### Final Grade & Feedback Q1: 15/15 Q2: 15/15 Q3: 15/15 Q4: 10/15 [No quantitative example provided] Q5: 10/10 Bonus: 0/10 [Only censoring mentioned, no distribution assumption] **Total: 65/80** --- Section B Pat Ovando Roche Makeda Mekonnen Ricardo Suarez Heredia Shiva Mehrotra Wee Hao Ng THE YEDIOTH GROUP: CASE STUDY REPORT Question 1. In the current distribution model, where each retailer is supplied once a week independently of all other retailers, what would be a good method to compute the quantity shipped to each retailer to guarantee that 99% of customers will be served? Apply your approach to compute recommended quantities to the 50 retailers. Method A: Estimating Demand based on Observed Sales (i.e. sales = demand) Let β€’ β€’ β€’ 𝑖 ∈ {1,2, … , 𝑁} be the index for retailers (N=50) 𝑑 ∈ {1,2, … , 𝑇} be the index for distribution weeks (2008-2009) 𝑆𝑖,𝑑 be the observed sales for retailer 𝑖 in week 𝑑 Step 1: Estimate Mean (ΞΌ) of Observed Sales (Demand) For each retailer, estimate the mean weekly demand (ΞΌ) (i.e., average of weekly sales): 𝑻 𝟏 𝝁 = βˆ‘ π‘Ίπ’Š,𝒕 𝑻 𝒕=𝟏 Step 2: Estimate Standard Deviation (Οƒ) of Observed Sales (Demand) For each retailer 𝑖,estimate the standard deviation of weekly sales: 𝑻 𝟏 πˆπ’Š = √ βˆ‘(π‘Ίπ’Š,𝒕 βˆ’ ππ’Š )𝟐 π‘»βˆ’πŸ 𝒕=𝟏 Step 3: Compute quantity to ship (Q) for 99% service level Assuming demand follows a normal distribution, the quantity to ship to retailer 𝑖 is: π‘Έπ’Š = ππ’Š + π’Œπˆπ’Š Where: β€’ π‘˜ = 2.3326 is the Z-score for a 99% service level. Step 4: Estimate total quantity to distribute (Q) 𝒏 π‘Έβˆ— = βˆ‘ π‘Έπ’Š 𝑰=𝟏 Total Q (π‘Έβˆ—π‘¨ ) = 393.5 β†’ 394 units Refer to the Appendix for full computation details Method Limitation: This method assumes observed sales is equal to demand, which is only true when there are no stockouts. In reality, censored demand exists. If a retailer sells out, true demand may be higher than observed sales. Method B: Estimating Demand with Censored Sales (Stockouts) (i.e. demand β‰  sales) Let β€’ 𝑖 ∈ {1,2, … , 𝑁} be the index for retailers (N=50) β€’ 𝑑 ∈ {1,2, … , 𝑇} be the index for distribution weeks (2008-2009) β€’ 𝑆𝑖,𝑑 be the observed sales for retailer 𝑖 in week 𝑑 β€’ 𝑄𝑖,𝑑 be the total quantity available to retailer 𝑖 in week 𝑑 (i.e., distributed + added) β€’ π‘†π‘’π‘™π‘™π‘‡β„Žπ‘Ÿπ‘œπ‘’π‘”β„Žπ‘–,𝑑 = 1 if all inventory was sold (i.e, stockout), 0 otherwise Step 1: Calculate the Stockout Rate (𝑃) We calculate the stockout rate for each retailer 𝑖 across all weeks 𝑇 𝑻 𝟏 π‘·π’Š = βˆ‘ π‘Ίπ’†π’π’π‘»π’‰π’“π’π’–π’ˆπ’‰π’Š,𝒕 = 𝟏 𝑻 𝒕=𝟏 Step 2: Calculating Demand Standard Deviation (Οƒ) We take the standard deviation Οƒ of weekly sales for each retailer. 𝑻 𝟏 πˆπ’Š = √ βˆ‘(π‘Ίπ’Š,𝒕 βˆ’ Μ… π‘Ίπ’Š )𝟐 π‘»βˆ’πŸ 𝒕=𝟏 Where: β€’ 𝑆𝑖̅ is the average of observed sales for retailer 𝑖 Step 3: Estimating Mean Demand (ΞΌ) To estimate demand 𝐷𝑖 , we consider the total quantity available for retailer (distributed and added) as Q. Assuming demand follows a normal distribution 𝐷𝑖 ~𝒩(πœ‡π‘– , πœŽπ‘–2 ), the stockout rate represents the probability of a stockout (i.e. demand exceeds available inventory): β„™(π‘«π’Š > π‘Έπ’Š ) = π‘·π’Š π‘Έπ’Š βˆ’ ππ’Š π‘Έπ’Š βˆ’ ππ’Š π‘·π’Š = 𝟏 βˆ’ β„™(𝐙 < ) = 𝟏 βˆ’ 𝚽( ) πˆπ’Š πˆπ’Š We can then calculate πœ‡π‘– which would be the estimated demand for newspaper sales for each retailer. Step 4: Compute Weekly Shipment Quantity for 99% service levels (Q) Having estimated both Οƒ and ΞΌ, we estimate Q for 99% service level for each retailer using: π‘Έπ’Š = ππ’Š + π’Œπˆπ’Š Where: β€’ π‘˜ = 2.3326 is the Z-score for a 99% service level. Step 5: Estimate total quantity to distribute (Q) 𝒏 π‘Έβˆ— = βˆ‘ π‘Έπ’Š 𝑰=𝟏 Total Q (π‘Έβˆ—π‘© ) = 421.8 β†’ 422 units Refer to the Appendix for full computation details Conclusion: We recommend Method B as it accounts for censored demand caused by stockouts. By adjusting for weeks where demand likely exceeded available inventory, Method B provides a more accurate estimate of true customer demand and a better basis for service-level-aligned inventory policy. 2 Question 2. If Yedioth could implement full pooling among all of the 50 retailers what would be the estimated benefit in terms of total production levels and returns if the required service level is 99%? (Note: Full pooling means that somehow all of the retailers could be supplied in-real-time from the same pool of inventory.) Method C: Estimating Aggregate Weekly Demand across Retailers Let β€’ 𝑖 ∈ {1,2, … , 𝑁} be the index for retailers (N=50) β€’ 𝑑 ∈ {1,2, … , 𝑇} be the index for distribution weeks (2008-2009) β€’ 𝑆𝑖,𝑑 be the observed sales for retailer 𝑖 in week 𝑑 Step 1: Estimate Total Weekly Sales Assuming that demand is equal to observed sales, for each of the weeks 𝑑, compute the total sales across all 50 retailers: 𝑡 𝑫𝒕 = βˆ‘ π‘Ίπ’Š,𝒕 π’Š=𝟏 This provides a time series {𝐷1 , 𝐷2 , … , 𝐷𝑇 } representing total weekly demand. Step 2: Estimate Mean and Standard Deviation of Weekly Sales Let β€’ β€’ πœ‡π· be the mean of total weekly demand 𝜎𝐷 be the standard deviation of total weekly demand 𝑻 𝟏 𝝁𝑫 = βˆ‘ 𝑫 𝒕 𝑻 𝒕=𝟏 𝑻 𝟏 πˆπ‘« = √ βˆ‘(𝑫𝒕 βˆ’ 𝝁𝑫 )𝟐 π‘»βˆ’πŸ 𝒕=𝟏 Step 3: Compute quantity to ship at 99% service level 𝑸𝑫 = 𝝁𝑫 + π’Œπˆπ‘« Where: β€’ π‘˜ = 2.3326 is the Z-score for a 99% service level. Refer to the Appendix for full computation details Standard Mean Demand (𝝁𝑫 ) Deviation of Demand (πˆπ‘« ) 189.6 20.0 Q* at 99% 236 units 3 Step 4: Compare total quantity to distribute between Method B (Question 1) and Method C (Question 2) Current Distribution Model (Method B) Total Quantity to Distribute (Q*) π‘Έβˆ—π‘© = 422 units Full Pooling (Method C) π‘Έβˆ—π‘ͺ = 236 units Then the benefit from full pooling is the reduction in total quantity required: πš«π‘Έ = π‘Έβˆ—π‘© βˆ’ 𝑸π‘ͺβˆ— πš«π‘Έ = πŸ’πŸπŸ βˆ’ πŸπŸ‘πŸ” = πŸπŸ–πŸ” π’–π’π’Šπ’•π’” Question 3. Suppose that one could implement full pooling only among retailers that are treated by the same sales agent. What would be the potential benefit in terms of production levels and returns, assuming 99% service level. Compare to your #2 answer. Method D: Estimating Weekly Demand by Sales Agent Let β€’ β€’ β€’ Ξ‘ be the set of sales agents with 𝑗 ∈ 𝐴 𝑑 ∈ {1,2, … , 𝑇} be the index for distribution weeks (2008-2009) 𝑆𝑗,𝑑 be the total number of copies sold by agent 𝑗 in week 𝑑 Step 1: Aggregate weekly sales per agent Assuming that demand is equal to observed sales, for each of the weeks 𝑑, compute the total sales across all 10 agents: 𝑨 𝑫𝒕 = βˆ‘ 𝑺𝒋,𝒕 𝒋=𝟏 This provides a time series {𝐷1 , 𝐷2 , … , 𝐷𝑇 } representing total weekly demand across agents. Step 2: Estimate Mean and Standard Deviation of Weekly Sales Let β€’ β€’ πœ‡π· be the mean of total weekly demand 𝜎𝐷 be the standard deviation of total weekly demand 𝟏 𝝁𝑫 = 𝑻 βˆ‘π‘»π’•=𝟏 𝑫𝒕 𝟏 πˆπ‘« = βˆšπ‘»βˆ’πŸ βˆ‘π‘»π’•=𝟏(𝑫𝒕 βˆ’ 𝝁𝑫 )𝟐 Step 3: Compute quantity to ship at 99% service level 𝑸𝑫 = 𝝁𝑫 + π’Œπˆπ‘« Where: β€’ π‘˜ = 2.3326 is the Z-score for a 99% service level. 4 Refer to the Appendix for full computation details Total Quantity to Distribute (Q*) Current Distribution Model (Method B) Full Pooling (Method C) Partial Pooling – Sales Agents (Method D) π‘Έβˆ—π‘© = πŸ’πŸπŸ π’–π’π’Šπ’•π’” π‘Έβˆ—π‘ͺ = πŸπŸ‘πŸ” π’–π’π’Šπ’•π’” π‘Έβˆ—π‘« = πŸπŸ–πŸ• π’–π’π’Šπ’•π’” Question 4. Propose more realistic processes/strategies that leverage the fact that the sales agent visits each retailer in the middle of the week. What would the benefit be of these processes/strategies? Proposal A. Mid-Week Inventory Replenishment ("Two-Shipment Model") β€’ Deliver a base quantity on Sunday (e.g., 60–70% of expected demand). β€’ Use the Wednesday visit to collect early-week sales data and replenish stock for high-performing retailers. Benefits: β€’ Reduces initial overproduction and overstocking at the start of the week. β€’ Maintains service levels by correcting early underestimates (i.e. captures missed demand due to early stockouts). β€’ Reduces unpredictable demand variability by splitting the fulfilment into two phases, allowing mid-week corrections based on actual trends. β€’ Improves predictable variability, making weekly planning more datadriven and reducing reliance on pure forecasts. Requirements: β€’ Method could requires basic IT (best-case scenario) or manual reporting (worst-case scenario). β€’ Method required logistic support and additional costs for mid-week deliveries. Proposal B. Early-Week Sales-Based Forecast Adjustment (Predictive Replenishment) β€’ Use early-week sales (e.g., Sun–Tues) to update full-week demand forecasts. β€’ Sales agents can manually report sales or estimate remaining inventory. Benefits: β€’ Enables proactive adjustments in future print runs. β€’ Builds a feedback loop between the field and the supply and operations team. β€’ Helps reduce unpredictable demand variability through near-real-time sales data-informed planning (smart inventory decision making). β€’ Improves service level without full pooling. Requirements: β€’ Method required historical data analysis (data collection devices) and training/validation of forecasting models. 5 Proposal C. Localised Redistribution Among Retailers (Intra-Agent Pooling) β€’ Agents identify overstocked and understocked retailers on Wednesday. β€’ Transfer magazines within their cluster to better match supply with demand (i.e. move unsold inventory from overstocked retailers to those experiencing stockouts). Benefits: β€’ Simulates pooling without systemic changes (i.e. centralized inventory). β€’ Reduces variability across the network by reallocating excess inventory to high-demand locations. β€’ Increases overall sales and customer satisfaction with minimal cost. β€’ Reduces waste and lost sales. Requirements: β€’ Method requires agent training, incentives as well as coordination and tracking tools for stock movement. Proposal D. Use of smart stands or RFID for real-time tracking User RFID enabled stands to track inventory levels automatically upon unit movement. β€’ RFID tags on magazines are read by smart stand scanners, updating the inventory level to the central database. β€’ Benefits: Automation of inventory tracking increases accuracy and requires minimal manual intervention. β€’ Enable real-time pooling and forecasting (Proposal B). Requirements: β€’ Considerable investment and development time for RFID infrastructure and suitable integration of tags into magazines at a sustainable cost. β€’ Experimentation through pilot studies with larger, medium and small retailers (small subset) for advantages and disadvantages. β€’ 6 Question 5. What do you think are the organizational challenges that Assaf will have to address? A. Cultural Resistance: β€’ Sales agents are incentivised on sales volume, not efficiency. β€’ Staff may resist changes that reduce shipments or increase workload (e.g. data collection). B. IT Limitations: β€’ Most kiosks lack EDI or digital sales systems. β€’ Requires investment in tech infrastructure (e.g. RFID, mobile apps, or smart stands). β€’ Build internal capabilities for statistical and analytical methods. C. Interdepartmental Alignment: β€’ Research, Distribution, and Sales must coordinate on forecasting and inventory. β€’ Requires training, role realignment, and perhaps changes in incentive structures. D. Trust and Change Management: β€’ Fear of stockouts and lost revenue is entrenched. β€’ New systems must demonstrate reliability and win buy-in gradually. E. Operational Coordination: β€’ Adapt current logistics to support additional deliveries. β€’ Coordination among agents for additional stock delivery and/or inventory transfer across retailers. F. New Inventory proposals aligned to strategy β€’ Changes in inventory and supply have to align with strategic goals and constraints: (1) free up printing capacity that can be monetized for external customers (growth target); (2)reduce costs while maintaining advertising revenue (profitability target); (3) balance efficiency with retailer satisfaction (brand management target); 7