MD Rosalba Torrisi
email: rosalba.torrisi@humanitas.it

Vincenzo Bagnardi

Nicole Rotmensz

Eloise Scarano

Monica Iorfida

Paolo Veronesi

Alberto Luini

Giuseppe Viale

Armando Santoro

Marco Colleoni

Aron Goldhirsch

Letrozole plus GnRH analogue as preoperative and adjuvant therapy in premenopausal women with ER positive locally advanced breast cancer

Keywords: locally advanced breast cancer, ER positive breast cancer, premenopausal, preoperative treatment, letrozole and GnRH analogue

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INTRODUCTION

Administration of preoperative chemotherapy induces a pathological complete response (pCR), which represents an independent long term prognostic factor, in up to 40% of patients, depending on tumor biology [START_REF] Kaufmann | Recommendations from an international expert panel on the use of neoadjuvant (primary) systemic treatment of operable breast cancer: new perspectives 2006[END_REF]. However, in hormone receptor positive (HR+ve) tumors the pCR rate after preoperative chemotherapy is about 4-fold lower than in HR negative (HR-ve) tumors [START_REF] Kaufmann | Recommendations from an international expert panel on the use of neoadjuvant (primary) systemic treatment of operable breast cancer: new perspectives 2006[END_REF]. In the formers, the potential benefit of the addition of an endocrine intervention has been suggested but few data are available and this remains a poorly addressed issue.

Concern about the concurrent administration of tamoxifen and chemotherapy was raised by results of the SWOG INT-0100 study, which showed that the sequential admnistration of tamoxifen and chemotherapy was more effective than their concurrent administration in the adjuvant setting [START_REF] Albain | Breast Cancer Intergroup of North America. Adjuvant chemotherapy and timing of tamoxifen in postmenopausal patients with endocrine-responsive, node-positive breast cancer: a phase 3, open-label, randomised controlled trial[END_REF].

A large randomized study did not show any synergistic or detrimental effect of the addition of tamoxifen to a preoperative anthracyclines + taxane combination but 40% of the patients included in this study turned out to have HR-ve tumors, thus underestimating the potential benefit of concurrent endocrine manoeuvre [START_REF] Minckwitz | Dose-dense doxorubicin, docetaxel and granulocyte colony-stimulating factor support with or without tamoxifen as preoperative therapy in patients with operable carcinoma of the breast: a randomized, controlled open phase IIb study[END_REF].

Other randomized studies demonstrated an increased activity of chemoendocrine therapy on tumor proliferation [START_REF] Bottini | Cytotoxic and antiproliferative activity of the single agent epirubicin versus epirubicin plus tamoxifen as primary chemotherapy in human breast cancer: a single-institution phase III trial[END_REF][START_REF] Bottini | Randomized phase II trial of letrozole and letrozole plus low-dose metronomic oral cyclophosphamide as primary systemic treatment in elderly breast cancer patients[END_REF]. However, international consensus panels currently recommend the use of preoperative endocrine therapy only in selected subsets of postmenopausal women with tumors showing high expression of hormone receptors [START_REF] Kaufmann | Recommendations from an international expert panel on the use of neoadjuvant (primary) systemic treatment of operable breast cancer: new perspectives 2006[END_REF].

Randomized studies have clearly shown that third generation aromatase inhibitors are superior to tamoxifen either in early and in advanced breast cancer [START_REF] Winer | American Society of Clinical Oncology technology assessment on the use of aromatase inhibitors as adjuvant therapy for postmenopausal women with hormone receptor-positive breast cancer: status report 2004[END_REF].

In premenopausal women aromatase inhibitors alone may lead to an increase in gonadotropin secretion because of the reduced feedback of estrogens on hypothalamus and pituitary and a subsequent stimulation of ovarian activity 7]. On the contrary, the combination of an aromatase inhibitor with GnRH analogue (GnRH-a) may induce a complete estrogen blockade by the concomitant suppression of ovarian function and of peripheral estrogen synthesis 7]. Estrogen levels were more deeply suppressed by the combination of letrozole and triptorelin than with tamoxifen and the same GnRH-a in premenopausal women with early breast cancer [START_REF] Rossi | Endocrine effects of adjuvant letrozole + triptorelin compared with tamoxifen + triptorelin in premenopausal patients with early breast cancer[END_REF]. However, limited experience on clinical activity of aromatase inhibitors in combination with ovarian function suppression in premenopausal women is available [START_REF] Forward | Clinical and endocrine data for goserelin plus anastrozole as second-line endocrine therapy for premenopausal advanced breast cancer[END_REF][START_REF] Gnant | Endocrine therapy plus zoledronic acid in premenopausal breast cancer (2009)[END_REF][START_REF] Park | Phase II Parallel Group Study Showing Comparable Efficacy Between Premenopausal Metastatic Breast Cancer Patients Treated With Letrozole Plus Goserelin and Postmenopausal Patients Treated With Letrozole Alone As First-Line Hormone Therapy (2010)[END_REF][START_REF] Carlson | Phase II trial of anastrozole plus Goserelin in the treatment of hormone receptor positive metastatic carcinoma of the breast in premenopausal women[END_REF].

In the present study we decided to retrospectively investigate the outcome in terms of pCR rate, decrease of the tumor proliferative fraction and DFS in a consecutive series of premenopausal women who received endocrine therapy with letrozole and a GnRH-a in combination with chemotherapy as part of the preoperative treatment for locally advanced ER positive breast cancer and as adjuvant treatment for five years after surgery.

The rationale for administering letrozole was suggested by the greater activity shown in preoperative treatment of postmenopausal women with ER positive tumors in comparison with tamoxifen [START_REF] Eiermann | Preoperative treatment of postmenopausal breast cancer patients with letrozole: A randomized double-blind multicenter study[END_REF]. In addition, the combination of letrozole and ovarian suppression achieved a 50% of instrumentally detected clinical responses, and a 3% of pCR in premenopausal women with locally advanced ER and PgR positive breast cancer [START_REF] Torrisi | Antitumor and biological effects of letrozole and GnRH analogue as primary therapy in premenopausal women with ER and PgR positive locally advanced operable breast cancer[END_REF].

Results were compared with clinical outcomes of a non randomized unmatched control group of premenopausal women who underwent surgery during the same time window in the same institution for locally advanced ER positive breast cancer, who received preoperative chemotherapy alone. As routinely recommended in premenopausal patients, control patients received tamoxifen and GnRH-a after surgery [START_REF] Cuzick | Use of luteinising-hormonereleasing hormone agonists as adjuvant treatment in premenopausal patients with hormonereceptor-positive breast cancer: a meta-analysis of individual patient data from randomised adjuvant trials[END_REF].

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PATIENTS AND METHODS

Patients

Since 2002 premenopausal women with histologically proven T2-T4 a-d, N0-N3 M0 ER and/or PgR positive (≥ 10%) breast cancer consecutively admitted to the European Institute of Oncology (EIO) received preoperative chemotherapy and endocrine therapy with letrozole and GnRH-a within institutional protocols.

Premenopausal status was assessed by measurement of circulating estradiol at the EIO laboratory, and/or regular menses in the past 6 months in the absence of any endocrine therapy. Investigations (chest X-ray, abdomen ultrasound and bone scan or FDG-PET) were performed to exclude distant metastasis, as well as blood tests to assess normal renal, hepatic and bone marrow function.

Eligibility criteria for participation to the preoperative protocols included no previous chemotherapy/hormonotherapy, performance status 0-2 (ECOG scale), measurable or evaluable lesions, age between 18-70 years, white blood cells > 4,000/mm 3 , platelets > 100,000/mm 3 , AST, ALT, LDH, gamma-GT < 2.5 x upper limit of normal and bilirubin < 1.5 mg/100 ml (unless a Gilbert syndrome was present) .

Treatment

Endocrine therapy included a GnRH-a (mainly triptorelin) which was started concurrently with chemotherapy and administered either every 28 days or every 3 months thereafter.

The aromatase inhibitor letrozole (2.5 mg/daily) was added when circulating estradiol levels fell within a postmenopausal range, according to the EIO laboratory reference values, and was administered till surgery. Estradiol and gonadotropin levels were tested approximately at monthly intervals during preoperative treatment, in order to verify the maintenance of ovarian function suppression.

Preoperative chemotherapy included various regimens according to preoperative clinical stage.

Patients with inflammatory breast cancer received mostly the combination of epirubicin, cisplatin and infusional fluorouracil (ECF) or ECF followed by weekly paclitaxel, or dose dense AC x 4 cycles followed by docetaxel x 4 cycles, while patients with cT2-Ta-b tumors received either the combination of vinorelbine, cisplatin and infusional fluorouracil (ViFuP), or fluorouracil, vinorelbine and folinic acid (FLN) , or capecitabine and oral vinorelbine, or trastuzumab + oral vinorelbine (for HER2 positive tumors). Results of these protocols have been previously published [START_REF] D'alessandro | Role of endocrine responsiveness and HER2/neu overexpression in inflammatory breast cancer treated with multimodality preoperative therapy[END_REF][START_REF] Torrisi | Preoperative concurrent chemo-and endocrine therapies for women with large operable breast cancer expressing steroid hormone receptors[END_REF][START_REF] Torrisi | A phase II study of primary dose-dense sequential doxorubicin plus cyclophosphamide and docetaxel in cT4 breast cancer[END_REF][START_REF] Iorfida | Preoperative therapy with trastuzumab and oral vinorelbine (+/-endocrine therapy) in patients with HER2-positive breast cancer[END_REF].

Patients were treated with preoperative chemotherapy given in 3-week cycles, except a small number of patients treated with the dose dense regimens. Patients were candidates to receive a maximum of 6-8 cycles.

Each patient gave a written informed consent and all protocols were notified to the Ethical Committee.

Patients not progressing during preoperative treatment continued endocrine therapy with 28-day GnRH analogue + letrozole up to 5 years.

Premenopausal patients with cT2-T4a-d N0-N3 M0 ER and/or PgR positive (≥ 10%) breast cancer who received preoperative chemotherapy and were submitted to surgery from 2002 and 2006 at the Division of Senology of the EIO were considered the control group. All patients were treated with chemotherapy out of the EIO internal protocols. These patients received endocrine treatment with a GnRH-a and tamoxifen administered after surgery.

Response evaluation

Responses were evaluated according to both radiological (breast ultrasound and/or mammography) and clinical evaluation, which were performed at baseline, after 3-4 cycles of chemotherapy and before surgery and were classified according to standard WHO criteria. pCR were evaluated according to Kuerer et al. criteria [START_REF] Kuerer | Clinical course of breast cancer patients with complete pathologic primary tumor and axillary lymph node response to doxorubicin-based neoadjuvant chemotherapy[END_REF] and thus defined by the absence of invasive cancer on both the primary breast tumor and axillary lymph nodes.

In case of inflammatory breast tumors without a palpable mass, changes in clinically evaluable skin criteria (erythema, edema, peau d'orange) other than breast enlargement and tenderness were considered as response criteria.

Pathology

All patients had pathological evaluation performed at the EIO. When available, the original receptor status determinations on both the preoperative tru-cut and on the surgical specimen were considered either for the patients treated with chemotherapy and letrozole and for the control patients; otherwise only the final pathology assessment was considered. Surgical specimens were extensively sampled for the evaluation of residual tumor after primary chemotherapy, as previously reported [START_REF] Colleoni | Chemotherapy is more effective in patients with breast cancer not expressing steroid hormone receptors: a study of preoperative treatment[END_REF].

The immunostained slides were evaluated independently by two pathologists . Only nuclear reactivity was taken into account for ER, PgR, and Ki-67 antigen. The results were recorded as the percentage of immunoreactive cells over at least 2,000 neoplastic cells.

HER2 status was defined at immunohistochemistry (IHC) as negative (lack of membrane staining or staining of 10% or less invasive tumor cells = 0; faint and partial staining in > 10% of cells= 1+), and equivocal ( faint and complete staining in > 10% of cells =2+). In the latter cases fluorescence in situ hybridization (FISH) was performed to assess HER2 gene status .

Statistical methods

The primary endpoints of the study were the change between pre-and post-operative values of Ki67 expression, pCR rate and DFS. Secondary endpoint was overall survival.

The Pearson 2 test was used to evaluate differences in the distribution of clinical and pathological variables between study and control group.

Wilcoxon test for paired data and Wilcoxon rank sum test were used to evaluate the change from preoperative biopsy to surgical specimen in the levels of ER, PgR and Ki-67 within and between groups, respectively. McNemar test was used to evaluate the change from preoperative biopsy to surgical specimen in the HER2 overexpression.

The DFS was calculated from the date of surgery to any relapse, including ipsilateral breast recurrence, contralateral breast cancer, the appearance of a second primary cancer, or death, whichever occurred first. The OS was calculated from the date of surgery until death (from any cause). The DFS and OS functions were estimated using the Kaplan-Meier method.

The effect of chemoendocrine treatment on DFS and OS was evaluated using Cox proportional hazards regression models adjusted for prognostic clinical and pathological features and it was expressed as Hazard Ratio (HR) with 95% confidence interval (CI).

The homogeneity of treatment effect over time was evaluated by means of a Cox models with a treatment by time (time-dependent) covariate.

To assess whether estradiol levels decreased or increased during letrozole administration, a linear mixed models for repeated-measures was used. In the regression analysis, estradiol levels were logarithmically transformed to reduce skewness.

All analyses were carried out with the SAS software (SAS Institute, Cary, NC). All reported p-values refer to two-sided tests. Premenopausal patients with ER and/or PgR positive (≥ 10%) breast cancer who underwent surgery at the EIO after preoperative chemotherapy during the same time window represent the control group. Patients who became amenorrhoic after chemotherapy and did not receive either GnRH a or tamoxifen after surgery were excluded .Ninety-five patients were included in the present analysis. Pre-treatment tumor biology assessment was available for two-thirds of these patients.

RESULTS

Premenopausal women with histologically proven clinical

Table 1 summarizes baseline patient and tumor characteristics. The two groups were well balanced except for significantly younger age for the patients in the control group and a significant excess of T4 tumors in the chemoendocrine therapy group.

In addition, the two groups differed significantly in the preoperative chemotherapy regimens received, which consisted in anthracycline or anthracycline + taxane based chemotherapy in the vast majority of control patients (93.7%) vs only 23.5% in the chemoendocrine treated patients. Pathological complete remissions were observed in 5.0% of the chemoendocrine therapy group vs 1.1% of the control group, but the difference is not statistically significant.

Figure 1 shows the changes of ER, PgR and Ki-67 levels in each patient between preoperative biopsy and surgical specimen, according to therapy. Preoperative chemoendocrine therapy induced a significant decrease in the expression of both hormone receptors, while in the control group only PgR was significantly downregulated. A significant interaction (p=0.01) between treatment and changes in ER expression was observed, because ER levels were decreased in the chemoendocrine group and increased in the control group. On the other hand, Ki67 labelling index (LI) was decreased both by chemotherapy alone and by chemoendocrine therapy. However the decrease of Ki 67 LI was significantly greater in patients receiving chemoendocrine therapy ( median difference: -16 vs -7, p=0.003).

When a cut off of <20% was considered for Ki67 LI according to our previously published data [START_REF] Colleoni | Chemotherapy is more effective in patients with breast cancer not expressing steroid hormone receptors: a study of preoperative treatment[END_REF], a significantly higher proportion of patients in the chemoendocrine group had ki67< 20% tumors at surgery, as compared to the control group (71.4 % vs 62.1%, respectively). A greater proportion of patients in the chemoendocrine group had HER2 positive tumors (23.5% vs 11.6%).

Interestingly, in the chemoendocrine group, HER2 was overexpressed in 22.8% of tumors at core biopsy and in 32.9% at surgery (McNemar p-value 0.035), with an overall discordance rate of 10% (95% CI 5%-17%). In particular 9 patients with HER2 negative disease at baseline had overexpression of HER2 at surgery, while 2 patients who were HER2 positive at the core biopsy (one of whom received preoperative trastuzumab) did not show HER2 overexpression at surgery. Median follow up after surgery was 59 months (range 13.2-93.6 months) Twenty-six events occurred in the chemoendocrine group vs 48 in the chemotherapy group . Five-yr DFS, was 78% in the chemotherapy + letrozole group vs 41% in the control group [HR adjusted for age, pathological size and nodal status, ER, HER2 and Ki 67 evaluated at surgery: 0.46 95%CI 0.27-0.79 p=0047] (Fig 2 ).

A significant treatment by time interaction was observed (p=0.015). In fact, the advantage in DFS from chemoendocrine therapy was not observed within the first two years of observation (HR 1.12, 95% CI 0.51-2.44, p=0.77), and became evident only afterwards (HR 0.22, 95% CI 0.08-0.61, p=0.0035).

Duration of GnRH-a was shorter in the control group than in the study group: in fact, the proportion of patients discontinuing GnRH-a at 4 years after surgery were 12% and 4%, respectively (Wilcoxon p-value, evaluating differences in time to discontinuation, 0.049).

Moreover, a significantly greater proportion of patients receiving tamoxifen discontinued GnRH-a in the last 3 years, as compared with those receiving adjuvant letrozole (24.7% vs 8.6%, respectively). However, time to discontinuation was not significantly associated with the risk of relapse when evaluated in a time-dependent Cox regression model: Thirteen (11%) deaths in the GnRH analogue + letrozole group vs 17 (18%) deaths in the control group were observed. Five-yr overall survival was 89% vs 81% in the chemotherapy + letrozole and in the control groups, respectively [HR, adjusted for adjusted for age, pathological size and nodal status, ER, HER2 and Ki 67 evaluated at surgery, 0.85 95%CI 0.37-1.94, p=0.71].

The analysis of the extent of ovarian suppression after the addition of letrozole to GnRH-a during preoperative treatment was performed. Circulating estradiol levels after administration of GnRH-a were available for 111 patients. Ninety-eight patients had estradiol assessment after 1month and 73 after 2-month letrozole treatment.. Estradiol levels were significantly suppressed (p <0.001) by the addition of letrozole (Figure 3). However, changes of estradiol levels were not associated with clinical and pathological response nor with type of chemotherapy (anthracyclineand/or taxane based vs other) (data not shown).

DISCUSSION

It is generally accepted that ER status is one of the most powerful predictors of pCR after preoperative chemotherapy in multivariate analyses [START_REF] Kaufmann | Recommendations from an international expert panel on the use of neoadjuvant (primary) systemic treatment of operable breast cancer: new perspectives 2006[END_REF][START_REF] Colleoni | Chemotherapy is more effective in patients with breast cancer not expressing steroid hormone receptors: a study of preoperative treatment[END_REF]. Locally advanced ER positive tumors respond only partially to preoperative chemotherapy and the rate of pCR in ER positive HER2 negative tumors is significantly lower as compared with those obtained in triple negative and HER2 positive tumors [START_REF] Guarneri | Prognostic value of pathologic complete response after primary chemotherapy in relation to hormone receptor status and other factors[END_REF][START_REF] Gianni | European Cooperative Trial in Operable Breast Cancer Study Group (2005) Feasibility Feasibility and tolerability of sequential doxorubicin/paclitaxel followed by cyclophosphamide, methotrexate, and fluorouracil and its effects on tumor response as preoperative therapy[END_REF][START_REF] Gianni | Neoadjuvant chemotherapy with trastuzumab followed by adjuvant trastuzumab versus neoadjuvant chemotherapy alone, in patients with HER2-positive locally advanced breast cancer (the NOAH trial): a randomised controlled superiority trial with a parallel HER2negative cohort[END_REF][START_REF] Colleoni | Expression of ER, PgR, HER1, HER2, and response: a study of preoperative chemotherapy[END_REF].

Despite the likelihood of achieving a pCR is almost negligible, long term outcome is consistently better in the former cohort of patients [22.25]. The impact of subsequent adjuvant endocrine treatment is generally pointed out to partly explain this outcome.

However the addition of endocrine therapy in the preoperative setting has generally been poorly endorsed and rarely pursued mainly due to the concern raised by the results of the SWOG study showing that patients receiving concurrent chemotherapy and tamoxifen fared worse than those receiving the sequential administration of these two therapies [START_REF] Albain | Breast Cancer Intergroup of North America. Adjuvant chemotherapy and timing of tamoxifen in postmenopausal patients with endocrine-responsive, node-positive breast cancer: a phase 3, open-label, randomised controlled trial[END_REF].

In the present study we investigated the effect on short and long term outcome of the addition of endocrine therapy as part of the preoperative treatment in a cohort of premenopausal women with large ER positive tumors.

We demonstrated a substantial clinical activity for the combination of chemotherapy and letrozole and GnRH-a either in terms of response to preoperative treatment (pCR rate, decrease of Ki67 LI) and of long term outcome (DFS).

The chemotherapy + letrozole group performed significantly better than the control group both in terms of decrease in tumor Ki67 LI, which is an independent prognostic factor of long term outcome, and in terms of DFS, with a 54% reduction of the relative risk of a new event. In addition, the pCR rate was higher in the chemoendocrine group as compared to the chemotherapy alone one (5.0 % vs 1.1%, respectively) but the difference was not statistically significant. The pCR rate observed in the chemoendocrine group was within the range reported in the literature for this tumor population, although less than one third of patients received anthracycline based chemotherapy and only a marginal proportion received taxanes [START_REF] Kaufmann | Recommendations from an international expert panel on the use of neoadjuvant (primary) systemic treatment of operable breast cancer: new perspectives 2006[END_REF].

The issue of the concurrent administration of chemotherapy and endocrine therapy in the preoperative setting has been poorly addressed. The GEPARDO study randomized 250 women with locally advanced breast cancer to receive 4 cycles of dose dense doxorubicin + paclitaxel with or without tamoxifen [START_REF] Minckwitz | Dose-dense doxorubicin, docetaxel and granulocyte colony-stimulating factor support with or without tamoxifen as preoperative therapy in patients with operable carcinoma of the breast: a randomized, controlled open phase IIb study[END_REF]. Patients were not selected for the tumor HR status. A pCR rate of about 10% was observed in both groups. In a subset analysis of the study, including 196 patients with available centrally reviewed core biopsies, about 40% of tumors turned out to be ER negative [START_REF] Von Minckwitz | Clinical response after two cycles compared to HER2, Ki-67, p53, and bcl-2 in independently predicting a pathological complete response after preoperative chemotherapy in patients with operable carcinoma of the breast[END_REF]. Patients with ER positive tumors treated with the combination of chemotherapy and tamoxifen had no pCR while 3.5% of pCR was observed in the same subset of tumors treated with chemotherapy alone.

However, the pCR rate in ER negative tumors was similar in the 2 groups, suggesting that the lack of benefit of additional tamoxifen was not attributable to a detrimental effect of the concomitant administration of the endocrine agent [START_REF] Von Minckwitz | Clinical response after two cycles compared to HER2, Ki-67, p53, and bcl-2 in independently predicting a pathological complete response after preoperative chemotherapy in patients with operable carcinoma of the breast[END_REF].

Further studies showed a positive effect in decreasing tumor proliferative fraction by the addition of an hormonal agent to chemotherapy, in postmenopausal women, although clinical response rates were similar [START_REF] Bottini | Cytotoxic and antiproliferative activity of the single agent epirubicin versus epirubicin plus tamoxifen as primary chemotherapy in human breast cancer: a single-institution phase III trial[END_REF][START_REF] Bottini | Randomized phase II trial of letrozole and letrozole plus low-dose metronomic oral cyclophosphamide as primary systemic treatment in elderly breast cancer patients[END_REF].

In premenopausal women limited evidence of activity of aromatase inhibitors is available, although aromatase inhibitors are routinely used in clinical practice after tamoxifen failure.

The combination of anastrozole and GnRH-a showed a significant activity in premenopausal patients either as 1 st line treatment for metastatic disease or upon progression on tamoxifen [START_REF] Forward | Clinical and endocrine data for goserelin plus anastrozole as second-line endocrine therapy for premenopausal advanced breast cancer[END_REF][START_REF] Carlson | Phase II trial of anastrozole plus Goserelin in the treatment of hormone receptor positive metastatic carcinoma of the breast in premenopausal women[END_REF].

More recently, 1 st line treatment of premenopausal women with letrozole combined with GnRH-a showed comparable efficacy to that of letrozole in postmenopausal women with HR +ve metastatic breast cancer [START_REF] Park | Phase II Parallel Group Study Showing Comparable Efficacy Between Premenopausal Metastatic Breast Cancer Patients Treated With Letrozole Plus Goserelin and Postmenopausal Patients Treated With Letrozole Alone As First-Line Hormone Therapy (2010)[END_REF].

To our knowledge, this is the first report showing substantial activity of letrozole in premenopausal patients with early breast cancer either preoperatively and in the adjuvant setting.

A number of considerations should be made while interpreting these results. First of all, we should recognize the retrospective design of the study and the choice of a non randomized unmatched control group.

In addition, comparative results may be affected by the poor outcome of the control group, although 95% of these patients received an anthracycline/taxane based preoperative chemotherapy and about 30% received additional adjuvant chemotherapy, and by the lower proportion of T4 and HER2 positive tumors included in this group.

Moreover, the dramatically increased risk of relapse observed in these patients after the first 2 years is not easy to be explained. We speculated that it could be attributable to a different duration of GnRH-a treatment. The earlier discontinuation of GnRH-a after 2 years intriguingly mirrored the increased risk of relapse observed thereafter in the control patients. However, statistical analysis did not confirm a correlation between GnRH-a duration and risk of relapse, albeit the relative small number of patients cannot allow us to draw definitive conclusions on the role of ovarian suppression duration on clinical outcomes.

On the other hand, the present results may speculatively suggest that anticipating ovarian suppression may represent a valuable approach to improve the outcome of premenopausal patients with ER positive tumors.

Conversely, results obtained in the chemoendocrine study group are comparable with literature data in terms of 5-yr DFS, although stratified information about the clinical outcome according to menopausal status is not generally reported in trials of preoperative therapy.

The GeparDUO study reported a pCR of 1.8% but a 3-yr DFS of 90% in a subgroup of 56 patients with ER +ve and HER2 negative tumors receiving dose dense vs standard anthracycline + taxane based chemotherapy [START_REF] Loibl | Identification of biology-based breast cancer types with distinct predictive and prognostic features: role of steroid hormone and HER2 receptor expression in patients treated with neoadjuvant anthracycline/taxane-based chemotherapy[END_REF].

Guarneri et al reported a pCR rate of 8% and a 5-yr progression free survival of about 60-66% in more than one thousand women with locally advanced HR+ve breast cancer treated with preoperative chemotherapy and the addition of endocrine therapy only after surgery, but both pre and postmenopausal patients were included [START_REF] Guarneri | Prognostic value of pathologic complete response after primary chemotherapy in relation to hormone receptor status and other factors[END_REF].

We should be aware that results reported herein derive from non randomized comparisons and that the favourable results observed in the chemoendocrine series may be biased by the inclusion of patients who had not progressed on preoperative letrozole + ovarian suppression treatment, being thus more likely to benefit of the same combination in the adjuvant setting.

The results of our study are also hardly comparable with those of the ABCSG 12 trial, a large randomized study comparing through a 2x2 factorial design 3-yr treatment with anastrozole or tamoxifen, both in combination with goserelin, with or without zoledronic acid (twice per year) in 1810 premenopausal women with HR+ve breast cancer [START_REF] Gnant | Endocrine therapy plus zoledronic acid in premenopausal breast cancer (2009)[END_REF]. After a median follow up of 48 months DFS was about 90% in both endocrine arms alone [START_REF] Gnant | Endocrine therapy plus zoledronic acid in premenopausal breast cancer (2009)[END_REF]. However the study population was entirely different, since in the Austrian study about 75% of the patients had 2 cm or less tumors and only 30% of the patients had positive nodes at surgery, while in the present study all patients had by inclusion criteria >2cm tumors at diagnosis and 20% of them had T4 tumors. Despite the marginal number of pCRs, women with ER+ve tumors experience a significant advantage in DFS, as compared with women with ER-ve tumors, which is consistent across all previous studies [START_REF] Guarneri | Prognostic value of pathologic complete response after primary chemotherapy in relation to hormone receptor status and other factors[END_REF][START_REF] Colleoni | Expression of ER, PgR, HER1, HER2, and response: a study of preoperative chemotherapy[END_REF][START_REF] Loibl | Identification of biology-based breast cancer types with distinct predictive and prognostic features: role of steroid hormone and HER2 receptor expression in patients treated with neoadjuvant anthracycline/taxane-based chemotherapy[END_REF]. It may thus be speculated that factors other than pCR rate may be relevant for predicting long term outcome after preoperative treatment in the former group. Ellis and colleagues showed that post-treatment proliferation combined with the amount of residual tumor in the axilla and in the breast, considered as continuous variables, constitute a powerful prognostic index in postmenopausal women with HR+ve breast cancer treated preoperatively with letrozole or anastrozole [START_REF] Ellis | Outcome prediction for estrogen receptorpositive breast cancer based on postneoadjuvant endocrine therapy tumor characteristics[END_REF]. We have previously reported that Ki67 LI represents an independent prognostic factor of long term outcome also in patients receiving preoperative chemotherapy [START_REF] Colleoni | A risk score to predict disease-free survival in patients not achieving a pathological complete remission after preoperative chemotherapy for breast cancer[END_REF] In our study we observed a significantly greater decrease of Ki67 LI in the group of patients receiving chemotherapy and endocrine therapy as compared to those receiving chemotherapy alone.

According to our results, the concern regarding the concomitant administration of chemotherapy and endocrine therapy should be banished Although our results derive from a non randomized comparison, the absolute decrease of Ki67 LI obtained with the chemoendocrine combination should relieve concerns about the possible negative effect of endocrine manoeuvre concurrent with chemotherapy. In addition, whatever is the reason of the poor outcomes observed in the conventional therapy arm, DFS results reported herein in patients receiving letrozole and GnHR-a are encouraging and do not point out a potential detrimental effect.

We observed an overall discordance rate of 10% in HER2 expression between core biopsy and surgical specimens. Possible explanations for this findings include tumor heterogeneity, limited tumor sampling of the core biopsy but also a change in HER2 expression as a possible effect of preoperative treatments. Nevertheless, the determination of tumor features in surgical specimens after preoperative treatment is warranted.

We confirmed that the addition of letrozole induced a further suppression of estradiol levels as compared to GnRH-a alone, which was independent from the variable potential gonadotoxicity of chemotherapy different regimens. Most women achieved estradiol levels below the detectable lower limit of the reference laboratory (5 pg/mL), while in a recently published evaluation of the combination of GnRH-a with anastrozole in premenopausal women with advanced breast cancer the mean lowest level of estradiol was about 15 pg/mL [START_REF] Carlson | Phase II trial of anastrozole plus Goserelin in the treatment of hormone receptor positive metastatic carcinoma of the breast in premenopausal women[END_REF]. These results suggest that letrozole is able to induce a greater estrogen suppression in premenopausal women, as previously demonstrated in postmenopausal women [START_REF] Geisler | Letrozole is superior to anastrozole in suppressing breast cancer tissue and plasma estrogen levels[END_REF]. In this view, obtaining a complete endocrine suppression could be even more clinically relevant in premenopausal than in postmenopausal women.

In conclusion, we demonstrated that endocrine therapy administered concurrently with preoperative chemotherapy in premenopausal women with locally advanced ER positive tumors is not detrimental in terms of pCR and may on the contrary potentally improve the decrease of either tumor proliferation and the risk of relapse. Letrozole in combination with GnRH-a in premenopausal women is active and may represent a safe option even in the adjuvant treatment, although results from randomized trials and long term safety data are needed before this treatment could become a standard, when tamoxifen is contraindicated . Randomized studies are also warranted to better establish the role of endocrine therapy as part of the preoperative treatment of large ER positive breast cancer.

  T2-T4a-d N0-3 M0 ER and/or PgR ≥ 10% breast cancer admitted at the Department of Medical Oncology of the EIO from January 2002 to June 2006 who received letrozole and GnRH-a preoperatively in combination with chemotherapy and as adjuvant treatment after surgery were eligible for the present study.. Patients who received letrozole only preoperatively and switched to a different endocrine agent as adjuvant treatment were excluded.. One-hundred nineteen patients were included in the final analysis. For all patients both preand post-surgical pathological tumor characteristics were available.

Table 1 .

 1 Patient and tumor characteristics at time of diagnosis of primary breast cancer and primary chemotherapy regimen received by study group.

		CT+Letrozole	CT
		(n=119)	(n=95)	p*
		No. (%)	No. (%)
	Year of diagnosis			0.0022
	2002-2003	29 (24.4)	42 (44.2)
	2004-2006	90 (75.6)	53 (55.8)
	Age (years)			0.0036
	<35	14 (11.8)	26 (27.4)
	35-49	105 (88.2)	69 (72.6)
	Histotype			0.49
	ductal	150 (76.1)	72 (87.8)
	lobular	29 (14.7)	0 (0.0)
	others	18 (9.1)	10 (12.2)
	Grade			0.57
	1-2	82 (68.9)	31 (32.6)
	3	32 (26.9)	15 (15.8)
	Unknown	5 (4.2)	49 (51.6)
	Clinical T			0.038
	2	65 (54.6)	58 (61.1)
	3	29 (24.4)	29 (30.5)
	4	25 (21.0)	8 (8.4)
	Clinical N			0.33
	Positive	78 (65.5)	71 (74.7)
	Negative	35 (29.4)	20 (21.1)
	X	2 (1.7)	1 (1.1)
	unknown	4 (3.4)	3 (3.2)
	ER/PgR			0.28
	ER or PgR 1-49%	77 (64.7)	35 (36.8)
	ER and PgR ≥50%	42 (35.3)	27 (28.4)
	unknown	0 (0.0)	33 (34.7)
	Her2/neu status			0.053
	negative	97 (81.5)	51 (53.7)
	positive (3+)	22 (18.5)	4 (4.2)
	unknown	0 (0.0)	40 (42.1)
	Ki-67			0.14
	<20%	28 (23.5)	19 (20.0)
	≥20%	90 (75.6)	36 (37.9)
	unknown	1 (0.8)	40 (42.1)
	Primary CT regimen			<0.0001
	antracyclines	18 (15.1)	40 (42.1)
	antracyclines and taxanes	10 (8.4)	49 (51.6)
	others	91 (76.5)	6 (6.3)
	Additional trastuzumab	14 (11.8)	3 (3.2)
	Response to primary therapy			0.10
	pCR
	partial response	6 (5.0)	1 (1.1)
	stable disease	62 (52.1)	41 (43.2)
	Others	51 (42.9)	53 (55.8)

Abbreviations: ER = estrogen receptor; PgR = progesterone receptor; CT = chemotherapy; pCR = pathological complete response. * 2 test comparing frequencies between CT+Letrozole group and CT group. Unknown were not considered in the pvalue calculation

Table 2 .

 2 Patient and tumor characteristics at time of surgery and adjuvant therapy, by study group. 2 test comparing frequencies between CT+Letrozole group and CT group. Unknown were not considered in the pvalue calculation Figure 1. Matched box plots showing changes of ER, PgR and Ki-67 levels in each patient between preoperative biopsy and surgical specimen, by study group. Patients achieving pathological complete response were not considered. Half boxes represent the interquartile range and the horizontal bold lines across the boxes indicates the median. Whiskers (standard span) were extended to 1.5×the interquartile range. Arithmetic means are indicated with + symbol. P-values are based on the Wilcoxon test for paired data.

		CT+Letrozole	CT
		(n=119)	(n=95)	p*
		No. (%)	No. (%)
	pT			0.45
	pT0, in situ	8 (6.7)	1 (1.1)
	pT1	38 (31.9)	31 (32.6)
	pT2	45 (37.8)	37 (38.9)
	pT3	21 (17.6)	21 (22.1)
	pT4	1 (0.8)	1 (1.1)
	pTX	6 (5.0)	4 (4.2)
	Positive lymph nodes (No.)			0.20
	None	32 (26.9)	18 (18.9)
	1-3	43 (36.1)	31 (32.6)
	4	44 (37.0)	46 (48.4)
	ER			0.34
	0	2 (1.7)	0 (0.0)
	1-49%	14 (11.8)	9 (9.5)
	50%	97 (81.5)	85 (89.5)
	Unknown	6 (5.0)	1 (1.1)
	Her2/neu status			0.17
	Negative	85 (71.4)	83 (87.4)
	Positive (3+)	28 (23.5)	11 (11.6)
	Unknown	6 (5.0)	1 (1.1)
	Ki-67			0.040
	<20%	85 (71.4)	59 (62.1)
	%	25 (21.0)	33 (34.7)
	Unknown	9 (7.6)	3 (3.2)
	Surgical treatment			0.91
	Total mastectomy	63 (52.9)	51 (53.7)
	Breast conservation	56 (47.1)	44 (46.3)
	Radiotherapy			0.12
	No	27 (22.7)	28 (29.5)
	Yes	92 (77.3)	67 (70.5)
	Adjuvant CT			0.0002
	No	109 (91.6)	69 (72.6)
	Yes	10 (8.4)	26 (27.4)
	Adjuvant Trastuzumab			0.0023
	No	105 (88.2)	94 (98.9)
	Yes	14 (11.8)	1 (1.1)
	Abbreviations: ER = estrogen receptor; CT = chemotherapy.

*

ACKNOWLEDGEMENTS

The Authors are indebted to Novartis FARMA S.p.A. for the help in the revision of English format

CONFLICT OF INTEREST

The Authors declare they have no conflict of interest


Luk N Van Wassenhove

Christos Zikopoulos

Luk; INSEAD Wassenhove

On the Effect of Quality Overestimation in Remanufacturing

Keywords: RE-MANUFACTURING, QUALITY MEASUREMENT, SUPPLIER SELECTION grading errors, quality of returns remanufacturing, reverse logistics, grading errors, quality of returns, supplier evaluation

We study a simple reverse supply chain consisting of a remanufacturing facility and a number of independent locations where used products are returned by the end-users. At the collection locations, the returned products are graded and classified based on a list of nominal quality metrics provided by the remanufacturer. It is assumed that this classification is subject to errors; specifically, the returns condition is overestimated because of a stochastic proportion of returned units which are classified in classes corresponding to better quality than the actual. The scope of the paper is to study how these classification errors affect the optimal procurement decisions of the remanufacturer as well as the associated profit for the cases of both constant and stochastic demand in a single-period context. Moreover, in the former case we study the impact of these classification errors on profit variability. The quantification of the impact of quality overestimation provides intuition on the value of reliable classification and on the extent of the necessary investments and initiatives to improve classification accuracy.

Introduction

The issue of information regarding the quantity and quality of used items in reverse supply chains has recently attracted a lot of attention by both practitioners and academics. The quality categorization of the returns is the first step among a series of necessary procedures before a used product can be considered suitable to satisfy demand for remanufactured products.

The present paper addresses the issue of overestimation of returned products quality and its impact on the operation and profitability of reverse supply chains. This study is motivated by the case of ReCellular, a firm that remanufactures and sells used mobile phones. ReCellular's practice is to collect used products at a number of different locations. At each location, a primary sorting of the returns is carried out based on a list provided by ReCellular itself. Specifically, there are several quality characteristics of a returned unit that determine the quality category in which the returned item will be classified. This list is shown in Table 1, adopted by [START_REF] Guide | Managing product returns for remanufacturing[END_REF].

Table 1 about here In total, there are 6 different product classes, which have been introduced with respect to the associated cost to remanufacture a unit of a certain quality standard.

Table 2 shows the remanufacturing cost for each product class as reported in [START_REF] Guide | Matching demand and supply to maximize profits from remanufacturing[END_REF], along with the estimated acquisition prices.

Table 2 about here

After returned products reach ReCellular's remanufacturing facility, they are sorted and graded at a grading station. Εach of the new quality classes that emerge is processed in a different remanufacturing cell. Although all quality classes can be remanufactured in any of the available cells, inaccurate sorting at ReCellular facilities may also increase remanufacturing time and cost. However, the procedure at ReCellular's grading station can be considered accurate. On the other hand, the classification of returns carried out by the suppliers is considered inaccurate, for a number of reasons, which are explained below. Therefore, despite the suppliers' categorization of a unit in a certain class, the cost that the firm bears during the remanufacturing process can be larger than estimated. This possible underestimation 1. The list of product characteristics which determine the specific class in which a unit falls can not be exhaustive. Considering the complexity of some products it is easily understood that there can be some characteristics which are not included in that list but can increase the remanufacturing cost.

2. Since the classification process involves, to some extent, the subjective evaluation of a number of characteristics, it is prone to errors. It is not actually reported by ReCellular that these classification errors lead to overestimation of the overall returns quality. However, since a supplier is paid more for a higher quality product, we believe that in the majority of reverse supply chains quality overestimation is rather common.

3. The remanufacturing cost for returned units with similar quality problems is not necessarily the same for all those units. The presence of a certain attribute induces a minimum remanufacturing cost because of the standard remanufacturing process.

However, in some cases more effort may be required, resulting in different remanufacturing cost for units classified in the same quality class.

The present paper examines how misclassification of returned products at the collection location (supplier) affects the profitability of remanufacturing and consequently, to what extent a firm should undertake some actions in order to improve the classification accuracy. Moreover, we provide some ideas on how the accuracy of quality evaluation can be incorporated in the procurement decision process.

Literature review

The management of products acquisition is an important issue in the reverse supply chains context. As [START_REF] Guide | Product acquisition management: current industry practice and a proposed framework[END_REF] point out, one of the complicating characteristics that the remanufacturing industry has to deal with is the increased uncertainty regarding returns' quality. The motivation of the current research comes from ReCellular practices regarding quality assessment and procurement of used products. An analytical description of ReCellular practices can be found in [START_REF] Guide | Managing product returns for remanufacturing[END_REF] and in [START_REF] Guide | Matching demand and supply to maximize profits from remanufacturing[END_REF]. It should be noted that in [START_REF] Guide | Matching demand and supply to maximize profits from remanufacturing[END_REF] [START_REF] Vadde | Optimal pricing of reusable and recyclable components under alternative product acquisition mechanisms[END_REF]. In the current paper these two parameters, as well as returns quantity and demand, are considered exogenous to the system, since our main interest is to study the effect of classification errors on procurement and production decisions as well as on the system profitability.

The problem of procurement and production planning at ReCellular is also examined in [START_REF] Jayaraman | Production planning for closed-loop supply chains with product recovery and reuse: an analytic approach[END_REF]. [START_REF] Jayaraman | Production planning for closed-loop supply chains with product recovery and reuse: an analytic approach[END_REF] formulates the problem as a mathematical programming model, considering however that the classification of returns into different quality classes is accurate.

The issue of timely classification of returns when multiple product classes exist has been addressed in a number of recent papers. In [START_REF] Guide | Time value of commercial product returns[END_REF] the value of time is explored: since the sorting of returns accelerates remanufacturing procedures it increases the value salvaged by the used products. An implementation of such practice in a real situation is included in [START_REF] Guide | Hewlett -Packard company unlocks the value potential from time -sensitive returns[END_REF]. [START_REF] Ferrer | Yield information and supplier responsiveness in remanufacturing operations[END_REF] studies the procurement and remanufacturing decisions in a single-period context under a number of different scenarios regarding the timing of information concerning the quality of returns. [START_REF] Aras | The effect of categorizing returned products in remanufacturing[END_REF] study a similar problem in a multi-period context. There is a recent stream of studies, in which the value of returns' quality information is evaluated. In most of these papers returns' quality is modeled as a random variable that follows a continuous probability density function. Each of the possible infinite degrees of quality condition is related to a different value of remanufacturing cost. In this context falls the work of [START_REF] Robotis | The effect of remanufacturing on procurement decisions for resellers in secondary markets[END_REF], [START_REF] Galbreth | Optimal acquisition and sorting policies for remanufacturing[END_REF] and [START_REF] Ketzenberg | Value of information in closed loop supply chains[END_REF].

The issue of grading errors during the sorting procedure of the returns has not been addressed extensively in the existing literature. Two contributions that fall in this context are those of [START_REF] Souza | Capacitated remanufacturing with service level constraints[END_REF] and [START_REF] Zikopoulos | On the attractiveness of sorting before disassembly in a remanufacturing facility[END_REF]. Both papers study the effect of grading errors on the value of advanced yield information, by simulation and analytical methods, respectively.

The contribution of the present paper is that a different aspect of grading errors is explored. Specifically, we study the effect of quality overestimation in a reverse supply chain, in order to quantify the loss that the remanufacturer suffers because of supplier classification errors. Thus, it is possible to evaluate to what extent it would be advisable for a remanufacturing firm to invest in the improvement of the classification system and to work on the supplier reliability issue. Moreover, we examine the effect In Section 3 we introduce the problem structure, the basic assumptions and the notation used throughout the paper. In section 4 the formulation and analysis of the problem are presented, for both deterministic and stochastic demand for remanufactured products. Section 5 includes a brief numerical example and, finally, Section 6 summarizes the paper and presents some extensions of the current work.

Problem description

We study a reverse supply chain consisting of a remanufacturer, R, and N independent suppliers of returned items. The suppliers collect the products from endusers and grade them according to a list provided by the remanufacturer. This grading procedure results in the categorization of returns in M distinct quality classes. Each quality class, j = 1, 2, …, M, is characterized by different acquisition price, α j , and remanufacturing cost, r j . The suppliers inform R about the number of units per class that they have available for sale and R decides from which suppliers to order and the amount of returns in each class (s ij ). The class with the best quality is class j = 1 which has the higher value of acquisition cost, j=1,...,M j 1 max α = α .

Upon receipt, returns are inspected at the grading station so that their actual condition is revealed. We assume that at this stage, the sorting procedure is error-free.

For each product of a certain class, there is a constant remanufacturing cost.

Obviously, the better the condition of a unit, the lower the remanufacturing cost is:

j=1,...,M j 1 min r = r . The remanufacturing cost of each unit is defined by the actual condition of a unit rather than by the supplier's classification. After classification, returns are remanufactured in order to reach a condition that makes them suitable to satisfy demand for remanufactured products, in a single-period context. Demand for remanufactured products is assumed known. This assumption is relaxed later permitting stochastic demand with known probability density function, f(.), and distribution function, F(.). After remanufacturing, all units are in the same condition regardless of their quality at the time that they were returned by end-users.

We assume that the suppliers tend to overestimate the quality of the returns.

Specifically, we assume that in a lot of returns that supplier i has classified as and, ( )

= i i i q s p ,
( 1) ( 1)
1-

- - = + ij ij ij i j i j q s p s p , j = 2,…, M.
Since p ij is a random variable, q ij is also a random variable. After the remanufacturing process all available units can be used to satisfy demand for remanufactured units.

The selling price, v, is the same for all units. When the remanufactured quantity does not match exactly demand the remanufacturer faces costs, related to shortage, b, or excess inventory, h, respectively. The cost of excess inventory is positive when the firm has to pay for the disposal of the unsold units, or negative if these units can be sold at a salvage value. Table 3 summarizes the notation used throughout the paper.

The reverse supply chain for the problem examined is shown in Figure 1. A technical issue that affects the plausibility of the analysis that follows is the method employed for the evaluation of p ij . A commonly used approach in similar situations is to follow a Bayesian update type procedure. Specifically, an initial estimation can be based on historical data. Each time that a specific supplier is used, the actual quality outcome is recorded and consequently the information is updated.

The use of distribution of the Beta family is advisable for three reasons:

1. Distributions of the Beta family are usually used to model fractions of a quantity with a certain property.

2. The resulting distribution from the Bayesian update procedure belongs also in the Beta distributions family.

3. By appropriate selection of the distribution parameters a large number of different characteristics can be captured. It should be mentioned that although the product has a limited sales period, this does not imply that the firm's relationship with its suppliers is not long-term. An issue that remains unanswered is the case of a new supplier for which no historical data is available. In this case the firm could use a rather rough estimation based on the experience with similar suppliers.

A key assumption of the model examined is that product misclassification is associated with the overestimation of product quality by one class; all classification errors result in classifying a quality j+1 return in j quality class. Although this assumption can be considered rather strict from a theoretical point of view, we argue that it is reasonable for practical situations. On the one hand, since suppliers are paid according to the quality of the collected products it is unlikely that a unit would be classified in an inferior quality class. On the other hand, it is not that probable that a unit's quality would be overestimated so dramatically in order to classify a j + 1 return in a class with superior quality than class j quality. For example, consider that returns are classified in 4 classes according to the presence of dirt, scratches, cracks or breaks, respectively. The required remanufacturing effort for correcting a certain problem may not be deterministic but it could be associated with a probability distribution. Figure 2 shows an example of associating a family of truncated normal probability distributions functions with the respective remanufacturing cost, shown on the horizontal axis.

Figure 2 about here

The four vertical lines in Figure 2 separate the remanufacturing cost to five regions (region 1 corresponds to the lowest remanufacturing cost). Obviously, the length of each quality class does not match exactly the length of a certain cost region.

Consider for example the returned units that have only some scratches. Although they are all classified in class 2, a proportion of them would induce remanufacturing cost comparable to the cost of the majority of class 3 units. Moreover, there is also a proportion of class 2 units with remanufacturing cost in the fourth cost region.

Assuming that each cost region extends for a width equal to the value of one standard deviation, σ, of the truncated normal distribution it would be easy to estimate the probability that a unit requires larger remanufacturing costs: there is a 68% probability of correct classification, 27% probability of quality overestimation by one class, 4% probability of quality overestimation by two classes, 0.2% probability of

Model formulation and analysis

The analysis that follows is presented in two sections, which differ in the nature of the single-period demand: firstly, the case of known demand is presented, followed by the analysis when demand is considered stochastic. In both cases, we derive the conditions for the determination of the optimal procurement policy. For the case of known demand the impact of the variance of p on the variance of the total profit is also examined.

Optimal procurement policy when demand is known

Since demand is known and equal to D, the objective function of the remanufacturing business depends on the relation between

1 1 = = ∑∑ N M ij i j
s and D. The objective function is given by:

E(π)= 1 1 min , N M ij i j v s D = =       ∑∑ ( ) 1 1 = = -∑∑ N M j ij i j r E q 1 1 = =   -    ∑ ∑ N M j ij i j a s 1 1 + = =   - -     ∑∑ N M ij i j h s D 1 1 + = =   - -     ∑∑ N M ij i j b D s (1)
where (x) + = max (0, x), and the terms in order that they appear stand for the sales revenue, the remanufacturing cost, the acquisition cost, the holding cost and the shortage cost, respectively. The first order partial derivatives of (1) with respect to each of the s ij are given by

( ) ij E s π ∂ ∂ = 1 ( ) 1 ( ) j ij j ij j r E p r E p a h +   - - - --   < 0 if 1 1 N M ij i j s D = = > ∑∑ ( ) ij E s π ∂ ∂ = 1 ( ) 1 ( ) +   - - - -+   j ij j ij j v r E p r E p a b if 1 1 = = ≤ ∑∑ N M ij i j s D
whereas, for every second order partial (direct or mixed) derivative holds:

F o r P e e r R e v i e w O n l y 9 2 2 ( ) ij E s π ∂ ∂ = 2 ( ) ij kl E s s π ∂ ∂ ∂ = 0,
and therefore, the optimal ordering policy can be evaluated using solely the first order conditions. It is obvious that

1 1 N M ij i j s D = = > ∑∑
can never be optimal. Therefore, the optimal solution is such that

1 1 = = ≤ ∑∑ N M ij i j
s D , and the Karush -Kuhn -Tucker (K-K-T) conditions are written as follows:

I. ( ) ∂ -- ∂ ij D ij E s π µ µ < 0 II. s ij [ ( ) ∂ -- ∂ ij D ij E s π µ µ ] = 0 III. ij ij s S -< 0 IV. µ ij ( ij ij s S -) = 0 V. 1 1 N M ij i j s D = = - ∑∑ < 0 VI. µ D 1 1 = =   -     ∑∑ N M ij i j s D = 0,
where µ ij , µ D , are non-negative constants.

If for some combinations of i and j holds (

) ij E s π ∂ ∂ < 0, condition (II) yields s ij = 0. Define R as the state space such that ij є R if and only if ( ) ij E s π ∂ ∂ > 0. If ∈ ≤ ∑ ij ij R S D ,
then the optimal decision is to procure all available quantities from classes ij є R. Based on the previous analysis, there is a simple procedure for determining the optimal ordering policy. The first step is to evaluate the value of

However, if ∈ ∑ ij ij R S > D , there should be a number of ij є R* (R* ⊆ R) combinations, for which s ij < S ij . For these ij combinations, by (IV) µ ij = 0. Since ( ) ij E s π ∂ ∂ > 0 for every ij є R* by (I) D µ > 0,
{ } 1 ( ) 1 ( ) +   + - + - -   j ij j ij j v b r E p r E p a .
For all ij such that:

{ } 1 ( ) 1 ( ) +   + - + - -   j ij j ij j v b r E p r E p a > 0, the sum of available quantities, ∈ ∑ ij ij R S is computed. If ∈ ∑ ij ij R
S < D, then the optimal solution is to order all available quantities from supplier i and category j, that is all units for which :

{ } 1 ( ) 1 ( ) +   + - + - -   j ij j ij j v b r E p r E p a > 0
Otherwise, all s ij are classified in a descending order according to the value of the expression:

{ } 1 ( ) 1 ( ) +   + - + - -   j ij j ij j v b r E p r E p a . ( 2
)
For the first ij in the aforementioned classification for which

∈ ∑ ij ij R*
S > D, the optimal procurement quantity consists of all available quantities from the previous ij and s IJ such that

∈ ∑ ij ij R*-{IJ} S +s IJ = D.
Since the values of v and b are constant across all suppliers and product classes, we rewrite (2) without taking into account these parameters. The selection of suppliers and product classes can be based on the expression:

1 ( ) 1 ( ) +   + - +   j ij j ij j r E p r E p a , (3)
by selecting those supplier-class combinations that yield small values of (3).

Therefore, not only the remanufacturing and acquisition costs are important, but also the classification error at the supplier. Expression (2) stands for the expected profit from the procurement, remanufacturing and sale of one retuned unit that supplier i has identified as a quality j return, while expression (3) stands for the respective variable cost per unit.

Since (3) yields the variable cost of each supplier -class combination, it can be used for the estimation of the deviation of the actual value of the variable cost from the one that the remanufacturer uses for the decision process. It is easy to show that the difference of these two values is given by:

a 1 ( ) ( ) ( ) e j j ij ij r r E p E p +   - -   . ( 4
)
where a ( ), ( )

e ij ij
E p E p are the estimated and actual, respectively expected values of p ij .

Setting ( ) 1

e ij E p = in (4) yields the difference in the product evaluation if the effect of misclassification is ignored. As can be observed by ( 4), the difference in product evaluation depends on the value of overestimation and the difference in the remanufacturing cost of the two classes involved in the misclassification phenomenon. On the other hand, the remanufacturer's cost related to the quality overestimation is associated with the difference in the acquisition cost of these two classes, namely:

a 1     j j+1 ij (α -α ) -E(p ) . (5)
Since (5) yields the savings in variable costs because of the improvement in the classification accuracy it can help in the estimation of a premium that can be established for encouraging suppliers to improve their classification accuracy. Figure 3 shows graphically the savings per product class by the implementation of an errorfree classification procedure (i.e. p ij = 1) for all possible values of a ( ) ij E p at a certain supplier j, using the ReCellular's α j and r j values (Table 2).

Figure 3 about here An interesting special case of the problem examined here, is the case in which the cost of procuring and remanufacturing of a returned unit is the same independently of the unit class, namely:

j j r + a = C , for j = 1, 2, …, M,
and, moreover, the probability of quality overestimation is identical for each product class at a certain supplier, namely: It can be shown that in this case, (3) simplifies to:

= ij i p p , for j = 1, 2, …, M-1.
[ ] 1 ( ) 1 ( ) + - - + j j i a a E p C . (6)
Thus, the procurement from a specific supplier can be based on the relationship of the acquisition cost between sequential returns classes. When considering procurement from different suppliers the criterion for procurement of a certain class, i, from supplier k over class j from supplier m is reduced to:

[ ] [ ] 1 1 ( ) 1 ( ) ( ) 1 ( ) + + - - < - - i i k j j m a a E p a a E p . (7)
That is the decision is affected by the supplier classification accuracy as well as the relationship between acquisition costs.

The impact of the variance of p

In this section we study the impact of the variance of the suppliers grading errors on remanufacturer's profitability. In other words, we examine how the variance of p affects the variance of π. The evaluation of the variance of π is important because of difficulties in the estimation of the actual percentage of misclassified units. The poor estimation of p can be expressed by selecting a distribution of p with a large variance. For example, an initial estimate for the distribution g(p) could be the uniform distribution with mean 0.5. Monitoring of the suppliers history and continuous updates of the distribution parameters result in better understanding of the procedure and therefore in more accurate estimation of E(p) and in different posterior distribution, g'(p), characterized by lower variance. Consequently, the quantification of the effect of the variance of p on π offers some information about the extent to which a firm should invest in order to minimize the variance of p.

There are two factors that are responsible for the non-zero variance of p. The first one is related to the fact that suppliers' errors are not the same at every replenishment instant. The second factor is related to the estimation of the value of p by the remanufacturing company. For example, when there is not enough information about the actual distribution of the errors of suppliers, the remanufacturer should use the distribution parameters that give a greater value of variance. As more information becomes available, this estimation can be updated and eventually the variance will be minimized. The case with zero variance can be considered as a rather optimistic bound for the variance of p. For clarity of illustration, we present the analysis in two parts. Firstly, we deal with the case that the optimal procurement policy calls for procuring only one class of returns from a single supplier. This is the simpler case which provides some intuition in order to proceed to the general case in which more than one of the suppliers and quality classes are used.

Procurement of a single quality class from a single supplier

Assume that the optimal policy is to procure only s ij . In such case the optimal profit for the remanufacturer is:

π = ij vs -j ij ij r s p 1 (1 ) + - - j ij ij r s p -j ij a s ( ) + - -ij b D s = ( ) ( ) 1 1 j j j j ij ij v r a r r p s + +   - - + -   ( ) + - -ij b D s . ( 8
)
Since π is a linear function of p ij , the variance of the profit when the optimal policy is implemented is given by:

Var(π) = ( ) ( ) ( ) 2 2 1 j j ij ij r r s Var p + - , (9)
while for the standard deviation holds:

StDev(π) = ( ) ( ) 1 j j ij ij r r s StDev p + -
.

The general case

When more than one of the suppliers and quality classes are used the optimal profit is given by:

π = 1 1 = = ∑∑ N M ij i j v s 1 1 = = -∑∑ N M j ij ij i j r s p 1 1 = =   -    ∑ ∑ N M j ij i j a s 1 1 + = =   - -     ∑∑ N M ij i j b D s , ( 10
)
where some s ij = 0, if certain combinations of quality class and supplier are not used. The optimal profit is a linear combination of the random variables p ij , therefore the variance of the optimal profit can be computed by: It is natural to assume that the covariance of the percentage of misclassified units can take non-zero values either between different product classes for the same supplier or for the same product class at different suppliers. For the former case, nonzero covariance can be attributed to the fact that at each supplier the classification process is carried out following a certain procedure which results in a certain tendency to overestimate the true returns quality. The covariance between products of the same class coming from different suppliers can be related to the nature of the product. For example consider that a certain product type has a particular defect that can not be easily detected. If this defect is such that it changes the classification of the returned unit, we expect to have non-zero correlation between the suppliers, and more specifically this correlation is expected to be positive.

Var(π) = ( ) ( ) 2 2 1 1 1 + = =   -     ∑∑ N M j j ij ij i j r r Var p s ( )( ) ( ) 1 1 1 1 1 1 , + + = = = = ≠ ≠   + - -   ∑∑∑ ∑ N N M M j j m m ij km ij km i k j m k i m j
In accordance with the former remarks, we can set in (11):

0 ij km Cov(p , p ) = , ( 12
)
0 ij kj
Cov(p , p ) ≠ , and (13)

0 ij im Cov(p , p ) ≠ . ( 14
)
It is interesting to note that if ( 13) and ( 14) indicate the presence of positive correlation both across different return's classes at a certain supplier and across different suppliers for a certain quality class, this results in an increase of the overall profit variability. Another interesting conclusion, derived by the previous analysis and the form of ( 11), is that the variance of remanufacturer's profit increases in

1 ( ) + - j j r r .
Therefore, the introduction of new quality classes of returned units may decrease the overall profit variability, given that a suitable low-error sorting procedure can be implemented.

Stochastic demand

Having defined the optimal procurement policy in the case of known demand, we proceed to the case that some uncertainty on the demand side exists. The objective function in this case is given by:

E(π) = 1 1 1 1 1 1 0 ( ) ( ) N M ij i j N M ij i j s N M ij i j s v xf x dx s f x dx = = = = ∞ = =   ∑∑     +     ∑∑   ∑∑ ∫ ∫ F o r P e e r R e v i e w O n l y ( ) 1 1 = = -∑∑ N M j ij i j r E q 1 1 = =   -    ∑ ∑ N M j ij i j a s 1 1 1 1 0 ( ) = = = = ∑∑   - -     ∑∑ ∫ N M ij i j s N M ij i j h s x f x dx 1 1 1 1 ( ) = = ∞ = =   - -     ∑∑ ∑∑ ∫ N M ij i j N M ij i j s b x s f x dx .
Taking derivatives with respect to the procurement quantities, s ij , the first and second order partial derivatives are obtained, as follows:

( ) ∂ ∂ ij E s π = 1 1 ( ) N M ij i j v b v b h F s = =   + -+ +     ∑∑ { } 1 ( ) 1 ( ) +   - + - -   j ij j ij j r E p r E p a 2 2 ( ) ∂ ∂ ij E s π = 2 ( ) ∂ ∂ ∂ ij kl E s s π = 1 1 ( ) = =   -+ +     ∑∑ N M ij i j v b h f s < 0.
The objective function has to be maximized subject to the ⋅ M N constraints of the form:

s ij < S ij .
The K-K-T conditions are similar to the ones presented for the known demand case. Examining the K-K-T conditions it is easy to conclude that the optimal solution will involve procurement of all the available quantity for a number of i and j combinations, plus a quantity that lies between 0 and S ij for a specific class and supplier combination and no procurement from all other classes. As the value of the expression

{ } 1 ( ) 1 ( ) ( ) j ij j ij j v b r E p r E p a v b h +   + - + - -   + + (15)
decreases it becomes less probable that the specific combination of class and supplier will enter the optimal solution. Since v, b and h are constant across all supplierquality class combinations, we conclude that the evaluation of each combination can be based on condition (3). Thus, although the nature of demand complicates the decision procedure, it does not alter the criterion for the supplier -product class classification.

It is interesting to note that since both (2) and ( 15) define the relevant profitability of a certain combination of supplier and quality class, it is the difference of the values of ( 2) and ( 15) for sequential classes that impacts the overall profitability and the importance of error-free classification. This feature is further explored in Section 5 via a numerical example.

Numerical illustration and discussion

In this section we present a couple of numerical examples in order to illustrate the optimization procedure proposed in the previous sections and to provide further intuition on some aspects of the problem studied. For the first of these examples we use some general parameter values while for the second we use real data that corresponds to ReCellular actual acquisition and remanufacturing costs. The numerical analysis is carried out for a reverse supply chain consisting of a remanufacturer and N = 2 suppliers. We assume that there are M = 3 different quality classes of returns characterized by different acquisition prices and remanufacturing costs.

In the first numerical example we use two different sets for these costs, as shown in Table 4, differing in the relevant profitability of the first two quality classes.

Table 4 about here

In the first case the sum of procurement and remanufacturing costs for class 1 returns is equal to $21, while for the class 2 returns is $52. The second value set assumes a $36 total cost for quality class 1 and $37 for class 2. However, the values selection is such that the cost of procuring and remanufacturing one class 1 and one class 2 units is equal for these two sets (i.e. $73). The procurement and remanufacturing costs for class 3 returns are equal in both cases, while the selling price exceeds by approximately 1.64% the sum of acquisition and remanufacturing costs of class 3 (v = 62). The demand for remanufactured products is assumed to be known and equal to 100 units. The quantity per quality class collected at each supplier is set equal to 25 units. Since there are 3 quality classes at the 2 available suppliers, there are in total 150 units available for the remanufacturer to purchase. It is assumed that the probability of misclassification at a certain supplier is constant across the first two quality classes, p ij = p i , i = 1, 2 and j = 1, 2, while p i3 = 1, i = 1, 2. Furthermore, it is assumed that p 1 follows a Beta distribution with parameters a 1 = 10 and b 1 = 2, which yield E(p 1 ) = a a The optimal procurement decisions are obtained using the conditions provided in Section 4. In all cases the optimal policy is to procure all available class 1 and 2 units. That is, the remanufacturing facility pays the acquisition cost of 50 class 1 units and 50 class 2 units. However, after the sorting and grading procedure the true quality condition of the returns is revealed. For example, for E(p 1 ) = 10/12 and E(p 2 ) = 8/12 there are on average 37.5 class 1, 50 class 2 and 12.5 class 3 units available.

Naturally, the remanufacturing cost depends on the actual quality condition of the remanufacturing quantity. Table 5 shows the expected profit for the optimal policy as well as the percentage profit reduction due to classification errors at the second supplier. Since the present study deals with the assessment of misclassification cost it can help in the evaluation of alternative methods that aim at the reduction of classification errors, given that they are important (i.e., the firm operates in the topright-hand region of Figure 4). The determination of corrective actions depends on a number of problem parameters, as for example, the relative market position of the suppliers and the remanufacturer. A major remanufacturer can impose some financial penalties according to the classification accuracy. On the other hand, a remanufacturer that cooperates with a major supplier could not take such strict actions. In both cases though, the quantification of the losses associated with misclassification is useful, for the penalty evaluation in the former case and as a negotiation tool, in the latter. In every case, if misclassification is due to malicious supplier intention, monitoring of classification accuracy is basic in order to ensure that there will not be a continuous reduction of classification accuracy. The study of alternative initiatives to the suppliers in order to improve this accuracy is an interesting area.

Another alternative, apart of the provision of initiatives, is the implementation of more accurate sorting methods. When misclassification involving a certain pair of sequential quality classes is highly costly the firm can implement a certain sorting method that ensures that the probability of misclassification in these classes is minimized or even vanished. For example consider the case of ReCellular, which uses a combination of objective and subjective criteria for returns classification, as shown in Table 1. Since a quality class 3 item differs from a quality class 4 item in that the latter fails to power up, the probability of misclassification between these two classes vanishes (i.e. p i3 = 1). Similar exact tests may be available or can be created for the discrimination of classes with high cost differences.

Some other interesting conclusions include the following:

-Demand uncertainty does not alter the suppliers' evaluation criterion.

-Introducing quality classes with values of the remanufacturing cost that lay between the costs of existing classes reduces the misclassification effect on remanufacturer's profit, as long as the respective sorting procedure ensures small classification errors. An interesting extension to the problem studied in the current paper would be the examination of the case in which the suppliers offer the possibility of acquiring the total quantity collected or nothing at all. The model formulation in such case would be the same, apart from the inclusion of a number of binary variables which would indicate if a certain supplier is used. Specifically, if we denote:

S i = 1 M ij j S = ∑ A i = 1 M j ij j a S = ∑ R i = { } 1 1 1 ( ) 1 ( ) M M iM j ij ij j ij ij j r s r S E p r S E p - + =   + + -   ∑
The objective function is given by:

E(π) =       ∑ N i i i=1 v min Q y ,D 1 = -∑ N i i i R y 1 = -∑ N i i i A y 1 + =   - -     ∑ N i i i h S y D 1 + =   - -     ∑ N i i i b D S y ,
where y i , i = 1, 2,…, N are binary decision variables.

A similar approach can be found in [START_REF] Lebreton | A quantitative approach to assessing the profitability of car and truck tire remanufacturing[END_REF] where the case of car and truck tires is examined. 2 Passes a functional and electrical test and with cleaning and buffing can produce a phone that is acceptable in appearance. Phones show no water or physical damage and have a good antenna, display, lens keypad, and a working primary charging system. Keypad and plastic may show fading or uniform discoloration.

F

3 Passes a functional and electrical test but will require some amount of rework to make this phone usable. Phone does not have a good display and working keypad. Phones may have some physical damage and may show signs of wear that will require the replacement of some parts.

4

Phones may have the same physical appearance as a grade 1 phone, but the lens may have some scratches. These phones failed the test or did not power up. Many of these phones are repairable and should produce a good yield with some technical knowledge.

5

Phones have the same physical appearance as a grade 2 phone, but failed the test or did not power up. Many of these phones can be repaired and should produce a good yield with some technical knowledge.

6

Phones have failed the test or did not power up. Phones have some damage but can be used for parts salvage.

  , which is a result of quality overestimation, can be attributed to three factors:

  in the returns classification on the expected profit of the remanufacturer.

  three classes, etc. Section 4 that follows introduces the mathematical model for the problem of returns' misclassification and comments on some of its properties.

  and consequently by (VI), optimal procurement quantity from each ij combination is defined as follows: by (I) µ ij > 0 and by (IV) s ij = S ij . for every ij combination for which ( ) the optimal s ij є [0, S ij ] so that condition (VI) holds.

  examined in two levels, low and high misclassification probability. In the former case the parameters of the Beta distribution are a 2 = 8 and b 2 = 4 while in the latter case they are a 2 = 4 and b 2 = 8, resulting in E(p 2 ) = 8/12 and E(p 2 ) = 4/12, respectively. The two different values of classification accuracy are examined comparatively to the case of error-free classification at the second supplier, i.e. E(p 2 ) = 1.

  is primarily affected by the extent of quality overestimation and the difference of acquisition and remanufacturing costs of sequential quality classes at the same or different suppliers.

  of acquisition prices may decrease the impact of misclassification errors on the total profitability.

Fig. 1 .

 1 Fig. 1. Schematic representation of the reverse supply chain.

Fig. 2 .

 2 Fig. 2. Example of a family of truncated normal distributions describing the relationship between quality class and remanufacturing cost.

Fig. 3 .Fig. 4 .

 34 Fig. 3. Remanufacturer savings by error-free classification.

  the procurement and selling price are considered

	decision variables which influence both return and demand rates. A similar issue is
	examined and in
	F o r
	P
	e
	e r
	R
	e
	v i e
	w
	O n l
	y
	4

Table 3

 3

about here Figure 1 about here

Table 5

 5

	about here

Table 1 .

 1 Nominal quality metrics for grading mobile telephones (adopted by[START_REF] Guide | Managing product returns for remanufacturing[END_REF].

	o r
	P
	e
	e r
	R
	e
	v i e
	w
	O n l
	y

Table 2 .

 2 Remanufacturing cost and acquisition prices in $[START_REF] Guide | Matching demand and supply to maximize profits from remanufacturing[END_REF].

	Class (j)	Acquisition price (α j ) Remanufacturing cost (r j )
	1	26.8	5
	2	17.3	20
	3	9.8	30
	4	6.3	35
	5	4.0	40
	6	2.0	45

Table 3 .

 3 Notation.

	j	returned units categories, j = 1, 2,…, M (1 best quality)
	i	supplier index, i = 1, 2,…, N
	a j	acquisition cost per unit classified in category j
	r j	remanufacturing cost per unit of category j
	v	sales revenue
	p ij	fraction of returns classified by supplier i as j returns that are indeed j returns (a random
		variable)
	g ij (.)	probability density function of p ij
	D	demand for remanufactured units (constant or random)
	s ij	quantity of returns classified as class j ordered from supplier i
	S ij	quantity of returns classified as class j collected at supplier i
	S i	total quantity collected at supplier i
	q ij	actual quantity of class j returns received by supplier i
	h	cost of unsold remanufactured unit
	b	shortage cost per unit of demand that is not satisfied

Table 4 .

 4 Parameters (α j , r j ) for the two cost sets.

	j		1	2	3
	set 1	α j	19	14	13
		r j	2	38	48
	set 2	α j	15	14	13
		r j	21	23	48

Table 5 .

 5 Optimal expected profit E(π) and percentage reduction.

	E(p 2 )	cost set	E(π)	%
	1	1	2454.17
		2	2493.75
	8/12	1	2070.83	15.6
		2	2268.75	9.0
	4/12	1	1687.50	31.2
		2	2043.75	18.0

Table 6 .

 6 Parameter values, expected profit E(π) and percentage reduction for ReCellular

		acquisition policy.
	Model	a 1	a 2	a 3	v	E[π|E(p 2 )=1]	% reduction of E(π) for E(p 2 )=8/12 E(p 2 )=4/12
	1	33.0	31.0	29.0	60.0	1497.92	13.9	27.8
	2	85.0	75.0	65.0	96.5	368.75	39.5	73.4
	3	110.0	105.0	100.0	132.0	1147.92	18.1	32.7
	4	40.0	35.0	30.0	61.0	1047.92	19.9	35.8
	5	26.8	17.3	9.8	40.5	542.92	34.5	57.6
			N
			i,2
			i=1

http://mc.manuscriptcentral.com/tprs Email: ijpr@lboro.ac.ukInternational Journal of Production Research

Acknowledgements

The present study is co-funded by European Union -European Social fund and National fund -PYTHAGORAS -EPEAEK II.

An interesting conclusion is that the remanufacturer can in some extent reduce the profit losses because of low classification accuracy by changing the acquisition prices offered to suppliers; an acquisition policy with rather small differences between sequential quality classes can result in greater robustness of the economical outcome of remanufacturing activities.

We proceed by presenting another numerical example, using real data for the acquisition and remanufacturing costs, α j and r j , respectively, corresponding to the ReCellular case. [START_REF] Guide | Managing product returns for remanufacturing[END_REF] report the fee that ReCellular pays to suppliers for each quality class for 4 different phone models. By repeating the numerical analysis for the first three quality classes of these 4 sets as well as for the α j values shown in Table 2 (referred to as model 5 in Table 6), we reach to the results presented in Table 6. The r j (j = 1, 2, 3) values are set equal to Table 2 values which correspond to ReCellular actual remanufacturing cost. Since for the remainder parameter values we were unable to obtain real data, the classification and demand characteristics are identical to those used in the previous numerical example. As before, v exceeds α 3 + r 3 by approximately 1.64%. Moreover, the returns quantity is set equal to 25 units per quality class and supplier, resulting into 150 available returned units.

Table 6 about here Table 6 reveals that the impact of quality overestimation is substantial. The relatively lower values of the expected profit of models 2 and 5 observed in Table 6 are due to the rather low profit margins of quality class 1 units of these models.

Although in these cases there is a large percentage profit reduction as classification accuracy deteriorates, this phenomenon can be attributed, to a certain extent, to scale differences. However, the absolute differences of the expected profit under different classification accuracy are comparable, indicating limited interaction of profit margins with the classification accuracy effect.

Extensions and conclusion

The current paper addresses the issue of returns quality overestimation by the suppliers and examines the effect of such misclassification on the remanufacturer's profitability. An interesting conclusion by the analysis is that the economical impact