Table of Contents

Background

James has been operating a sandwich stand in the lobby of his office building during the lunch hour for the past two years.He has been tracking sandwich demand over the two years and he has carefully recorded the number of each type of sandwich demanded, the number he brought with him to sell, and his prices for each type of sandwich.

James provided his data set for analysis.

Overview of Datasets

sales.csv

The file sales.csv contains the demand and availability by date for each of the three sandwiches that James sells.

summary(historical_data[,c("date_dt")])
##                  Min.               1st Qu.                Median 
## "2014-03-03 00:00:00" "2014-04-16 06:00:00" "2014-05-31 12:00:00" 
##                  Mean               3rd Qu.                  Max. 
## "2014-05-31 12:02:18" "2014-07-15 18:00:00" "2014-08-29 00:00:00"
stat.desc(historical_data[,c("demand.ham","demand.turkey","demand.veggie","available.ham","available.turkey","available.veggie")])
##                demand.ham demand.turkey demand.veggie available.ham
## nbr.val       130.0000000   130.0000000   130.0000000   130.0000000
## nbr.null        0.0000000     0.0000000     0.0000000     0.0000000
## nbr.na          0.0000000     0.0000000     0.0000000     0.0000000
## min             6.0000000    13.0000000     4.0000000    14.0000000
## max            25.0000000    37.0000000    24.0000000    18.0000000
## range          19.0000000    24.0000000    20.0000000     4.0000000
## sum          2073.0000000  2867.0000000  1698.0000000  2050.0000000
## median         16.0000000    21.0000000    13.0000000    15.0000000
## mean           15.9461538    22.0538462    13.0615385    15.7692308
## SE.mean         0.3398255     0.4335803     0.3141949     0.1588339
## CI.mean.0.95    0.6723532     0.8578491     0.6216422     0.3142567
## var            15.0125820    24.4389386    12.8333930     3.2796661
## std.dev         3.8746073     4.9435755     3.5823725     1.8109848
## coef.var        0.2429807     0.2241593     0.2742688     0.1148429
##              available.turkey available.veggie
## nbr.val           130.0000000      130.0000000
## nbr.null            0.0000000        0.0000000
## nbr.na              0.0000000        0.0000000
## min                14.0000000        8.0000000
## max                20.0000000       11.0000000
## range               6.0000000        3.0000000
## sum              2240.0000000     1230.0000000
## median             18.0000000       10.0000000
## mean               17.2307692        9.4615385
## SE.mean             0.2346132        0.1070858
## CI.mean.0.95        0.4641879        0.2118718
## var                 7.1556351        1.4907573
## std.dev             2.6750019        1.2209657
## coef.var            0.1552456        0.1290452

As we can see from the data above, mean-demands for each sandwich type are 15.94(Ham), 22.05(Turkey) and 13.06(Veggie). The best selling sandwich is Turkey

details.csv

This file contains cost and sale prices according to sandwich type:

(pricing)
##     type price cost
## 1    Ham   6.5  3.5
## 2 Turkey   6.5  4.0
## 3 Veggie   5.0  2.5

Supply vs Demand

From the plot below we can see that the productions of Turkey and Veggie sandwiches are below the demand.

Seasonal Variation of Demand

Before we proceed any further, we want to know if there are any seasonal statistically significant variations. We want to prove the significance of any of the following variations by sandwich type:

We conducted an analysis of variance of the demand in order to accept or reject each of our hypothesis.

The results are as follows:

summary(aov(demand ~ sandwich:month+sandwich:day_of_week+sandwich:month:day_of_week
            ,data=historical_pivoted
            )
        )
##                             Df Sum Sq Mean Sq F value Pr(>F)    
## sandwich:month              17   5648   332.2  18.743 <2e-16 ***
## sandwich:day_of_week        12    226    18.8   1.063  0.391    
## sandwich:month:day_of_week  60   1034    17.2   0.972  0.538    
## Residuals                  300   5318    17.7                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

As we can see in the results above, the only statistically significant variation(normally p<0.05) in the distribution of the demand is the month.

The chart below illustrate the actual fluctuations of the demand by sandwich type and month:

Based on these findings, we will recommend monthly sandwich produtions to James.

Increasing James’ Profit

James often produces less sandwiches than the actual demand, particularly turkey and veggie sandwiches. We also, found that there exists variation in the demand from month to month. Therefore, adjusting his supply levels according to this will help him maximize his profit.

We recommend that James be adjusting his production levels like the following table:

##   month Ham Turkey Veggie
## 1   Mar  15     21     15
## 2   Apr  15     20     13
## 3   May  16     23     13
## 4   Jun  16     21     13
## 5   Jul  16     22     13
## 6   Aug  16     22     13

Current and Expected Profit

The table below shows James’ current profit and expected profit based on the recommended production levels.

##   sandwich profit_current profit_expected increase
## 1      Ham           4837            4967     2.7%
## 2   Turkey           5106            5586     9.4%
## 3   Veggie           2885            3350    16.1%
## 4    TOTAL          12828           13903     8.4%

The expected profit was calculated by applying the recommended production levels to the provided historical data. As we can see, James’ profit would have increased by 8.4%.

Conclusion

This recommendation is based on the data that James collected from Mar.2013 to Aug.2013. As we analysed above, the main reason that James could not maximize his profit was on supply deficiency of Turkey and Veggie sandwiches. Therefore, if he adjust the supply like we recommended, he would make more money, about $180 monthly