Joseph S. Martinich

Price uncertainty and the optimal production-location decision

Abstract The integrated production-location decision involves the simultaneous choice of facility design (input mix) and plant location. This paper generalizes earlier work by incorporating price uncertainty and risk preferences into the problem. Properties of the optimal solution are characterized, and detailed comparative statics analyses are performed to identify the effects of price uncertainty, risk preferences, and production structure on the optimal solution. These results, which illuminate the economic mechanics and parametric sensitivity of such decisions, can be useful for developing and evaluating national and local public policies. An example of their potential use is given.

College Football Rankings: Do the Computers Know Best?

The bowl-championship-series (BCS) committee uses 10 ranking schemes, including eight computer rankings, to select college football teams for bowl-championship-series bowl games, including the national championship game. The large financial benefits of participating in BCS bowl games make it imperative that the selection process accurately select the best teams. I evaluated the performance of the 10 ranking schemes the BCS committee used during the 1999 and 2000 seasons to select bowl teams. I found that almost all are equally accurate, but theSeattle Times scheme clearly underperforms the others. In addition, two proposed changes to the BCS selection formula, (1) to prohibit computer ranking schemes from considering the margin of victory in their rankings, and (2) to include explicitly the outcomes of head-to-head games among teams being considered for BCS bowls, could do more harm than good and could decrease the likelihood of the committee selecting the best teams for the BCS bowls.

Generalized comparative statics for the production-location problem

Abstract This paper presents a general parametric analysis of deterministic production-location and design-location problems. The analysis characterizes the effects of changes in output level, input and output prices, and transport rates on the firms optimal production and location solutions. The approach, which uses arguments similar to those used in revealed preference analysis, does not rely on differential methods, so that it is applicable to more general situations, such as non-differentiable production and transport cost functions, and does not assume interior optimal locations. Several numerical examples are provided to explain major results and to illustrate apparent anomalies which can occur in spatial economic models.

The Critical Few Minutes in Scheduling Time‐Varying Queuing Systems

For nonstationary queuing systems where demand varies over time, an important practical issue is scheduling the number of servers to be available at various times of the day. Widely used scheduling procedures typically involve adding servers at natural time points (e.g., on the hour or at half past the hour) during peak demand periods. Scheduling is often complicated by restrictions on the minimum amount of time (human) servers must work, the earliest (or latest) time a server is available, and limits on the maximum number of servers that can be used at any one time. This paper was motivated by experience with actual queuing systems that embodied such complications. For these systems common scheduling methods that used “natural” starting times for servers resulted in needlessly long customer waits. This research demonstrates that changing the starting times of servers by only a few minutes can have dramatic impacts on customer waiting times for extended periods. In addition, the results highlight the importance of server punctuality.

Network production-location problems under price uncertainty☆

Abstract The scope of the network plant location problem is extended in three significant ways: (i) The ‘design’ of the facility, including consideration of input substitution and the level of output, is combined with the location decision; (ii) input and output prices are treated as random variables, and (iii) the risk preferences of the decision maker are considered explicitly in the decision making process. Node optimality properties are developed for several model variations. An elimination-by-bound solution algorithm is presented along with suggested upper and lower bounds and methods of simplification. Under certain conditions, the optimal input ratios and plant locations are shown to be invariant with some parametric changes. The potential for influencing the location decisions of firms, depending upon the characteristics of their risk preferences, production functions, and the demand functions for their input, through manipulation of the risk they face, is illustrated.

Takt Time Grouping: implementing kanban-flow manufacturing in an unbalanced, high variation cycle-time process with moving constraints

One-piece flow and kanban/pull methods have been used to reduce work-in-process (WIP) and flowtime in manufacturing flow processes; however, these methods have limitations. For example, one-piece flow does not work well when there are relatively large set-up times required between different components. One-piece flow also requires operations to be well balanced with a minimum of variability in processing times at each operation. Unfortunately, these conditions often do not exist. The theory of constraints drum-buffer-rope (DBR) method is designed for unbalanced processes, and it has been shown to be effective for products with large operation time variation. However, DBR does not generally optimise flowtime and cannot handle a process with moving constraints (bottlenecks). We have developed a method called Takt Time Grouping (TTG) for implementing kanban-flow manufacturing, when one-piece flow or DBR do not provide good results. TTG combines one-piece flow manufacturing, transfer-batch sizing and DBR concepts through the use of a constraints-based transfer-batch sizing formula. Using a discrete event simulation model, it is shown that TTG increases throughput rate as compared to one-piece flow, CONWIP and DBR approaches, with much lower WIP inventory and faster flowtime than CONWIP and DBR.

Stochastic Production/Location Models on Networks or a Plane

This chapter extends the analysis of stochastic production/location problems presented in chapter 5 from the line as the location space to network and planar spaces. The inclusion of parametric uncertainty in these more general spaces makes algorithmic solution of these problems, and especially analysis and characterization of optimal solutions using comparative statics methods, extremely difficult. This probably explains why so little published work exists on these types of production/location models. Although little work has appeared for either type of space, the work on stochastic network production/location problems is more extensively developed than the work on planar models, so the bulk of this chapter will focus on network models. The material in this chapter naturally builds upon the certainty models in chapters 3 and 4, and many of the methods and results extend to the stochastic case, though sometimes in altered form.

Policy Evaluation: Incentives and Regulation

Much has been written about the importance of incentives and regulations in the site selection decision making of firms. However, very few papers and books on these subjects treat the potential impact of parametric (environmental) uncertainty on such decisions. Furthermore, we are able to find only a single published work that uses the production/location frame-work to evaluate government regulation, and only our own work uses this framework to evaluate locational incentives. This is unfortunate in view of James B. Cannon’s admonition that, “choice of location cannot be identified as an independent characteristic of a strategic investment decision... .The impact of locational incentives must be seen in the broader context of the total investment decision” [Collins and Walker 1975, p. 112].

Policy Evaluation: Taxation

Models of the sort developed in this volume have several important, potential, applications. On the one hand, they are normative in nature and may serve as the basis of planning models for individual decision-making entities. On the other hand, they may be descriptive of the general reaction of typical or “average” individual decision-making entities to exogeneous parametric changes. As descriptions of “average” decision-making entities (i.e., firms) and of their sensitivity to parametric manipulation, the models become potential instruments for the evaluation of governmental policies that influence parameters of firms’ decision making. For purposes of discussion, three types of governmental activities will be considered here, namely: taxation, regulation, and locational incentives.

Deterministic Production/Location Models on Networks

By restricting the production process to two inputs and the location space to a line segment, in chapter 2 we were able to investigate many of the salient features of the production/location interrelationships. Now the problem is generalized both in terms of the production variables and, more importantly, the feasible location set. In a practical sense most plant location decisions must be made with respect to some transportation network. Consequently, in this chapter we assume that the firm must make its production/location decision so as to locate on some given transport network. Any finite number of spatially distinct input and output markets are allowed, with their locations being at nodes of the network. First, a single-plant network problem is formulated along with a numerical example. Using methods similar to those in chapter 2, we then show that in many cases the set of optimal plant locations can be reduced to the node set of the network.