### Final Grade & Feedback
Q1: 10/15 [Calculated 393, outside ±5% range of 419]
Q2: 15/15
Q3: 15/15
Q4: 10/15 [No quantitative example provided]
Q5: 5/10 [Generic points without specific stakeholders]
Bonus: 0/10
**Total: 55/80**
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15.778 Introduction to Operations Management
Section B
Yedioth Case
Raghavendra Polanki
Alexey Ershov
Brendan Owen
SiTing Han
Susana Tamayo
1. In the current distribution model, where each retailer is supplied once,
independentlyofallotherretailers.Whatwouldbeagoodmethodtocomputethe
quantity shipped to each retailer if one wishes to guarantee that 99% of
customers will be served? Apply your approach to compute recommended
quantities to the 50 retailers (explain the methodology in the body ofthereport
and provide the results in appendix).
The method we used to determine the quantity shipped to each retailer was as follows:
● We created a pivot table to consolidate the complete sales data for each retailer.
● For each retailer, we calculated the sum, average, and standard deviation of
sales.
● We then applied the formula for the optimal order quantity q* =μ + Kσ , where
K corresponds to the desired service level (99%).
● Finally, we summed theq*values across all retailersto obtain the total
recommended quantity.
This approach gives the following outputs:
Mean: 204.6 |
Standard Deviation: 81.3
| 99% stock level: 393 magazines 🚨calculated 393, outside range🚨
2.IfYediothcouldimplementfullpoolingamongallofthe50retailerswhatwould
be the estimated benefit in termsoftotalproductionlevelsandreturns(assume
thattherequiredservicelevelis99%).Note:Fullpoolingmeansthatsomehowall
of the retailers could be supplied in real time from the same pool of inventory.
Fullpoolingmeansthatall50retailersaretreatedasasingleentity,andinventorycan
bemovedbetweentheminreal-timetomeetdemand.Toestimatethebenefitinterms
of total production levels and returns for a 99% service level, we will:
1. Aggregate the sales data for all 50 retailers for each week to get the total sales.
2. Calculate average of weekly sales aggregate data.
3. Calculate standard deviation of the weekly sales data aggregate.
15.778 Introduction to Operations Management
Section B
4. Using the optimal quantity formulaq* =μ + Kσwe know mean, standard
deviation K = 2.32 for 99%, we calculate q*.
This approach gives the following outputs:
Mean: 189.6 |
Standard Deviation: 19.9
| 99% stock level: 236.1 magazines 🚨correct pooling🚨
3. Suppose that one could implement full pooling only among retailers that are
treated by the same sales agent, whatwouldbethepotentialbenefitintermsof
production levels and returns (assume 99% service level). Compare to 2) above.
Full pooling among retailers served by the same sales agent can be simulated via the
following approach:
- For each of the 46 weeks, sum up the total sales (across each salesperson’s five
stores serviced) for each of the 10 sales agents
- Calculate the mean and standard deviation across weeks for each sales agent
- Sum these numbers for an overall mean and standard deviation across agents
- 99% service level can then be computed using the formulaq* =μ + Kσfor the
“agent pooling” setup
This approach gives the following outputs:
Mean: 189.6 |
Standard Deviation: 41.7
| 99% stock level: 286.49 magazines 🚨correct agent pooling🚨
This is a clear improvement in all metrics from our original approach. Compared to
question 2:mean is the same(makes sense, as we arestill looking at total sales per
week) but thestandard deviation has increaseddueto the variation between agents.
4.Proposemorerealisticpoliciesthatleveragethefactthatthesalesagentvisits
each retailer in the middle of the week. What would the benefit be of these
policies?
Whenanalyzinginventoryrequirementsunderthecurrentdistributionmodel,thecentral
poolingmodel,andthedistributedpoolingmodelforeachsalesagent,weobservedthat
reducing thestandarddeviationofdemandacrosstheweekcansignificantlydecrease
variability. This, in turn, reduces the amount of inventory required to meet customer
demand without increasing the risk of stockouts.
Given that each sales agent visits retailers midweek, a more realistic and effective
policywouldbetoleveragethesevisitstogatherreal-timeinsightsoninventorylevels.
15.778 Introduction to Operations Management
Section B
Specifically, sales agents could report whether inventory is accumulating (indicating
lower-than-expecteddemand)orifretailersanticipatehigherdemandthancurrentstock
levels can support.
This midweek feedback provides valuable data that can be used by headquarters to
reduce uncertainty fortheremainderoftheweek.Usingthisinformation,headquarters
could reallocate inventory dynamically—shifting stock from sales agents with excess
inventorytothosefacingpotentialshortages.Thisapproachhelpsavoidoverproduction
and minimizes the risk of underserving customers, all without the need to print
additional copies. 🚨reallocation mechanism🚨
5. What do you think are the organizational challenges that Assaf will have to
address?
He needs to build a centralized pool system and establish a distribution process from the pool to
the points of sale. One of the key challenges is how to ensure regular circulation of magazines
from the pool to the sales outlets. The more frequently this distribution occurs each week, the
lower the standard deviation in demand, which means the company can print fewer excess
copies.
The ideal scenario would be real-time supply, but that is not feasible because each sales agent
is responsible for about 10 sales points. On the positive side, the agents are motivated to
increase sales, which aligns well with this approach. However, increasing the number of agents
is not an option because it would reduce the average income per agent.
-
-
-
-
The agents don’t have incentive to optimize a stock.
Hove to collect information from all points of sales
Need to be close connection with agent and redistribution team
We need to rely on integrity of agent about information from point of sales 🚨generic challenges🚨
15.778 Introduction to Operations Management
Section B
Appendix 1: data for mean, standard deviation, 99% supply level across customers (Q1)
15.778 Introduction to Operations Management
Appendix 2: total sales per week under pooling system (Q2)
Section B
15.778 Introduction to Operations Management
Section B
Appendix 3: total sales per week per sales agent under agent pooling system (Q3)