# WRITING 141: READING NOTES ON AH’S PAPER

[20min, 6:40pm-7:00pm]

AH focuses on the endogenous quality decision on ENC. It extends A’s 07 model with the consumer heterogeneity on quality, so that M can quality differentiate (QD).

In the canonical setup, it is well-known that QD reduces end market competition and thus increases the profits of all firms. When M can operate dual channels, however, the issue is more involved.

That is because now M has three levers—the wholesale price, the direct sell quantity, and the quality. The quality level gives M more flexibility. First, he can use the quality to stimulate demand directly, instead of using the wholesale price indirectly. Second, he can use the quality to differentiate two channels, to soften the downstream competition.

Associated with the three levers are three effects. First, the competition effect: because the retail and direct channels compete directly in the end market, the retailer may lose, when M shifts the demand to the direct channel. Second, the wholesale price effect: M may reduce the wholesale price to boot the retailer demand (positive effect). Third, the quality adjustment effect: M may use quality to stimulate demand directly (hinged on the assumption that the price $p= u(1-q)$).

Depending on the selling cost $c$ and the production cost (convex in quality) $ku^2$, the three effects can create different outcomes, e.g., win-win, win-lose, lose-lose, and lose-win.

Anyway, I am not impressed.

[INSIDE PARADISE INN, MOUNT RAINIER, 9/2015]

# WRITING: NOTES ON AO

This morning I had a discussion with A, mainly on the pooling equilibrium.

The basic model is as follows. The supplier S has two distribution channels: direct sell to the end consumers, and through a retailer R. The retailer is more efficient in retail operations with less retail cost. However, the retail channel suffers efficiency loss due to  double marginalization (DM) (we assume that the channel is managed by the wholesale price contract). In addition, the supplier’s type of retail cost $c_i$ is his private information, high or low. The consumer demand is linear. Both parties are risk-neutral and profit maximizing.

We frame the problem as a signaling game. First, S learns his type $c_i$ and sets wholesale price $w(c_i)$. Second, R orders quantity $q_R$. Finally, S delivers $q_R$ and sells $q_S$ directly to the market. Hence the market clearing price is $P= a - b(q_R+ q_S)$. The payoffs for R and S are
$(P-w)q_R$ and $Pq_S + c_i(q_S + q_R)$, respectively.

A will have a draft this weekend. Afterwards I need one more week to finalize it.

[Key West, FL, Spring, 2015]

This paper studies container fleet management for an oil supplier. The demand and spot freight rate are random. The supplier must adjust charter contracts and options to manage capacity shortage. The objective is to minimize weighted, conditional value-at-risk.

The authors formulate the problem as a nonlinear program. To simplify the computation, they use simulation to generate scenarios for linearizing the nonlinear program. They also calibrate the model with real data and numerically show that properly chosen portfolio of contracts and options can reduce risks.

I applaud the authors’ effort to tackle a realistic operational problem with well-known methods. But that alone is insufficient for publication. Unless I misread, the paper makes neither theoretical nor managerial contributions, in any significant sense.

Indeed, as its literature review session shows (the journals researchers barely read),  the paper is targeting a wrong audience. Perhaps application oriented journals are more appropriate outlets.

[Antelope Canyon, 8/07/2009]

# Writing: TQ2

This project seeks to make two points: (1) customers’ waiting behavior is context dependent, and (2) he may change mind over time. It models two new features: the partial information environment, and the dynamic decision making.

But these alone would not make the top journal: its analysis follows the footstep of XGO’s work. We must do more to strengthen the case. Instead of assuming two customer behaviors—context dependency and dynamic decision making—we can distill them from the data. Fortunately, KK has the bank data. If used properly, they can provide direct connection between theory and practice. Taken together, the data and model should make a compelling story.

We have drafted the model part. It remains to show that existence of dynamic behavior in practice. Though simple, this step is crucial to sell the story. Now KK has drafted the empirical part. Next week, he will integrate it with the modeling part. Afterwards, it is my turn to finish the project.

Above all, we are still struggling with our punch line.

# Writing: paper review

The paper studies the procurement strategies for the A-systems. It concerns a firm producing a product of multiple components. The components’ procurement lead time are different but deterministic. The spot price for the key component fluctuates as a Brownian motion; other components have stable prices. The product demand is random with fixed selling price.

The firm seeks to maximize the expected profit by making proper quantity and procurement timing decisions. Buying earlier, it pays higher cost for holding inventory; delaying procurement, it must pay tardiness penalty for late delivery.

The paper considers two supply contracts. Under the strict contract, the firm must decide the quantity and timing at time 0. It trades off holding cost of early procurement and penalty of delaying. The quantity decision follows the newsvendor logic, while the timing is given by the optimal stopping problem. (In fact, the quantity part can be removed to make the logic cleaner.) Under the flexible contract, the firm can observe the price movement and hence buy at a lower price, thereby lowering the cost. Essentially it is an optimal stopping problem.

Despite the interesting setup, the paper falls short on both methodological and managerial ground. Its analysis hinges on the single random price assumption, which makes the characterization straightforward. The most interesting case is when the prices have the downward trend; but the paper does not make much headway here. That would be fine if the paper makes substantial managerial contribution. But here it fails, too. The two managerial points the paper makes are common sense.

In summary, the paper must go a step deeper.

# Writing: HLD notes

I took three days to work out the missing steps.

In this project, we argue that the flexible regime dominates the mandatory one. Intuitively the logic is simple. But the math is not straightforward. This is because two regimes differ substantially in objectives and hence policies, which defy the direct comparison.

We solve this problem by relating them to the second best. We do so in two steps. First, we define the common structure. The central notion here is the virtual cost. Second, we parameterize each regime by its deviation from the second best (in terms virtual cost).

This approach provides a unified framework to compare the flexible and mandatory regimes. It overcomes the structural difference by teasing out their the common core.

There are two caveats, though. First, in the flexible regime the agent decides production, whereas in the mandatory regime the principal decides. Second, although each the principal may not see all the types, we still define its payoff function for each type. This hypothetical treatment poses no harm.

Currently, PL is working on the case with additional budget constraint. That constraint is necessary for explaining the logic of exporting trade. It makes economic sense and numerically it works. Just wait to see the details.