Measuring Demand Smoothing in Service Operations

Measuring Demand Smoothing in Service Operations

Avi Dechter

Department of Management Science

College of Business Administration and Economics

California State University, Northridge

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Abstract

Coping with uneven demand is one of service management's toughest challenges. Efforts to smooth the demand (e.g., using a reservation system) are a very common response to this problem. This paper proposes a paradigm for measuring both the degree of smoothness and the effort required to achieve smoothness of varying degrees.

Introduction

Coping with uneven demand is one of service management's toughest challenges (e.g., Heskett et al. 1990). Most service organizations experience cyclical (daily, weekly, monthly, etc.) fluctuations in the level of demand which result, if not addressed properly, in either reduction in service level (when demand is high) or in under-utilized resources (when demand falls). Mitigating these consequences requires that the service organization adjust its capacity in accordance with the variations in demand (capacity management), endeavor to change the demand pattern to better match the available capacity (demand management), or use these two strategies in combination.

Most demand management efforts may be characterized as demand smoothing as they primarily aim to increase the demand during slow periods and reduce the demand during peak periods. The reason for this is clear: smoother demand lessens the need for costly adjustments in capacity. Service organizations smooth their demand by either trying to influence their customers to change the timing of using the service (e.g., differential pricing) or by scheduling the arrival of customers (e.g., advance reservations).

While the need for, and the benefits of, demand smoothing are well recognized both in the literature on service management and in practice, the discussion is largely qualitative in nature. For example, Rising et al. (1971) discuss a strategy used to smooth the number per day of patients’ arrivals at a university outpatient clinic. They report the results of implementing that strategy using a graph clearly showing that the new demand is indeed smoother than old one, but without quantifying the degree by which the new demand is smoother than the old or indicating why this demand pattern was better than others. Similarly, Crandall and Markland (1996) use a graph (see Figure 1) to define four generic demand management strategies. The “match” and “control” strategies are extreme – “match” leaves the original demand unchanged while “control” transforms it into a perfectly smooth demand. The “influence” strategy represents an intermediate approach where some degree of smoothness is required. In this, middle-of-the-road case, the questions of how various degrees of smoothness are to be distinguished from one another remains unanswered. By contrast, Klassen (1997) points out the importance of measuring the leveling of the demand and proposes a number of demand-smoothing measures.

This paper is intended to add to the discussion on demand smoothing. We start by introducing a simple measure of smoothness, which may be used to compare demand patterns to one another. Next, we propose a measure of the cost of smoothing based on the notion of demand shifting. Then we explore briefly the relationship between these measures. We conclude with a discussion of the type of future research that might benefit from such measures.

Measuring the Degree of Smoothing

Consider the actual demand pattern and the modified demand under the “influence” strategy in figure 1.

How do we know that the “influence” demand pattern is smoother than the actual demand? There are many possible ways to assess the degree of smoothness. We suggest that a meaningful way to measure the smoothness is to add up the absolute values of the changes in demand from one period to the next. Smoother demand will have a lower value of this smoothing index. The tables below calculate the smoothing index for the two demand patterns:

As expected, the “influence” demand pattern, which is smoother than the actual demand, has smaller smoothing index.

A Transportation-type Demand Shifting Model

The smoothing index (or a similar measure) is necessary to ascertain that one demand pattern is smoother than another, but it only provides part of the picture. One should be concerned with the cost of, or the effort associated with, smoothing demand. For example, while it is clear that the “influence” demand pattern of Figure 1 is smoother than the actual demand, the question arises as to whether the same improvement is smoothness may be achieved at a lower cost. What is needed is a measure of the distance between the original demand and the modified, smoother demand.

The distance model depends on how smoothing actually is achieved. We adopt the view that smoothing is achieved by shifting demand between periods. Under this view, a reasonable measure of distance is the minimum amount of shifting required to move from the original demand to the modified demand. This quantity is calculated by the transportation model, which is illustrated in figure 2. This model is patterned after the classical application of the transportation model to production smoothing in manufacturing operations (e.g., Bowman 1956). The difference, of course, is that in manufacturing smoothing is achieved by carrying inventory from one period to another rather than by shifting the demand itself. The unit transportation “costs” merely count the number of periods associated with each shift. It is assumed (although it is not necessary) that only forward shifting is allowed.

Figure 2 shows an optimal solution of the transportation model for moving from the actual demand to the “influence” demand of the previous discussion, indicating that the minimum shifting required in this case is 7 periods.

The question raised above, namely, whether one could achieve the same degree of smoothness (4) with less shifting, can now be addressed. By joining the transportation model with the smoothing index model we can determine the minimum shifting required to achieve a given degree of smoothness. In this model, the priod-to-period changes in demand are also decision variables, and the smoothing index of the modified demand, rather than the demand itself, is a constraint. The joint model, with an optimal solution, is shown in Figure 3. As the optimal solution of the joint model indicates, a
demand pattern with a smoothing index of 4 may be obtained by shifting only 4 periods of demand.

The Relationship of the Amount of Shifting and the Degree of Smoothness

Obviously, more smoothing requires more demand shifting. In order to gain insight into the relationship between these quantities, we calculated, using the joint model, the amount of shifting needed to obtain increasing degrees of smoothness in our example. The results are shown in Figure 4 (notice that in this small example there are only two degrees of smoothness possible between the actual demand, and the perfectly smooth “control” demand). It is evident that increasing the degree of smoothness requires increasingly more demand shifting.

Conclusion

In this paper we propose a simple, intuitive, measure for ranking demand patterns according to their degree of smoothness. Such measure is necessary if one wishes to perform any quantitative analysis of demand management. We also propose a transportation-type model of demand shifting which may be used to find the best way to achieve various degrees of demand smoothness. Both of these models deal with aspects of demand management but ignore the issue of capacity management. An extension of this study, which is currently underway, uses them in combination with a model of capacity management to develop a model for the simultaneous management of demand and capacity.

References

Bowman, E.H., “Production Scheduling by the Transportation Method of Linear Programming.” Operations Research, Vol. 4, 1956, 100-103.

Crandall, R.E. & Markland, R.E., "Demand Management - Today's Challenge for Service Industries." Production and Operations Management, Vol. 5, No. 2, 1996, 106-120.

Heskett, J.A., Sasser, W.E. & Hart, C.W., Service Breakthroughs. New York: The Free Press, 1990.

Klassen, K.J., “Simultaneous Management of Demand and Supply in Services.” Ph.D Dissertation, The University of of Calgary, Alberta, Canada, 1997.

Rising, J.R., Baron, R. & Averill, B., "A System Analysis of a University Health-Service Outpatient Clinic." Operations Research, Vol.21, No. 5, 1973, 1030-1047.

Showalter, M.J. & White, J.D., "An Integrated Model for Demand-Output Management in Service Organizations: Implications for Future Research." International Journal of Operations and Production Management, Vol. 11, No. 1, 1991, 51-67.