Writing 2.363: the DSM project

Firms often rely on salespeople to promote demand and gather information. Because of the proximity to customers, salespeople have better information on customer preference, sales potential, and market trend. Such information is critical for new product development, production planning, and salesforce compensation. A critical question is, how can a firm motivate its salesforce so that they work hard to stimulate demand,  and at the same time, truthfully disclosure market information they gather?

It is now well-known that a menu of linear contracts can elicit the market information and encourage hard work [Chen05]. This insight relies on a stylized static framework with several restrictions: Linear-contract, Exponential-utility, and Normal distribution (LEN model), and binary effort. Yet salespeople may work in a changing market, adjusting their efforts continuously over time. So the conventional insight may be a poor guide of what is really going on in practice. In this project, we develop a new model, accounting for continuous efforts and dynamic incentive. We highlight the blind spot of the existing framework, as well developing new insights.

Our main story goes as follows. There are two forces. First, the diminishing forecasting accuracy of the agent means that he will face more uncertainty in the future, because both the firm and the agent are equally uncertainty of the future. Second, the agent is risk averse, so that he hates the future uncertainty. The firm should take the advantage of this situation by offering him a long-term contract. Doing so can take out the agent’s information/forecasting advantage in the future.


Writing 2.363: the DSM project


Good news! Tons of work, but doable.


I enjoyed reading this paper, and find its topic interesting. I also appreci­ate the approach taken by the authors, which combines an empirical study, a modelling effort and corresponding analysis, and finally managerial recom­mendations which are of real practical interest. I do have a few comments on the interpretation of the results in the empirical section of the paper, some as­sumptions in the modelling framework, and the results of the numerical section. However, if these comments could be addressed, then I believe that this paper would make a nice, comprehensive, contribution to the literature.

2016-10-23 18.31.53

2016-10-22 12.04.24-1


Learn from others mistakes

We had a candidate come in for interview this afternoon. With a few red flags already on her resume, she arrived 52 minutes late.

During the half hour task, she was very quiet and did not ask any question. This deemed to be another red flag because it was exactly her chance to make an impression by showing her thinking, her approach to problems, her interest in the position, and being engaging with us. As she started to speak, her voice sounded neither confident nor assertive.

Incidentally, Monte Carlo simulation was mentioned on her resume. The manager had no idea at all what that is so he asked. Her answer, not surprisingly, was very tedious, unclear, and technical, using terms like Brownian motion. But how would you expect those laymen to understand Brownian motion? Even more so if that’s not something they normally deal with, they wouldn’t be interested in either. Instead, a straightforward, simple but attractive answer would be much better.

Interview really isn’t about how good you are. Now I feel strongly that everything is personal branding.

Learn from others mistakes


This paper studies a dynamic pricing problem in the SS industry. First, the paper formulates the problem as an inventory control model, with random demand (move-ins) and supply (move-outs). In each period,  the firm sets the price to control demand, collects revenue from sales, and pays penalty for oversell (or shortage in the newsvendor parlance).

Second, the paper provides theoretical underpinning of  the price controller practice. The price controller is a weighted average of performance metrics, including the occupancy change, the vacancy change, and the managers’ incentive. It uses a linear combination of past vacancy levels, demand and supply. The paper shows that the price controller approach can be optimal for four-period cases (since it has three parameters). For longer horizons, the price controller can be adjusted over time, depending on the trends of the recent history. In the stationary environment, because of the updating, the price controller can converges to the optimal. The paper also proposes an improvement of the price controller practice by exploring the similarity between the updating practice and the sub-gradient method.

Third, the paper addresses three managerial questions. Through numerical examples, it shows that the benefit of long-term leasing is limited, that certain myopic pricing (limited to linear form) is inferior, and that the the convergence of the price controller to the optimal can be speeded up by using step length instead of step side.

I read the paper with great interest. The main strength is on the practical side. To my knowledge, it is the first to formalize and validate the practice of the price controller method. As a first order approximation of the optimal solution, the controller can converge to the optimal over time through updating.

The paper is less compelling on the theoretical ground. It is certainly valuable to explicate the link between the practice and the optimal solution. The numerical studies are also important to understand the practice of the self-storage industry. However, without further analytical results, the answers to the three managerial questions are not entirely satisfactory.

I would like to see more analytical results. For example, the paper uses computation to show that the rental lease may not deliver substantial benefits, since it mainly reduces the supply variation. This result can be rigorously established by stochastic comparison. The efforts along this direction will certainly strengthen the conclusions and enhance the contribution.

The exposition can be much improved. For the content it delivers, the paper is way too long. For example, the section 3.1 on the demand function is quite standard, and it should be shortened to a paragraph or two. The formulation in section 3.2 should also be tightened, as it is quite standard in the inventory literature.

In summary, the paper deals with the practice of an interesting operational problem. However, it needs to strengthen the analytical content. I recommend major revision.

2016-10-21 19.26.05



I read the revision with great interest. It claims two contributions: characterizing the optimal dominant mechanism, and proposing a hybrid algorithm. I don’t find either claim compelling.

First, the paper has little intellect content.  Essentially, it applies a well-known economic result straightforward to the assembly context. Its core, the characterization of the optimal dominant mechanism, is a textbook result in economics. For example, see chapter 7 in \cite{borgers2015introduction}.  The only part new is the balancing ordering property. But once we see that the final production quantity of assembly  is $\min(q_1,\dots, q_n)$, the balancing ordering comes immediately.

It is truly that \cite{fang2014optimal}, though dealing with the same problem, did not have the balance ordering property. But that is because \cite{fang2014optimal} make realistic assumptions on contracts: they depend only on a specific supplier, not others. This assumption is consistent with the business reality: most contracts are between \emph{two} trading parties. For execution, their terms must be verifiable. Allowing the contract depending only on the type of contracting supplier is precisely to respect this reality.

In contrast, this paper allows each contract to depending on the private information of \emph{all} other suppliers, \emph{unverifiable to the current supplier}. Given the unverifiablity and the self-interested nature of all players, why would the supplier trust the assembler not to lie about others’ types? This is very {troubling}: the dependence on all suppliers make sense in the regulatory context (where the core result comes from) \cite{salanie2000microeconomics}, but it makes no sense in private sectors with self-interested firms. In fact, I would love to see a real example of such grand contract in action.

Second, the hybrid algorithm is straightforward. It simply truncates the computation by virtual cost ranking. I also don’t find computation study of much value. (1) The demand uncertainty  is to change the curvature of the profit function, and hence the newsvendor solution \citep{cachon2008matching}. This is well-known in OM. (2) The result that the optimal dominant mechanism outperforms Fang’s mechanism is the direct consequence of removing a constraint from Fang’s model. True, such a simple algorithm can be efficient. The real question is, what is its intellect contribution?

Third, the exposition can be much improved. Overall, the paper reads more like a homework exercise than a scholar paper. The notions of virtual cost and information rent, the property of no distortion to low cost type, and the relaxation method, these are all standard for a mature reader; see \cite{wolfstetter1999topics}, \cite{salanie2005economics}, \citet{laffont2001theory}, and  \citet{bolton2005contract}. So I don’t see the need for repeating these known results. Relabeling them is not a contribution.

Also, the discussion of supplier section in \S4.2 is superficial and self-defeating. If the assembler can use the second-price auction to make the suppliers to reveal their prices, and there is a one-to-one mapping between bid price and the true cost, then the auction is sufficient for screening the cost. This eliminates the need for offering another single, grand contract to all suppliers.

The bottom line is, what are genuinely new? Having read the paper in detail, I fail to find a compelling result for publication.

2016-10-05 09.42.17