At this point we want to share the main results of two field-studies we performed to ob-tain informations about the performance of the price optimization with receding hori-zon POP-RH, see 2.5.4. Price optimization was performed every sales week again exploiting latest sales figures, i.e. the knowledge about the scenario in effect. The DISPO-team performed different experiments from which we want to sketch out the results of the two last ones where the test set-up described above was applied. While for the first outlined experiment we were mainly concerned with the evaluation we per-formed and evaluated the second experiment completely. At first we will show that mark-downs can have a significant influence on the sales. Then our focus lies on the realized revenue.
10.3.1 Performing price optimization with receding horizon – POP-RH
In the field studies in terms of price optimization both, the test branches and the control branches, were supplied by our industrial partner. The control branches were com-pletely managed by our partner who performs the mark-downs there. Two weeks after sales start the DISPO-team/we began to perform the price optimization process in the test branches. This time is needed to assign the scenario in effect according to the observed sales figures.
To exploit always the latest sales figures, at the end of each week. the demand estimation according to the observed sales was updated, see Chapter3,3.2.6. Then, price optimization was applied to compute an updated price policy. If the optimal price trajectory suggested a mark-down in the following two time periods the industrial partner was advised to implement exactly this mark-down.
We want to remark at this point, that because of the high amount of data our project partner had to transfer to the DISPO team, the proposed mark-downs could not exactly be applied the week after the evaluation of the latest sales figures. The mark-downs were applied one week later. In detail the sales data was available for the DISPO-team between Monday morning and Tuesday evening. Then the in terms of latest sales figures optimal price trajectory was computed. The partner obtained the by the POP-RH proposed mark-downs at the latest on Tuesday evening. Depending on the sales start of the article the mark-downs were performed the week after on Tuesday or Friday.
The partner provided all transactions and additional data on a server. Additionally to the about 8 GB of data that was needed for empirical demand estimation at the beginning of the field studies every week 4 GB of new data which included latest transaction data were transferred.
10.3.2 Sales increase by mark-downs
From the beginning of November 2009 until the end of March 2010 the DISPO-team performed a field study in terms of price optimization at the industrial partner. Com-pared were 26 test branches with 26 control branches.
There was one specialty. Because the partner had to get rid of old articles – old means winter products – to create space for the spring articles the DISPO-team decided to include penalty costs in the objective of the POP (without mark-down costs).
For Periodkthe penalty costs per remaining item are given by pen(k) :=
(0.1ap·212(k−ω+6) k∈K:k≥ω−6,
0 otherwise. (10.5)
The penalty costs depend on the current period, the current stock and the acquisi-tion price. It isω the number of weeks for the product from the sales start until the end of the field study. Penalty costs only arise in the last 6 weeks of the experiment.
Because of the factor 12 in the exponent, the penalty costs which depend from10%of the acquisition price double all two weeks. For each non-sold item at Periodkthese costs were added in the objective of the POP. The idea is that each remaining item uses space that is needed for new products. Because at that time the DISPO-team had no estimation of the cost that remaining items would cause this artificial penalization was used.
The remaining parameter setting is given as stated in Table 10.3 (from the line four)1. POP-RH is performed as described in10.3.1.
For the reason to get unbiased results the DISPO-team restricted the complete test set of 3050 articles to 1037 articles which were supplied to all test and control branches (we also performed an evaluation for all articles, the main result does not distinguish).
While in the control branches for the 1037 articles only 980 mark-downs were performed including the penalty costs led to 1928 mark-downs in the test branches.
In Figure10.1the effect of mark-downs for a sample of 66 of the 1037 articles is recognizable. We see that 6 weeks before the field study ends the “bad sellers” start to boom. If we look for example at the article which is depicted by the green rhombus, we see that this product is mark-downed at sales week 12 to about 0.25 of the starting price. We see that the sales increase rapidly in the next two sales weeks. We made this observation also for other articles and different sales weeks, see AppendixB.
We observed an average sales rate of84.6 for the control branches and 90.4for the test branches, respectively. This result is highly significant (in terms of Wilcoxon signed-rank test) with a p-value of nearly0.00%.
The observed increase of sales by applying POP-RH (with penalty costs for non-sold items) in contrast to manual decisions on mark-downs is significant.
Because of the artificial penalty costs in the objective at this point we are not able to make a statement about the influence on the realized revenue. For this purpose we performed another field study.
10.3.3 Earnings increase by mark-downs
To compare POP-RH with manual decision making about mark-downs also in terms of money we performed another field study. Analogously to the previously described experiment all articles were supplied by our industrial partner. From 30 pairs of com-parable branches the categorization in test and control branch happened randomly.
For this experiment we tried to model the reality as exactly as possible: POP-RH based on realistic estimations on all occurring costs. Our partner estimated fixed and variable mark-down costs. The fixed mark-down cost amount toµf = 7.0while the variable mark-down costµvper item lie between0.12and0.21depending on the com-modity group. It isqkmax = 2, that means after the last real sales periods two additional mark-downs are assumed. The remaining parameters are as stated in Table10.3.
1In order not to reveal company internals, we state all values/costs with respect to artificial but consistent monetary units.
0.1 0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
price level
sales week ratio price/starting price
sales start 18 weeks before field study’s end 66 articles
mean median
0.1 0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
rel. sales
sales week rel. sales
sales start 18 weeks before field study’s end 66 articles
mean median
Figure 10.1: Effect of mark-downs
sample relative realized objective gross yield sales
test 0.4774 0.6524 0.7891
control 0.4698 0.6494 0.7945
Table 10.1: Performance metrics – 2nd field study POP-RH
Originally there were4668 products included in the test. To get possibly non-biased result our evaluation uses only2298from them which were supplied to all test and control branches.
We state some performance metrics for the test and control branches in Table10.1.
We will focus on therelative realized objectivewhich we will define in the follow-ing.
For each test-control pair of branches, therealized revenues over all articles inA were compared. That means, in particular, that expensive articles have a larger influ-ence on the result than cheap articles. This point of view is in line with our partner’s point of view.
For reasons of comparability we divide the realized revenue by maximum possible revenue in terms of the objective of the POPˆe.
This means for an initial stockIb,sa for the considered branchb, sizesand article aand a starting priceπ0awe compute therelative realized objectiveof the mark-down decisionta = (ta0, ta1, . . . , tak Depending on Articlea,apadenotes the acquisition price,π0athe starting price and Ib,sa the initial stock per branch and size. During the sales process, we observedˆrk,b,sa (the realized yield for Branchband Sizesin Periodk) for Articleaandnˆak(mark-down in Periodk– yes or no).
Since we only consider a subset of branches we have to take into account that fixed mark-down costs must be scaled with respect to the number of considered branches.
This way, we get mark-down costsµ˜akfor periodk.
Because all test and control branches were supplied by our partner and now our focus lies on the price optimization stage we do not regard costs for supply in terms of lots as lot-opening costs and pick costs as they appear in ISPO.
We see that the mean relative realized objective in the test branches is about 0.76 percentage points higher than in the control branches. Also in terms of the other perfor-mance metrics POP-RH beats the manual price optimization. Yet, with a rank-sum of 285andP30(X ≥285) = 14.47%andP30(X ≤285) = 86%Wilcoxon signed-rank test yields no significance. Still, the p-value for a better performance caused by pure chance is with14.47%comparatively small.
0 5 10 15 20 25 Change of supply by ISPO
vs. sellout date by LDP
amount of sizes per branch with sellout date
weeks until sellout date
supply ISPO - supply LDP
0