📈 economics

Paying Customers for Patience:An approach for pricing slotted deliveries for Quick-Commerce

This study proposes an analytical pricing framework for quick-commerce platforms to incentivize customer patience by offering optimal slot discounts that pass through a calibrated portion of marginal cost savings, revealing that discounts should be flat across time windows, scaled by distance, and sufficient to maintain fleet utilization below 65%.

Original authors: Milon Bhattacharya

Published 2026-10-05

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Milon Bhattacharya

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the bustling world of modern logistics, a quiet tension exists between speed and efficiency. On one side stands the promise of instant gratification, where a courier picks up a single package and races directly to a customer's door. On the other lies the logic of the shared journey, where a driver collects several orders in a neighborhood and delivers them in a single, winding route. This second approach saves the company significant time and money by reducing the number of trips needed, but it requires the customer to wait. The central question for the platforms that manage these deliveries is how to bridge this gap: how much should a company pay a customer to be patient, and how much of the money saved by waiting should be passed back to that customer? This is not merely a matter of accounting; it is a complex puzzle involving how drivers move through cities, how orders arrive in waves, and how people value their own time.

A researcher at the Indian Institute of Management Visakhapatnam has tackled this puzzle by building a detailed model of how quick-commerce platforms operate. The study focuses on "dark stores," small warehouses located within cities that serve as hubs for rapid delivery. The researcher asked three specific questions. First, if a customer agrees to wait for a delivery slot, how much of the cost saving should the platform return to them as a discount? Second, does waiting longer always yield a bigger reward, or is there a point where extra patience stops adding value? Third, at what times of day is it actually possible to group orders together, and when is it better to just deliver immediately? To answer these, the author analyzed real-world data from major delivery services, including Amazon, Grubhub, Instacart, and Olist, to understand how drivers actually move and how orders cluster in time and space.

The investigation revealed a surprising limit to the value of patience. While it might seem that waiting longer allows for more orders to be grouped together, creating greater savings, the math shows that these savings hit a ceiling very quickly. Once a driver's vehicle is filled to its capacity—roughly twelve orders in the model—the marginal benefit of adding another order to the route drops sharply. The time saved by adding a thirteenth order is negligible compared to the time saved by adding the second or third. Consequently, the optimal discount for a customer does not keep growing as the waiting window expands from fifteen minutes to three hours. Instead, the best strategy is to offer a discount that encourages enough people to wait just long enough to fill one driver's vehicle, and no longer. Extending the wait beyond this point costs the customer time without providing any additional financial incentive, as the platform has already captured nearly all the possible efficiency gains.

The study also calculated exactly how much money should change hands. When a customer switches from an instant delivery to a shared slot, the platform saves money, but it does not give all of that saving back. The research found that the platform keeps a significant portion of the savings as profit, passing through only about forty to fifty-five percent of the marginal cost reduction to the customer. In concrete terms, this translates to a discount of roughly fifty cents to ninety cents per order. This pass-through rate is lower than what would happen in a perfectly competitive market, where the full saving would be passed on, reflecting the platform's power to set prices. Furthermore, the model suggests that if platforms were to charge fees based on distance—giving larger discounts to customers living farther away—they could increase their total profit by twenty-eight percent. However, the data shows that real-world platforms currently charge flat fees regardless of distance, missing out on this potential efficiency.

Timing plays a crucial role in whether these shared slots are even viable. The researcher mapped out the flow of orders throughout the day and found that grocery delivery demand behaves differently than meal delivery. While food orders tend to spike sharply at lunch and dinner, grocery orders form a broad, steady plateau throughout the afternoon, from ten in the morning until four in the afternoon. This consistency means that for grocery services, there is almost always enough demand to fill a driver's vehicle, making short, same-hour delivery slots a viable option for most of the day. The only time it makes sense to ask a customer to wait for a later wave of deliveries is during very quiet periods, such as late at night, when the number of orders drops so low that grouping them is impossible.

Finally, the study highlights a critical constraint on the entire system: the need for idle capacity. For instant deliveries to remain fast, the fleet of drivers cannot be fully utilized. The simulations showed that if a company tries to keep its drivers busy nearly all the time, the wait times for instant orders balloon, defeating the purpose of "quick" commerce. To keep instant delivery times under ten minutes, the fleet must operate at less than sixty-five percent capacity, meaning a significant number of drivers are often waiting for the next order. This finding underscores that the speed customers enjoy is bought at the price of operational slack, a trade-off that pricing strategies must carefully balance. The research concludes that the most effective approach is not to offer a menu of increasingly long waits, but to offer a single, short waiting window that perfectly matches the capacity of a single driver, incentivizing just enough customers to wait to fill the vehicle without overcomplicating the system.

Technical Summary: Paying Customers for Patience

1. Problem Statement

Quick-commerce (Q-commerce) platforms promise sub-10-minute deliveries but increasingly offer "slotted" delivery options where orders are batched and delivered via shared routes to achieve operational efficiency. However, current pricing models often fail to provide financial incentives for customers to choose these slotted options, despite the significant cost savings they generate for the platform.

The paper addresses three core questions regarding the pricing of these slotted deliveries:

Q1 (Pass-through): How much of the marginal cost savings generated by batching should be passed back to the customer as a discount? Does this depend on whether fees are flat or distance-based?
Q2 (Value of Patience): How does the economic benefit of batching change as the time slot length ( $\Delta$ ) increases? Is there a point of diminishing returns?
Q3 (Scope of Slotting): Given intraday demand patterns, during which hours is it viable to offer slots, and how long should they be?

The study assumes fixed total demand (groceries are purchased regardless of fees); thus, pricing acts as a mechanism to steer orders between instant (solo) and slotted (batched) fulfillment.

2. Methodology and Analytical Framework

The paper constructs an analytical framework integrating exact routing geometry, stochastic batching, and endogenous customer adoption feedback.

2.1 Routing and Cost Modeling

Modified Tour Geometry: The author critiques standard continuum approximations (e.g., Beardwood et al., 1959; Daganzo, 1984) which use the form $k\sqrt{mA}$ for tour length. This form incorrectly charges a "stem leg" to solo trips ( $n=1$ ), distorting costs for small batches. The paper introduces a corrected tour-time function $H_1(n)$ featuring a $(m-1)_+$ term under the square root, ensuring exact calibration for solo trips while preserving asymptotic scaling for large batches.
Capacity Constraints: A courier carries at most $C$ orders. Dispatches of $n$ orders are split into $q = \lceil n/C \rceil$ tours. The total time $H(n)$ accounts for this splitting.
Cost Structure: Courier pay is modeled as a two-part piece rate (per drop + per km) clearing a reservation wage $\bar{w}$ . The cost of an instant delivery is $c_I(r)$ , while the marginal cost of a slotted order is $c_{mg}(L)$ , where $L$ is the mean batch size.

2.2 Delay and Adoption Dynamics

Endogenous Delay Feedback: A critical innovation is modeling the delay $x_S$ as endogenous. As more customers adopt a slot, the batch size $L$ grows, increasing the in-tour delay $\theta(n)$ . This creates a feedback loop: higher delays deter further adoption.
Customer Utility: Customers minimize the sum of the fee and disutility from excess delay ( $u(x; \beta) = \min(\beta x, \bar{V})$ ). Adoption $a$ is determined by a fixed-point equation where the adoption share depends on the discount $d$ relative to the realized delay $x_S(aN, \Delta)$ .

2.3 Optimization

The platform maximizes profit per window by choosing the optimal discount $d^*$ . The objective function balances the revenue lost from the discount against the courier costs saved. The model distinguishes between:

Flat Fees: A uniform discount regardless of distance.
Per-Kilometre Fees: Discounts graded by distance.

3. Key Contributions and Theoretical Insights

3.1 Optimal Pass-Through Rate

The paper derives the optimal pass-through rate $\rho^*$ (the fraction of marginal savings passed to the customer).

Result: Under uniform customer time values, $\rho^* = 1/(2 + \epsilon)$ , where $\epsilon$ is the elasticity of slot delay to batch size.
Implication: Unlike standard monopoly models (which suggest 50% pass-through under linear demand) or competitive markets (100% pass-through), the presence of delay feedback attenuates the pass-through. The calibrated $\rho^*$ ranges from 0.40 to 0.55. This means the platform retains 45–60% of the savings, passing only $0.50–$ 0.90 per order to the customer.

3.2 Saturation of Savings (The "Capacity Kink")

Result: Cost savings saturate rapidly once a single courier load ( $C$ ) is filled. The marginal tour time per stop drops from 5.8 minutes (2nd stop) to less than 2 minutes (12th stop).
Implication: The optimal discount $d^*$ remains flat for slot lengths ranging from 15 minutes to 3 hours, even though customer delay continues to grow. The optimal strategy is to set the slot length just long enough to fill a courier ( $\Delta^* \approx C / (a\lambda(t))$ ). The global optimum typically sits on "capacity kinks" (multiples of $C$ ), where marginal costs are lowest.

3.3 Distance-Based vs. Flat Fees

Result: Theoretically, distance-graded discounts could increase slotting surplus by 28% by better matching discounts to the higher marginal savings of distant customers.
Empirical Finding: However, analysis of Olist data reveals that real-world metro delivery fees are strictly flat (distance explains only 1.4% of fee variance). The paper identifies a gap between theoretical efficiency and market practice, noting that current flat fees effectively cross-subsidize distant customers.

3.4 Operational Scope and Timing

Grocery Demand: Unlike meal delivery (bimodal), grocery demand follows a broad daytime plateau (10:00–16:00).
Implication: Same-hour slots are viable across most operational hours (08:00–21:00). Deferring off-peak orders to a peak wave is only beneficial if the trough demand falls below ~15% of the peak, a condition rarely met in grocery demand.

4. Empirical Calibration and Results

The model is calibrated using open-source datasets from Amazon (routing geometry), Grubhub (meal delivery clock), Instacart (grocery clock), and Olist (fee structures).

Parameters: Calibrated zone area $\approx 7.77$ km², mean distance $\bar{r} = 1.09$ km, courier capacity $C=12$ , and reservation wage $\bar{w} = \$ 12$/h.
Pass-Through: Calibrated pass-through rates are 0.41 on smooth segments and 0.50–0.58 at capacity kinks.
Discounts: Optimal discounts range from $0.48 to $0.83 per order.
Slot Length: A 15–30 minute slot is optimal to fill a courier. Extending the slot to 2 hours increases delay significantly (from ~20 to ~74 minutes) without increasing the discount or profit.
Fleet Utilization: A day-long simulation reveals that instant fulfillment requires fleet utilization below 0.50–0.65. Above this threshold, instant orders face significant delays, undermining the value proposition of "quick" commerce.

5. Significance and Limitations

Significance

The paper establishes that the optimal pricing for slotted deliveries is not a simple transfer of cost savings but a complex trade-off involving routing geometry, capacity constraints, and customer impatience. It provides a rigorous justification for why platforms should offer modest discounts (40–55% of savings) and why the shortest slot that fills a courier is superior to longer, more patient slots. It also highlights a structural inefficiency in current market practices where flat fees ignore the spatial variation in savings.

Limitations

The author explicitly notes several limitations:

Idle Time: The model omits idle time between dispatches; simulations suggest this effectively doubles the wage cost if fleet utilization is low.
Batch Noise: The model assumes Poisson batching, whereas real data shows overdispersion (variance/mean $\approx 3$ ).
Tour Curve: The routing curve is calibrated on parcel data with a relocated store centroid, which is a modeling approximation for dark stores.
Demand Side: The distribution of customer time values ( $\beta$ ) and the satiation cap ( $\bar{V}$ ) are assumed, as no open data substitutes for a discrete-choice survey. Consequently, while the optimal discount level is robust, the predicted adoption rates (ranging from 7% to 45%) and total hourly gains are sensitive to these assumptions.

In summary, the paper argues that for Q-commerce, the "value of patience" is front-loaded and capped by courier capacity. Platforms should incentivize patience with modest, flat discounts for short slots that fill a single courier, rather than offering deep discounts for long delays.