, the 67% CR rate we observed is remarkable, if we consider that 65 % of patients had unfavorable cytogenetics and no one of them were found positive for NMP1 mutation in absence of FLT3/ITD mutations. Indirectly, our findings seem to confirm previous data suggesting that NPM1+/FLT3-AML is associated with peculiar sensitivity to conventional chemotherapy, mainly to anthracyclines [START_REF] Falini | Acute myeloid leukemia with mutated NPM1: diagnosis, prognosis and therapeutic perspectives[END_REF][START_REF] Falini | Altered nucleophosmin transport in acute myeloid leukaemia with mutated NPM1: molecular basis and clinical implications[END_REF]. Such an assumption was recently suggested by data in young adults with AML, in whom intensifying induction therapy with a higher daily dose of daunorubicin improved the rate of complete remission and the duration of overall survival, as compared with the standard dose, only in patients with intermediate cytogenetics, in whom most NPM1+ AML cases are found [START_REF] Fernandez | Anthracycline dose intensification in acute myeloid leukemia[END_REF][START_REF] Löwenberg | High-dose daunorubicin in older patients with acute myeloid leukemia[END_REF].

As expected, hematologic toxicity was substantially higher in patients receiving DI as compared to historical controls, who achieved CR after one course of chemotherapy. This did also result in need for more transfusion support and prolonged hospitalization. On the contrary, there was no difference in the overall non hematological toxicity and all remitters were able to receive further

than 5 %

 5 Patients aged up to 60 years with de novo AML were given induction treatment consisting of ICE [idarubicin 10 mg/ sqm on days 1, 3 and 5; cytarabine (ARA-C) 100 mg/sqm as continuous infusion (c.i.) on days 1-7; etoposide 100 mg/sqm on days 1-4]. As second induction, we administered the combination of fludarabine (F), intermediate dose cytarabine (ARA-C) and G-CSF (FLAG). More in detail, F was given at 30mg/ m 2 /day as 30min intravenous perfusion and ARA-C 2g/m 2 /day 3 hour and half after the end of F from day 1 to 5. G-CSF at 300 µg was concomitantly given from day 1 up to CR achievement. Patients were judged as eligible to receive DI, provided that neither active infections, nor non hematologic toxicities > 2 according to WHO criteria were registered at day 15 from the start of induction. Criteria for CR included normal peripheral blood count in the absence of blast cells, bone marrow blast percentage less and absence of extramedullary leukemia. Remission failures were classified as either due

  and died; finally, 1 patient died for severe graft versus host disease after allo-SCT. Nine patients received consolidation with FLAG, followed by two courses of high dose ARA-C. Among these, three are in continuous CR, 6 relapsed while waiting for allo-SCT from unrelated donor. One patient achieved second CR and is in a waiting list for allo-SCT. Eight relapsed patients died in the setting of refractory disease. OS and DFS for the whole patient population are 12 and 15 months, respectively, as shown in fig 1.

  use of double induction to treat all patients with AML seems inappropriate: a substantial proportion might have unnecessary life-threatening toxic effects, not justified by stratification for risk factors at diagnosis. The potential utility of DI was also investigated in a randomized study aimed at comparison of double induction and timed-sequential induction to a "3+7" induction in adults with AML. Treatment related mortality, either during the induction or the postremission

Table 3 -

 3 Comparison of hematopoietic recovery and non hematologic toxicity between patients managed with double induction and a control groups of 30 patients, matched for age, achieving CR after one cycle of induction.

		Double induction	Controls	P value
	Toxic death	2 (6%)	2 (6%)	1
	Neut > 0.5x10E9/L, days*	38(30-49)	21 (17-25)	0.001
	(range)
	Plat > 20x10E9/L, days*	43 (33-48)	23 (16-29)	0.003
	(range)
	FUO	22 (73%)	20 (67%)	0.58
	Documented infections	8 (27%%)	6 (20%)	0.45
	Bacterial	5	4	0.67
	Fungal	3	2
	Grade 3 or 4 non
	hematological toxicity
	Liver Stomatitis Diarrhea	4 (13%) 4 (13%) 3 (10%)	2 (7%) 3 (10%) 3 (10%)	0.67 0.99 1
	RBC units	15 (7-21)	9 (5-14)	0.32

* From the start of induction chemotherapy

  Of note, in this series no patient had favorable cytogenetics, i.e. either t(8;21) or inv[START_REF] Kern | Early blast clearance by remission induction therapy is a major independent prognostic factor for both achievement of complete remission and long-term outcome in acute myeloid leukemia: data from the German AML Cooperative Group (AMLCG) 1992 Trial[END_REF] or NPM1 isolated mutation.Therapeutic results and non hematologic toxicity are summarized in table 2. Overall, CR was achieved in 20 patients (67%), while 8 patients (27%) were classified as refractory. Finally, two patients ( 6 %) died from severe infectious complications while severely cytopenic. Of interest, all refractory patients had unfavorable cytogenetics. All patients experience fever; more in detail, there were 22 episodes of FUO (fever of unknown origin) and 8 documented infections (5 bacterial and 2 fungal, both lung aspergillosis). The median number of days for recovery to neutrophils > 0.5 x 10 9 /l and platelets > 20 x 10 9 /l from the start of DI was 20 and 22, respectively, while from the start of the first induction 38 (30-49) and 43 days[START_REF] Ferrara | Fludarabine, cytarabine, and G-CSF (FLAG) for the treatment of acute myeloid leukemia relapsing after autologous stem cell transplantation[END_REF][START_REF] Falini | Acute myeloid leukemia with mutated NPM1: diagnosis, prognosis and therapeutic perspectives[END_REF][START_REF] Falini | Altered nucleophosmin transport in acute myeloid leukaemia with mutated NPM1: molecular basis and clinical implications[END_REF][START_REF] Fernandez | Anthracycline dose intensification in acute myeloid leukemia[END_REF][START_REF] Löwenberg | High-dose daunorubicin in older patients with acute myeloid leukemia[END_REF](38)(39)(40)(41)(42)(43)(44)(45)(46)(47)(48) were needed, respectively. Patients

	neither FLT3 nor NPM1 mutations.
	F o r
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	morphological and immunophenotypic evaluation of day 15 blast cells (30 % by morphology, 28 %
	by immunophenotype, p:0.86). According to cytogenetic examination, 11 patients had normal
	karyotype (median blast count: 18%), while 19 patients were found with unfavorable patterns,
	including complex karyotype in 14 patients and chromosome 5 or 7 abnormalities in 5 patients). In
	this subgroup, the median day 15 blast count was 58 % and was significantly higher than the group
	with normal karyotype (p:0.004). Among patients with diploid karyotype, 6 patients had FLT3/ITD
	mutation, which was found as concomitant with NPM1 mutation only in 1 patient; 4 patients had
	6

(91%) were judged as clinically eligible to receive further chemotherapy with FLAG. Reasons for exclusion in three patients included in all cases active pulmonary infection (bacterial in two and fungal in one patient) in the context of severe pancytopenia. Notwithstanding, as summarized in table 1, all patients were severely neutropenic at day 15 (median WBC count: 0.4 x 10E9/L, range 0.1-1.0; median neutrophil count 0.3 x 10E9/L, range 0-0.5). The median percentage of day 15 bone marrow blasts, as evaluated at morphological examination, was 35 % (15-90). Of note, there was no statistically significant difference between received a median of 15 packed red cells (range: 7-21) and 16 platelet units (range: 7-26). Data concerning hematopoietic recovery and supportive therapy are summarized in table

3

, in which a comparison between DI patients with a series of 30 patients matched for age, in whom CR was achieved after one course of chemotherapy, is also showed. The control group, in which CR was achieved in 25 out of 30 patients (83%), was selected within the same sequential cohort as the patients with persistent blasts. Of note, in this group more patients presented with favorable and intermediate cytogenetics as well as with favorable molecular findings (p:0.001 and 0.02, respectively) as indicated in table 1.

Table 1 -

 1 stem cell transplantation. Better therapeutic results were achieved in patients who did actually receive allo-SCT, confirming that persistent leukemia at day 15 represents a main adverse prognostic factor in AML, needing appropriate management based on more aggressive induction followed by allo-SCT. In this study, donor research was started after CR achievement. However, it seems more reasonable to start research as soon as persistent leukemia at day 15 is documented; in addition, any potential alternative stem cell source, including haploidentical donors or cord blood, would be considered.In conclusion, day 15 bone marrow driven DI represents a safe and effective therapeutic strategy in AML. As compared to conventional DI, which is usually administered irrespectively of bone marrow status, it offers the potential to avoid unnecessary toxicity in a consistent proportion of patients. Finally, any effort should be made to offer allogeneic stem cell transplantation to patients with persistent leukemia at day 15 examination. Main characteristics of 30 patients with persistent leukemia at day 15 receiving double induction

	intensification followed by
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	9


Pedro L Gonzalez-R

Jose M Framinan

Rafael Ruiz-Usano

A multi-objective comparison of dispatching rules in a Drum-Buffer-Rope production control system

Keywords: PRODUCTION CONTROL, PRODUCTION MANAGEMENT, OPTIMIZATION user): Theory Of Constraints Production Control systems, Drum-Buffer-Rope, Theory Of Constraints, Taguchi, Multiobjective

The advantages of the TOC (Theory of Constraints) philosophy have been extensively documented in the literature since its introduction during the 80s. At the operational level, TOC is implemented by means of the well-known DBR (Drum-Buffer-Rope) production control system. In a multiproduct manufacturing environment, the performance of DBR is greatly affected by the dispatching rules employed in front of the bottleneck station. Furthermore, it has been proved that no single Dispatching Rule (DR) performs globally better than any others. Therefore, for systems usually influenced by variability conditions, the selection of a robust DR could help practitioners to reach a good system performance. In this paper we propose a methodology to obtain a robust DR (by means of Taguchi signal-to-noise ratio) from a set of previously selected rules according to the performance measures of the system pursued by the practicing managers. We study the performance of different dispatching rules for several conflicting objectives (namely average tardiness, maximum tardiness, and WIP) from a robustness viewpoint and for a range of manufacturing scenarios in a shop floor formed by five stations in line and three different products.

Different variability sources, such as processing times, breakdowns and set-ups, are discussed. The results obtained are of special interest for practitioners.

-3 -as global scheduling seems to be unsuitable in these cases. Indeed, [START_REF] Aytug | Executing production schedules in the face of uncertainties: a review and some future directions[END_REF] and [START_REF] Lawrence | Heuristic, optimal, static and dynamic schedules when processing times are uncertain[END_REF] remark that for systems with high uncertainty (as in the system under consideration in our work), completely reactive algorithms (i.e. dispatching rules) can be used with relative confidence and question the benefits of global scheduling procedures. In this line, the influence of priority rules on the performance of different production control systems has been studied by several authors (see e.g. [START_REF] Montarezi | Analysis of scheduling rules for an FMS[END_REF], Kayton et al. 1997[START_REF] Lixing | Scheduling MEMS Manufacturing[END_REF], or [START_REF] Lee | Multiple-Objective scheduling and real-time dispatching for the semiconductor manufacturing system[END_REF].

The previous works compare the performance of a set of dispatching rules for a specific manufacturing scenario according to a single criterion. However, when selecting a suitable dispatching rule in practice, one should balance several (usually conflicting) criteria. This is a key issue, as previous simulation studies show that no single dispatching rule outperforms the other for every objective (see e.g. Montazeri and Van Wassenhove, 1990, or Pierreval andMebarki, 1997). Focussing specifically on the DBR system, some contradictory results are found. [START_REF] Chakravorty | An evaluation of the DBR control mechanism in a job shop environment[END_REF] stressed in his conclusions that more research regarding the influence of the DRs in DBR systems should prove to be useful for both researchers and practicing managers. The author only studied the SPT and FCFS rule, obtaining better results for the SPT rule. These results seem to be contrary to those obtained by [START_REF] Schragenheim | Drum-buffer-rope shop floor control[END_REF] and [START_REF] Umble | Synchronous Manufacturing: Principles for World Class Excellence[END_REF] which obtained a poor performance of SPT. Furthermore, Kayton et al. (1996) and Kayton et al. (1997) studied the FCFS and the CR rule, showing that the best performance was obtained by the CR rule. [START_REF] Daniel | Scheduling with priority dispatching rules y drum-buffer-rope in a recoverable manufacturing system[END_REF] focused their work in the influence of the DRs for non-bottleneck buffers, obtaining the better results for the FCFS and EDD rules. Other results have been obtained for different shop floor conditions, such as assembly and shared machines (Kayton et al. 1997), reprocessing [START_REF] Daniel | Scheduling with priority dispatching rules y drum-buffer-rope in a recoverable manufacturing system[END_REF], or job shop environments [START_REF] Chakravorty | An evaluation of the DBR control mechanism in a job shop environment[END_REF].

It is clear that DR performance is highly influenced by the production scenario, but it is also obvious that changes in the manufacturing environment due to the inherent variability of the shop floor can influence this performance as well. Therefore, it is not useful to select a dispatching rule if its performance quickly -4 -deteriorates when the initial conditions change due to breakdowns, unbalancing, set-ups, etc. In order to correctly select a DR, two possible approaches can be distinguished: (1) introducing a more or less sophisticated mechanism that dynamically switches in real-time the DR and select the best one, according to the environmental conditions, or (2) selecting a robust DR, i.e. using a DR which can stand different environmental changes. The former approach is known as Switch From Standard Rules (SFSR) heuristics (see [START_REF] Ramesh | Dynamic job shop scheduling: a survey of simulation research[END_REF] for a survey of dynamic DRs). Some recent works used a Neuronal Network for a dynamic selection of DRs (see e.g [START_REF] Mouelhi-Chibani | Training a Neural Network to select dispatching rules in real Computers & Industrial Engineering[END_REF]. [START_REF] Lee | Multiple-Objective scheduling and real-time dispatching for the semiconductor manufacturing system[END_REF] based their approach on a model based on the extended object oriented Petri nets (EOPNs). To our best knowledge, the second approach (selecting a robust DR) is novel and constitutes the main contribution of this paper.

Although the main advantage of the SFSR approach is its efficiency, these methods are too much sophisticated and require a real-time monitor in order to be implemented in practise. This aspect goes against the TOC philosophy and DBR, which advocate easy methods to be used in practise. Therefore, our work focuses on the second approach, analysing the influence of dispatching rules in the performance of a DBR system and trying to determine the most robust one under certain variability conditions.

In order to do that, we first conduct an experimental design based on several sources of variability taken from real manufacturing environments, i.e.: stochastically time process, unbalanced lines, machine breakdowns or set-up times. By using simulation, three locally performance measures widely used in manufacturing practice, i.e.: average tardiness, maximum tardiness, and average work in process (see e.g. Blackstone et al., 1982[START_REF] Baker | The effects of input control in a simple Scheduling model[END_REF][START_REF] Lalas | A simulation-based hybrid backwards scheduling framework for manufacturing systems[END_REF] are calculated. Finally, the global performance of each dispatching rule for different scenarios is computed according to its robustness, employing Taguchi's robustness concepts, which are widely used in selection problems (see Taguchi, 1996 and[START_REF] Moeeni | A robust design methodology for Kanban system design[END_REF].

The remainder of this paper is organised as follows: In section 2, the DBR production control system is described. Section 3 is devoted to describe the conditions of the experiments, such as flow line parameters, The DBR production control system is derived from the Theory of Constraints (TOC) introduced by Goldratt during the 80s (see e.g. [START_REF] Goldratt | The Goal: An Ongoing Improvement Process[END_REF]. It is known that a great number of companies have implemented TOC successfully [START_REF] Mabin | The World of the Theory Of Constraints: A Review of the International Literature[END_REF], while there is a certain interest in the mechanism among practicing managers (Erenguc et al. 1997). This methodology was a result of previous studies and the development of the production planning software known as OPT (Optimized Production Technology). TOC is based on the premise that the rate of goal achievement is limited by at least one constraining process. Only by increasing flow through the constraint can overall throughput be increased (see e.g. [START_REF] Goldratt | The Goal: An Ongoing Improvement Process[END_REF]. From the 90s up to now, TOC concepts were opened to the management field, being this extension known as Thinking Process, TP (see e.g. Goldratt, 1990, or Ye and[START_REF] Ye | Determination of buffer sizes for drum-buffer-rope (DBR)-controlled production systems[END_REF].

The Five Focusing Steps of TOC are [START_REF] Goldratt | The Haystack Syndrome, sifting information in the data ocean[END_REF]:

1. Identify the system constraint(s) 2. Exploit the constraint(s) 3. Subordinate all other decisions to step 2 4. Elevate the constraint 5. If constraint has moved, return to step 1. Don't let inertia become the constraint.

At the shop floor level, TOC is usually implemented by means of the DBR production control system. DBR is composed by three elements: Drum, Buffer and Rope. [START_REF] Goldratt | The Goal: An Ongoing Improvement Process[END_REF] show that the lower capacity station governs the throughput rate of the entire manufacturing line. This station is known as the 'drum', or CCR (Capacity Constraint Resource). The input control mechanism is the 'rope', and it is -6 -based on the utilization of the bottleneck. Finally, the 'buffer' represents the time period for an early arrival of jobs to the bottleneck from the entrance in the system. A detailed description DBR production control system can be found in [START_REF] Goldratt | The Goal: An Ongoing Improvement Process[END_REF], [START_REF] Goldratt | The Race[END_REF], [START_REF] Schragenheim | Drum-buffer-rope shop floor control[END_REF] or [START_REF] Spencer | Optimum production technology (OPT) and the theory of constraints (TOC): analysis and genealogy[END_REF].

Two alternative input control mechanisms could be employed in the DBR system [START_REF] Goldratt | The Haystack Syndrome, sifting information in the data ocean[END_REF]): In the first case ('time buffer'), an input rate is established, while the work in process (WIP) upstream the CCR fluctuates according to the stochastic behaviour of the system. Note that this rate should be periodically adjusted, otherwise it can result in infinite WIP. In the second case ('WIP buffer'), WIP upstream the CCR is established, while input rate fluctuates. Most authors (see e.g. [START_REF] Lambrecht | Buffer stock allocation and assembly type production lines[END_REF][START_REF] Ramsay | Push, pull and squeeze shop floor control with computer simulation[END_REF][START_REF] Gilland | A simulation study comparing performance of Conwip and bottleneck-based release rules[END_REF] adopt the latter mechanism in their works, thus describing a DBR control system which limits the maximum WIP upstream the bottleneck by using cards to authorise the entrance of jobs in the system. This mechanism is similar to the Conwip production control system [START_REF] Spearman | Conwip: a pull alternative to Kanban[END_REF], although the latter limits the WIP in the whole system. In Figure 1 is shown a typical implementation of the WIP-buffer DBR system for a line formed by five stations in tandem, with a bottleneck station in the central position.

[Insert Figure 1 about here] Figure 1. WIP-buffer DBR implementation

In Figure 1, the flow of material is shown in continuous line, while the flow of cards is represented in doted lines. The input control procedure is as follows: a job can enter the system if there is at least one card in the control panel. If so, the card is attached to the job until the job finishes it operation in the CCR.

Once the job exits the CCR, the card is released and sent back to the control panel. Clearly, the maximum WIP is bounded by the number of cards in the system, being this number the main parameter governing its performance. As discussed before, the WIP upstream the CCR is limited by employing cards. As we consider a multiproduct environment, individual cards counts can be set for each job (M-Closed input rule), or by establishing a single card count for all jobs (S-Closed input rule). Since [START_REF] Duenyas | A simple release policy for network of queues with controllable inputs[END_REF] and Framinan et al. (2000) show that M-Closed is more effective than S-Closed, different card counts are employed for each product type (see Figure 2). In the system under consideration, the type of product that is allowed to enter the system is determined by the type of cards available in the control panel, and consequently there is no need to establish an input sequence for the jobs. Although in the long term time-buffer and WIP-buffer approaches are intertwined with Little's Law, in the sequel we adopt the latter, as it is the most often described and employed in practise.

Research Methodology

The research methodology is presented in five sections. First, we describe the model and hypotheses considered in the subsequent experiments. Next the selected DRs are introduced. Local performance measures for the system working under a certain DR are explained and the global performance measure to be computed for each DR over all scenarios is explained through the robustness concept, as well as the way to compute it. Finally, the scenarios to be conducted are presented. The proposed methodology can be summarized in the following steps:

1. System description. As mentioned earlier, DRs are very sensitive to the type on system (flow-shop, job-shop, assembly, etc,...). Detail all sources of variability in the system: set-up, breakdowns, reentrant flows, etc,... They will be considered as noise factors in order to compute the robustness.

2. Selection of local performance measures. Take into account the performance measures for the environment as well as the management point of view: average tardiness, WIP, service level,... These local criteria will be used also as noise factors, in order to obtain robust DRs under different performance measures.

System description

Our study focuses on a flow-line formed by five stations in tandem using the DBR system shown in Figure 2. The problem under consideration is based on a real-life problem encountered at a gear-box factory, where three types of parts have to be produced in the same line, sharing the same machines, and later assembled in the gear box. In this line, the machines had breakdowns as well as set-up times were necessary in order to change the tools. These variables, based on a real-life problem are introduced in our model. We consider infinite raw material availability in the first station, i.e. jobs may enter the system if there are kanbans available for this job type in the control panel. The work in process (WIP) start counting once the job is entered the system. This is a common assumption in this type of simulation studies (see e.g. [START_REF] Bonvik | A comparison of production-line control mechanisms[END_REF]. Each station is composed of an input buffer and a machine. We consider three different types of products (I, II and III), sharing the same bottleneck under a make-to-order environment.

The bottleneck is located in the central station of the line. Every buffer operates under a FCFS (First Come First Served) dispatching rule as suggested by [START_REF] Umble | Synchronous Manufacturing: Principles for World Class Excellence[END_REF], with the exception of the CCR buffer, which could follow different dispatching rules. For every type of job is defined a target level of jobs produced in the simulation period, defined as the 20%, 30% and 50% for jobs type I, II and III respectively.

The system variability was modelled through processing time variation, CCR downtime and set-up times inclusion, following the recommendations of [START_REF] Law | Simulation Modeling and Analysis[END_REF] and trying to reproduce a hypothetical situation of a real environments. Processing times were generated from a log-normal -9 -distribution with means 15.0, 10.0 and 5.0 and a coefficient of variation (cv) equals to 0.2. The system performance is studied according two different levels of the CCR processing times, increased a 15% or 30% regarding to the processing times of the non-bottleneck stations. Additionally, we consider system downtime and set-up in the CCR for certain scenarios. These are only considered for the bottleneck station, as it has been shown that fluctuations in the bottleneck station influence the performance of the system more than similar fluctuations in other stations (see e.g. [START_REF] Fry | An analysis and discussion of the optimized production technology software and its use[END_REF]. Breakdowns were generated by exponential distributions with mean of 100 for the MTBF (Mean Time Between Failures) and 25 for the MTTR (Mean Time To Repair). This constitutes a system down time of 20%, or an availability of MTBF/(MTBF+MTTR) equals to 0.8. The CCR utilization rate was established to 95% for those scenarios without downtimes and 80% for those with breakdowns. For those scenarios with set-up times, a set-up time generated by a log-normal with mean a set-up time of 100 and a cv of 0.2, each time a new type of job is processed on the bottleneck. Finally, in order to set the due-dates of each job, we consider that at least a 10% of the jobs are considered as urgent, similar to Kayton et al. (1997). Thus for jobs released at time t, the due dates i DD of job i are given by

∑ + = j ij i t K t DD •
, where: By using this method we can obtain a certain guarantee about the independence of the i DD , avoiding the correlation of due dates with certain rules. Additionally, has been taken into account some constrains regarding the throughput for every product type. Therefore, it was established that the percentage of finished jobs in the simulation horizon for every type of job should be greater than a target value less an allowance factor of 5%. Thus, the target throughput mix is 20%, 30% and 50% for products I, II and III respectively.

Local performance measures

The system's performance was measured locally for every scenario using three different criteria. Two criteria were used to asses the system's ability to deliver in time. One criterion was the mean tadiness.

Previous research has shown that mean tardiness, T , measured as the average amount of positives times by wich the completion time of a job exceeds its due date, are good measures to evalute the performance of scheduling systems (Blackstone et al., 1982). The other criterion was the maximum tardiness, max T , (see e.g. [START_REF] Lalas | A simulation-based hybrid backwards scheduling framework for manufacturing systems[END_REF]. The last studied criterion was the average work in process, WIP , i.e. the average amount of jobs in the line (see e.g. [START_REF] Chang | Ranking dispatching rules by data envelopment analysis in a job shop environment[END_REF]. Usually, the mean flow time is measured, however, [START_REF] Baker | The effects of input control in a simple Scheduling model[END_REF] has shown that there is a direct relationship between WIP and mean flow time.

Selected Dispatching rules

The selection of a set of candidate DRs is not an easy task, because of the contradictory results reported in literature and the vast research regarding the topic. There are several reviews: see e.g. Blackstone et al. (1982), [START_REF] Baker | The effects of input control in a simple Scheduling model[END_REF], [START_REF] Montarezi | Analysis of scheduling rules for an FMS[END_REF], [START_REF] Ramesh | Dynamic job shop scheduling: a survey of simulation research[END_REF], Engell and Moser (1992),

or [START_REF] Panwalkar | Dynamic selection of dispatching rules for manufacturing system scheduling[END_REF] who classified 113 DRs. However, a universally accepted result of these studies is that no DR performs globally better than any others (Pierreval and Mebarki, 1997). Therefore, in our study it seems reasonable to use some DRs according to the environment and performance measures selected in the previous steps. According to that we have selected the following DRs: SPT, SRPT, LPT, SI, EDD, LS, CR, FCFS and SRO. DRs based on times (such SPT or SRPT) performs well on minimising the mean flowtime (or minimising the WIP), but obtain poor results for other criteria such minimising the maximum tardiness. The LPT is introduced as a benchmark for a comparison against other time-based rules. Rules based on due dates could work well in order to produce a delivery of jobs in time. This is the reason to include EDD, LS, CR, and the SI rules (in the appendix, the reasons to consider the SI rule as a due date based DR are explained). The NSUT rule could be interesting for this environment under set-up events. The FCFS rule is also included because it works well for a wide variety of conditions. Finally, the Note that the selection of these rules has been done taking into account also those focused on their influence in the performance of a DBR system (see e.g. [START_REF] Schragenheim | Drum-buffer-rope shop floor control[END_REF][START_REF] Daniel | Scheduling with priority dispatching rules y drum-buffer-rope in a recoverable manufacturing system[END_REF][START_REF] Chakravorty | An evaluation of the DBR control mechanism in a job shop environment[END_REF]. Finally, we also take into account the work of [START_REF] Fry | An analysis and discussion of the optimized production technology software and its use[END_REF], who discuss the influence of set-up times in the bottleneck.

Scenarios

In our analysis we consider two different scenarios depending on the absence or existence of set-up times (scenarios A and B, respectively). For each scenario, we consider two different situations depending on the values of two parameters: b t ∆ , the increment of processing time in the bottleneck station (which can take the values +15% or +30% compared to those in other stations, as described in a previous section), and the existence or not of machine breakdowns (typed as YES or NOT), with the MTBF and MTTR values described in section 3.1. The combinations of the mentioned two variables -that is, a 2 2 or full factorial design-yields four different experiments for each scenario to test each dispatching rule. The full study implies a total amount of 228 experiments. For each mean value, a 99% confidence interval has been taken into account. For each scenario has been obtained the best set of kanbans that reach the best performance for the studied scenario using the ARENA 12.0 simulation software and the OptQuest optimization tool.

Regarding the simulation horizon, some pilot experiments were conducted to appropriately set a single long run of 350 10 3 time units and a warm-up of 10 3 in order to obtain statistically reliable results.

Global performance measure: Robustness

As mentioned earlier, there is a vast body of research dealing with the DR, and a few works studying their influence in the DBR system under different criteria. However, to our best knowledge, there is not study trying to determine the DR under different variable conditions and taken into account all different criteria globally. Regarding to this concern, the robustness concept may play an important role in order to assess the practitioners for a DR -or a ranking of DRs -which may be applicable to some real life scenarios. The Taguchi's robustness concepts were traditionally used as tools to select among different products, process or services (see e.g. [START_REF] Moeeni | A robust design methodology for Kanban system design[END_REF][START_REF] Taguchi | Introduction to Off-line Quality Control[END_REF][START_REF] Taguchi | Introduction to quality engineering: designing quality into products and processes[END_REF]. Although

Taguchi methods are not free of criticism, they have been successfully applied on a great variety of industrial environments. Taguchi methods are based on the concept of off-line quality, trying to identify the products, process or services which are robust in the sense that are less variable under changes in the environmental conditions, employing a signal-to-noise ratio to select the most robust product/process (see [START_REF] Taguchi | Introduction to Off-line Quality Control[END_REF][START_REF] Taguchi | Introduction to quality engineering: designing quality into products and processes[END_REF].

Therefore, one could address the selection among the different dispatching rules, working under some variability conditions, as a Taguchi Robustness problem. To do so, the relative utilization of the bottleneck by using different increase ( b t ∆ ) of processing time at bottleneck station, and breakdowns can be considered as environmental noise factors. Furthermore, the different performance measures are also computed as noise factors, because the global performance over all responses is also a robustness aspect of interest. The distance, d, measured as the percentage deviation of the obtained performance of a certain DR respect to the best result can be considered a quality characteristic to be computed. Hence, the main idea is to select the dispatching rule reaching the smallest distance to the efficient solution for every combination of environmental noise factors. This can be done by means of the following expression [START_REF] Taguchi | Introduction to quality engineering: designing quality into products and processes[END_REF]:

      - = ∑ = n i i d n 1 2 1 log 10 η (1)
where:

η is the signal-to-noise ratio (in decibels) n is the number of experiments (12 in this case) -13 -Signal-to-noise ratio is computed for different noise factors. Under Taguchi's point of view, one system is better if its signal-to-noise ratio is higher. Finally, note that the expression (1) is advised to be employed in quality responses under 'smaller the better criterion', which is the case in our study as the response is the i d distance. In our case (minimization problem) the signal-to-noise ratio is a simple transformation of the squared difference across different scenarios. Nevertheless, for different optimisation criteria, alternative expressions should be employed (see e.g. [START_REF] Taguchi | Introduction to quality engineering: designing quality into products and processes[END_REF].

Results

Mean values for d on every local performance criterion are shown in order to obtain an idea of the distance from a particular DR to the DR which better performs. Values close to zero indicate that the system performs near to the best obtained DRs. Finally, we compute the signal-to-noise ratio, which takes into account the mean values and variance effects. The so-obtained results are presented for the different scenarios.

Scenario A (set-up times not included)

In this scenario, the NSUT rule is omitted in the comparisons, as it is only applicable in scenarios with setup times. Tables 1 to 3 show the results for the distance, d, of the best solution found for each DR respect to the best. The distance has been divided in zones of preference from ) 1 ( z , were results are promising to ) 4 ( z , containing DR far to be the best. Each table contains the results for a different local performance measure.

For the criterion of minimising the average tardiness, it was expected that those DR based on due dates may obtain a better result than other rules. Thus, rules EDD, SI and CR are always in the best interval, ) 1 ( z , respect to the best result found. However, the LS rule, also based on due dates, does not reach competitive results reaching 3 results in the zone ) 2 ( z . This performance may be produced by the influence by the variability in cycle times, which are used to compute the priority. CR obtains better results in the For the criterion of minimising the maximum tardiness, the results are still clearer that in the previous criterion, in the sense that due date based DR should obtain better results. The SI, EDD, FCFS and LS rules reached the best results always in ) 1 ( z . Exceptionally, the FCFS rule is the only one that is not based on due dates. It is important to note that the LS rule, which obtained poor results under the criterion of minimizing the average tardiness, seems to work well under maximum tardiness minisation. The CR rule, although due date -based, obtains poor results -close to the SRO rule -, under this criterion. As expected, the time-based rules do not obtain good results, with the exception of the LPT rule, which works in acceptable manner for scenarios under breakdowns. As a summary, the best results are reached for this criterion by the SI, EDD and FCFS and LS rules. [START_REF] Duenyas | A simple release policy for network of queues with controllable inputs[END_REF][START_REF] Baker | The effects of input control in a simple Scheduling model[END_REF]. The FCFS rule produces a stable flow of jobs and cards, obtaining the best way to optimally flow, maintaining low the inventory. The FCFS rule for the Conwip systems, which contains certain similarities with the card based DBR, is also recommended by Hopp and Roof (1998).

Furthermore, the SI and EDD rules obtain good results. The implemented SI rule does not allow a job to spend more time than a certain amount of time in the queue (see Appendix sections for the definition of the DRs), being perhaps this aspect the reason for its good performance. Surprisingly, the EDD rule also works fine. In our opinion the behaviour of this rule is also strongly connected to the relation between the input control and the DR. Jobs sorted according to their due dates imply that urgent jobs are pushed to the completion of the process. When jobs finish their processing, a new job of the same type can enter the line.

The results seem to indicate an efficient reduction of the WIP is reached with a suitable number of cards.

The CR rule obtains a moderate performance, probably for the same reason. similarly to SRO. LPT, CR and LS perform similarly. In general, it can be observed that those DRs based on the estimation some average times (SPT, SRPT, LPT, LS, CR) have a higher variance in the results as compared to those DRs independent of that estimations. In our opinion these it could be influenced by the variability on processing times (exponentially distributed) and the other source of variability in the shop as well.

Scenario B (set-up times)

Tables 5 to 7 (for every local performance measure) show the results for the distance, d. The NSUT rule is included in the study. The inclusion of set-up times produces a strong increase of the variability in the system. For the first criterion studied, the DRs that are always contained in ) 1 ( z are SI and FCFS rules. It is also important to highlight the performance of the NSUT rule, obtaining results below 25.5%. The NSUT performance deteriorates for accurate bottlenecks ( % 30 = ∆ b t ). The CR rule obtains good results for those scenarios without downtimes, and a poor performance for scenarios with downtimes. Time based rules obtained, in general, results far from the best positions. The SRPT rule obtains always better results than the SPT rule.

Furthermore, increasing the variability in scenarios with set-ups produces worst results for the LS rule as compared with Scenario A. As a summary, the best results are reached for this criterion by the FCFS, NSUT, and SI rules. For the minimisation of the maximum tardiness, the same effect than in Scenario A is observed, being FCFS, SI, and EDD the rules obtaining the best performance. As expected, the NSUT rule is also competitive. It is important to highlight that the use of DRs always obtain better results than a random selection. The CR rule obtains the worst results, compared to those obtained for the minimisation the average tardiness criterion. As a summary, best results are reached for this criterion by the FCFS, SI, NSUT, and EDD rules. From a managerial point of view, it is important to remark that each DR implies a different sophistication level regarding its implementation. For example, the FIFO rule can be implemented easily either by exploiting the conveyors layout or visually in human manipulations. However, more sophisticated DR (e.g. EDD, or CR) require the support of an information system or a MES (Manufacturing Execution System) in order to be implemented. However, it is important to consider that for some local performance measures ( max minT , and WIP min

) the FIFO rules obtain the best or similar results than EDD for those scenarios including set-up times and machine breakdowns (see Tables 2 and3). Furthermore, in Table 4 it can be observed that the second and third robust DRs correspond to the SI and FIFO rules, which need less sophisticated controlling mechanisms in order to be implemented.

Conclusions

In this work it has been shown that DRs are dependent of the production nature (job-shop, flow-shop, assembly, etc,...) as well as of stochastic variability conditions, produced by times, breakdowns, set-ups, etc... In order to correctly select a DR, two possible approaches can be distinguished:

introducing a dynamic procedure in order to switch in real-time to the most profitable DR, or (2) selecting a robust DR which can stand different environmental changes. TOC and particularly DBR -21 -advocate for simple procedures, avoiding complex procedures like (1). Thus, the selection of robust DRs can be a good option to be used in practise for DBR systems. Furthermore, this approach is related to nowadays market performance, since in the global era the markets are characterized for a more volatile demand, where from the design processes of new products, the production processes and later distribution to customers have to adapted to its requirements. From a production point of view, these changes can produce a behaviour in manufacturing, and therefore, mechanisms and policies trying to absorb changes are welcome. In this sense, the proposed methodology can be used in order to provide the DBR production with the most profitable dispatching rules for a given scenario.

stated previously, DRs are sensitive to the production environment under study. In order to correctly explain the proposed methodology for robust DR selection under DBR systems we focus on a simple, but widely common in practise, flow-line system. In our approach, we study different scenarios, including different relative utilization of the bottleneck, machine breakdowns, and set-up times. Local performance measures were computed and discussed for each scenario and every DR. Finally, the global performance of every DR is evaluated using Taguchi's robustness concept. Results shown that the most robust DRs are the EDD, SI and FCFS for environments without set-ups; and FCFS and SI for the case of set-ups. It is also worth noting that, for scenarios with set-up times, NSUT could be also a good alternative. Another interesting result is that some rules perform worst that the SRO rule. These results are consistent to the work of [START_REF] Chang | Ranking dispatching rules by data envelopment analysis in a job shop environment[END_REF], who observed the same phenomenon for different performance measures.

The results are also consistent with those of [START_REF] Fry | An analysis and discussion of the optimized production technology software and its use[END_REF], who point out that the dispatching rules used in the OPT software were based on a trade of customer due-dates avoiding bottleneck set-ups times.

In our analysis we have consider only ten dispatching rules. Future research could extend the study to additional dispatching rules. Additionally, it could be interesting to extend the study to the effect of changes in the product mix, trying to identify those rules most robust under product mix variability conditions. Chakravorty and Atwater (2005) • SPT, Shortest Processing Time [START_REF] Montarezi | Analysis of scheduling rules for an FMS[END_REF]. Select the job with the shortest processing time, i.e., selects the minimum ib Z , where:

i ib CT Z = .

• SRPT, Shortest Remaining Processing Time [START_REF] Wu | Scheduling a hybrid MTO/MTS semiconductor fab with machine-dedication features[END_REF]. Select the job with the shortest remaining processing time, i.e., selects the minimum ib Z , where:

∑ = + - - = n j ij i i ib t A t CT Z ) ( .
• LPT, Longest Processing Time [START_REF] Montarezi | Analysis of scheduling rules for an FMS[END_REF]. Select the job with the longest processing time, i.e., select the minimum ib Z , where:

i ib CT Z - = .
b) Due-date based:

• EDD, Earliest Due Date [START_REF] Panwalkar | Dynamic selection of dispatching rules for manufacturing system scheduling[END_REF]. Select the job with the earliest due-date, that is, select the minimum ib Z , where:

i ib DD Z = .
• CR, Critical Ratio [START_REF] Seagle | Application of work center control rules in a job shop environment[END_REF]. Select the job with the minimum ratio, computed as the remaining time to the due-date divided by the remaining processing time, that is, select the minimum ib Z , where: ) /( ) ( ) (

1 i i ib A t t DD t Z - - = .
• SI Truncated (see e.g. Blackstone et al., 1982 andPierreval andMebarki, 1997). A modified version of the SI X was implemented because obtained better results. Two queues are formed.

Randomly some α % of jobs go to first queue, while the rest go to the queue ordered by the due date.

• LS, Least Slack (Pierreval and Mebarki, 1997). Select the job the minimum slack time, that is, select the minimum ib Z , where:

1 i i i ib A CT DD Z - - = .
c) Set-up time based:

• NSUT, No Set-Up Time [START_REF] Panwalkar | Dynamic selection of dispatching rules for manufacturing system scheduling[END_REF]. Select the job that requires no set-up time.

d) Arrival Times and Random based:

• FCFS, First Come First Served [START_REF] Panwalkar | Dynamic selection of dispatching rules for manufacturing system scheduling[END_REF]. Jobs are selected according to the arrival time. The priority is computed selecting the minimum ib Z , where: -24 -

ib ib AT Z = .
• SRO, Select in Random Order [START_REF] Panwalkar | Dynamic selection of dispatching rules for manufacturing system scheduling[END_REF]. Job is randomly selected. The priority is computed selecting ib Z , where: Random Z ib = .

Usually it is possible that priority of different jobs reach the same value. These tie situations are usually solved by the FCFS rule, which was also followed in this work.

  selected DRs, local and global performance measures, and scenarios. Section 4 shows the main results of the experiments, while the last section is devoted to obtain conclusions and remark future research work.2 Drum-Buffer-Rope production control system

  Figure 2. WIP-buffer DBR implementation for three type of products

  selection, according to the local performance measures can be selected some DRs than shown in literature to perform well literature. We could also based on previous experiences. 4. Definition of the Scenarios, taking into account every source of variability and every performance measure. The system is modelled and a simulation design of experiments is conducted. 5. Definition of Global performance measures. Compute the robustness of the different DRs in order to obtain the most robust DR or a ranking of rules.

ijt

  is the mean processing time of job i in machine j at time t. K is the allowance factor generated by a uniform distribution )

  rule, SRO, it is included in the study as a benchmark for all the DRs. Details of these DRs are included in the appendix section.

F

F

  i DD , the due-date of job j i AT . the arrival time of job at the queue of the station j.The rules under comparison are the following: a) Processing time based:

  FIGURES

Figure 1 .

 1 Figure 1. WIP-buffer DBR implementation Figure 2. WIP-buffer DBR implementation for three type of products Figure 3. Signal-to-noise ratio for Scenario A Figure 4. Signal-to-noise ratio for Scenario B

Figure 3 .

 3 Figure 3. Signal-to-noise ratio for Scenario A

Table 1 .

 1 Results for scenario A, T min

	more balanced scenarios,		∆ b t	=	15	%	. FCFS obtains moderate results, since	11	.	9	≤ d	≤	26	.	2	. Regarding to
	the time based rules, it is important to note that SPRT always obtains better results than SPT. Furthermore,
	SPT yields the worst results in balanced scenarios (	∆ b t	=	15	%	), even when compared with the random
	selection rule SRO. LPT rule is included in ) 1 ( z for 3 of the 4 experiments, reaching better results than
	other time based rules. As a summary, the best results are reached for this criterion by the SI, EDD, and
	CR rules.
	Breakdowns F b t ∆ o r	NO EDD 0.0 SI 15% SI 0.3 EDD 1.1 EDD 0.8 EDD 1.0 YES 30% 15% 30% 0.0 SI 0.0 SI 0.0
	z	) 1 (	:	0	P 25 < ≤ d	LPT 5.6 SPT 14.9 LPT 20.6 CR CR 0.4 CR 6.6 CR 4.5 FCFS 13.3 15.4
	z	(	2	)	:	25	< d	FCFS 11.9 FCFS 20.5 e SRPT 20.7 LS 47.1 LPT 27.9 FCFS 26.2 SPT 30.9 LPT 18.7 SRPT 22.2 e r LS 32.0 SRPT 38.4 50 ≤ LS 39.7
	z ( z	3 ) 4 (	)	50 75 : :	< d < d	≤ ≤	75 100	SRO 76.9 SRO 100.0 SRO 80.5 SRO 83.2 R e SRPT 78.8 SPT 100.0 LS 100.0 SPT 100.0
																v i e
																w
																O n l
																y
																-14 -

Table 3 .

 3 The performance for the SPT and SRPT rules are around those of the random selection for the case without downtimes and moderate for As a summary, the best results are reached for this criterion by the SI, EDD, and FCFS rules. Results for scenario A, WIP min Regarding the robustness global criteria, results are summarized in Table4and in Figure3. In order to obtain positive robustness values, results (distance d) are given as a fraction of unity.

	the case containing breakdowns. Breakdowns	NO	YES
											t ∆	b	15%	30%	15%	30%
													EDD	0.0 SI	0.0 FCFS 0.0 FCFS 0.0
													SI	10.4 EDD	6.7 EDD	4.9 SI	9.0
				z	(	) 1	:	0	≤ d	<	25	FCFS 10.7 FCFS	8.1 SI	7.5 EDD	9.1
													LPT	23.5 CR	14.8 CR	7.7 LPT	14.8
		F o 25 : ) 2 ( < d z r ≤ 50 : ) 3 ( ≤ < d z	50 75	LS CR SRO 53.4 SPT 25.6 26.7	61.3	LPT SRPT 25.6 CR 13.7 LS SRPT 21.6 20.8 31.5 SPT 39.6 SPT 48.1
			z	(	4	)	:	75	SRPT 63.2 LS SPT 100.0 LPT SRPT 82.3 LS 72.4 79.1 SRO 81.7 SRO 100.0 100.0 e P 100 ≤ < d SRO 100.0
													e r
													R
													e
		Criteria Breakdows	v i e ∆ SPT SRPT LPT SI b t	EDD LS CR FCFS SRO
		min	T								NO NO YES	15 1.000 0.788 0.056 0.003 0.000 0.471 0.004 0.119 0,769 w 50 0.149 0.207 0.279 0.000 0.011 0.320 0.066 0.205 1,000 15 1.000 0.384 0.206 0.000 0.008 0.397 0.045 0.262 0,805
	Noise Factors	max minT WIP min						YES NO NO YES YES NO NO YES	O n l 50 0.309 0.222 0.187 0.000 0.010 1.000 0.154 0.133 0,832 15 1.000 0.840 0.334 0.000 0.003 0.067 0.433 0.007 0,740 50 0.648 0.847 0.704 0.000 0.001 0.046 1.000 0.011 0,806 15 0.365 0.384 0.055 0.000 0.000 0.011 0.537 0.001 1,000 50 0.104 0.343 0.156 0.000 0.001 0.013 0.277 0.003 1,000 15 1.000 0.632 0.235 0.104 0.000 0.256 0.267 0.107 0,534 y 50 0.613 0.823 0.791 0.000 0.067 0.724 0.148 0.081 1,000 15 0.396 0.256 0.137 0.075 0.049 1.000 0.077 0.000 0,817
											YES	50 0.481 0.216 0.148 0.090 0.091 0.208 0.315 0.000 1,000
													var η	0,117 0.072 0.056 0.002 0.001 0.130 0.078 0.008 0.021 3,432 5.065 8.988 26.909 28.924 5.848 8.287 18.739 1.210
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Table 4 .

 4 Robustness results for scenario AIn this scenario DRs can be clearly divided in two groups. One group is formed by the DRs which reach the highest values of the signal-to-noise ratio (i.e. the most robust DRs): EDD, SI and FCFS rules, while the other group is formed by the rest of rules. The worst results are obtained by SRPT, SPT, performing

	[Insert Figure 3 about here]
	Figure 3. Signal-to-noise ratio for Scenario A
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Table 6 .

 6 Results for scenario B, minT

						Breakdowns	NO	YES
													t ∆	b	15%	30%	15%	30%
													FCFS	0.00 FCFS	0.00 FCFS	0.00 FCFS	0.00
													NSUT 0.29 SI	0.32 SI	0.26 SI	0.43
													SI	0.38 EDD	0.39 EDD	0.63 EDD	0.75
		z		(	) 1		:	0	≤ d	<	25	EDD LS	0.50 NSUT 0.85 NSUT 2.06 NSUT 2.61 3.84 LS 3.07 SRPT 2.60 LS 3.92
													SPT	5.22 SPT	24.34 SPT	2.70 SPT	4.58
													SRPT	8.49 SRPT 27.16 LS	3.10 SRPT 18.70
													CR	18.70	LPT	7.58
													FCFS	0.00 FCFS	0.00 FCFS	0.00 FCFS	0.00
	z	(	2	)	:		25	< d	≤	50	LPT	45.96 LPT	35.44
													CR	38.71
	z	(	3	)	:	50	< d	≤	75	LPT	70.98
													SRO 100.00 SRO 100.00 CR	80.21 CR	83.32
	z	(	4	)		:	75	< d	≤	100	SRO 100.00 SRO 100.00

Table 7 .

 7 Results for scenario B, WIP minUnder the criterion of minimising the average work in process, the same behaviour than in Scenario A is obtained, but now including the NSUT rule. It is also important to mention that the SRPT rule obtains always results lower than 27.16%. Results obtained by the SPT are moderate. The LS rule seems to be not competitive under the studied conditions. As a summary, best results are reached for this criterion by the SI, FCFS, ESS, and NSUT rules.Regarding the robustness global criteria, results are summarized in Table8and in Figure4.In this case, the gain (signal-to-noise ratio) is decreasing linearly from the best to the worst DR. The highest values of the signal-to-noise ratio (i.e. the most robust DRs) are obtained by FCFS, SI, NSUT and EDD, and the worst by LPT, LST, performing similarly to SRO. The results in this scenario show that the use of FCFS, SI, NSUT and EDD rules has important advantages with respect to not considering any rule (SRO). Regarding to variability, the same behaviour than Scenario A was found. According to the results, we recommend the use of FCFS or SI under set-up conditions, and EDD or SI if there is not set-up.

					Breakdowns	NO	YES
										t ∆	b	15%	30%	15%	30%
														SI	0.00 SI	0.00 FCFS	0.00 FCFS	0.00
														EDD	0.06 FCFS	0.23 SI	0.13 SI	6.23
														FCFS	0.13 EDD	0.27 EDD	0.16 EDD	9.91
			z	(	) 1	:	0	≤ d	<	25	NSUT 0.95 NSUT 0.97 NSUT 3.98 SRPT 19.34 SRPT 12.55 SRPT 8.06 SPT 18.03 NSUT 20.29
														SPT	16.12	LPT	20.51
														SRO 20.91
														CR	24.48
														SI	0.00 SI	0.00 FCFS	0.00 FCFS	0.00
			z	(	2	)	:	25	< d	≤	50	SPT	29.44	SRPT 27.16 CR	26.12
														CR	30.89	SRO 29.11
			z ( z	3 ) 4 (	75 r 50 ≤ < d o : ) 100 75 : ≤ < d	SRO 47.61 LPT 68.79 LPT LS 100.00 LS	LS 69.40 CR 100.00 LPT 100.00 SRO 100.00 41.65 59.73 SPT 53.40 LS 88.33
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		Criteria Breakdows	w ∆ SPT SRPT LPT SI b t EDD LS CR FCFS SRO NSUT
	Noise Factors	T max minT min							NO NO YES YES NO NO YES YES NO	15 0.729 0.657 0.711 0.197 0.297 0.805 0.160 0.000 1.000 0.131 50 0.235 0.232 0.277 0.041 0.101 1.000 0.033 0.000 0.356 0.255 15 0.323 0.291 1.000 0.129 0.416 0.067 0.622 0.133 0.989 0.000 O n l y 50 0.562 0.151 0.600 0.000 0.153 1.000 0.226 0.065 0.358 0.233 15 0.052 0.085 0.460 0.004 0.005 0.038 0.187 0.000 1.000 0.003 50 0.243 0.272 0.354 0.003 0.004 0.031 0.387 0.000 1.000 0.009 15 0.027 0.026 0.076 0.003 0.006 0.031 0.802 0.000 1.000 0.021 50 0.046 0.187 0.710 0.004 0.007 0.039 0.833 0.000 1.000 0.026 15 0.294 0.125 0.688 0.000 0.001 1.000 0.309 0.001 0.476 0.010
		min	WIP							NO YES	50 0.161 0.081 0.694 0.000 0.003 1.000 0.245 0.002 0.209 0.010 15 0.180 0.272 1.000 0.001 0.002 0.416 0.597 0.000 0.291 0.040
										YES	50 0.534 0.193 0.205 0.062 0.099 0.883 0.261 0.000 1.000 0.203
												var η	0.050 0.027 0.087 0.004 0.019 0.208 0.069 0.002 0.119 0.010 9.027 11.537 3.992 22.941 15.950 3.301 6.697 27.401 1.990 18.224
														Table 8. Robustness results for scenario B
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  point out that DBR is very sensitive regarding the availability in front of the shop. This aspect could be included in a future research. Finally, it seems interesting address a hybrid combination of a global scheduling system and dispatching rules, such as pointed out by[START_REF] Roundy | A price directed approach to real-time scheduling of production operations[END_REF]. Dynamic DRs selection in real-time by means of human-computer interactive systems for DBR can also be of interest (see e.g.Baek et al. 1999, or Kuo and[START_REF] Kuo | The development of a human-computer interactive scheduling system[END_REF].Despite the voluminous literature on the topic, there are no homogeneous definitions for some dispatching rules. Sometimes the same rule has different acronyms, or one acronym has different meanings. Therefore, in order to unambiguously describe the dispatching rules employed in our study, we briefly define them and indicate the reference from which each definition has been obtained. In order obtain practical results it was assumed that real processing times of job are unknown in advance. The following notation is used: , the average cycle time of job i at time t. n , the number of stations in the line.

	of raw material Appendix: Definition of the dispatching rules
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ij

Z , the priority of job i in station j at time t. Small values have greatest priority. ib Z refers for the priority of job i in bottleneck station.

, the current time. ij t , the mean processing time of job in machine j. ib

Acknowledgements

The authors wish to thank the anonymous referees for their helpful suggestions. This research has been supported by the Spanish National Research Plan under DPI2007-61345 project and by the Andalusian Government Research Plan under P08-TEP-3630 project.