Quality Assurance for Imports and Trade: Risk-Based Surveillance

Abstract

American consumers continually demand more fresh produce and food throughout the year, in particular during nonproductive seasons in the Northern Hemisphere. Consumer demand escalates food imports and requires delivering more tonnage through the current U.S. Ports of Entry (POE). Increased volumes of imported foods with ever-increasing velocity have been associated with significant food safety risks (unintentional food contamination from pathogens, chemical, or physical agents) and food defense risks (intentional food contamination by disgruntled employees or terrorists). While import inspections should help protect against outbreaks of food-borne illnesses, as well as plant or animal pests and diseases, it is neither possible nor optimal to inspect all produce at the POE. This chapter focuses on the impacts of increased international trade on the marketing system, emphasizing the sourcing of products from other countries, inspection and surveillance activities, and policies to mitigate potential market failure from food safety/defense risks. A framework to evaluate economic efficiency of policies and tools used to ensure imported food quality is discussed.

Model to Assess Operational Efficiency and Information Gain

The concept of information gain (IG) introduced by Verduzco et al. (2001) to generate a dynamic inspection strategy becomes the framework for this sampling design. Ideally, the inspection strategy that will be generated is based upon the information provided by the various tracking and tagging devices that have been placed along the produce supply chain. This inspection strategy generation problem is a particular case of an inspection effort allocation that has dynamic and real-time characteristics. For the purposes of this discussion, the devices that provide information about the container or the cargo being transported will be classified under the generic term of “sensors.” Each one of the sensors will provide a certain amount of information that can be used to make inspection decisions.

However, the information provided by any sensor is subject to classification errors, which should to be avoided completely which is operationally impractical. For instance, based on the information of a single sensor, a container can be declared “safe” and allowed to proceed into the USA when in fact the contents of the container are not safe. This type of error, discussed earlier, is a Type II error and its associated probability is represented with the Greek letter β. On the other hand, based on the information of the same sensor, a container can be declared “not-safe” and impede its importation into the USA when in fact the contents are safe. This second type of inspection or classification error is a Type I error and the associated probability of this error is represented with the Greek letter α. To design an effective sampling process for border produce inspection requires a plan that minimizes the costs caused by both types of errors. This approach conforms to the current border inspection objective of minimizing the expected total cost associated with a particular inspection procedure.

One of the approaches explored in this chapter is to develop inspection strategies that capture the problem faced by the federal agents at U.S. POE, based on the concept of IG. Under the concept of IG, the quality of the information provided by a particular sensor is not the same for all the objects being targeted. For instance, consider that two containers are being inspected using the same sensor, if linear misclassification costs are assumed, then a cost structure similar to the one depicted in Fig. 11.3 can be obtained. The shaded triangle represents the reduction in cost when the information of an additional sensor is included to assess the container. Thus, this shaded region represents the value of the information gained by including information from an additional sensor in the decision-making process. Notice that the level of IG is, through Π, dependent on the characteristics of the sensor being considered, the information provided by other sensors already used, and the probability that the content of the cargo are safe. Also notice that in some cases the information provided by a sensor does not contribute at all to minimize the total cost of the inspection and should be avoided.

Once IG values and the individual inspection time requirements are available for all sensors, the question that needs to be answered becomes what set of sensors need to be used to minimize the total cost of a potential misclassification. A proposed strategy to answer this question is based on including those sensors in the decision-making process that contribute to maximizing the overall IG. In particular, it is a problem of optimal control of partially observable Markov decision processes (POMDP). The approach is that for each one of the sensors being considered for inclusion in the decision-making process, the IG is computed. Once the IG is available for each sensor, a decision about which sensors to use will be made. A common constraint imposed on the problem is the total time available to reach a decision, or conversely, the maximum total time to use for inspecting a particular shipment. let Y _i be a binary value such that Y _i  =  1, 0 if C-TPAT and FAST are used or not. Then the problem becomes:

Maximize the total information gain (Z), where:

$$ Z={\displaystyle \sum _{i=1}^{N}{G}_{i}{Y}_{i}}$$

(11.1)

subject to:

$$ {\displaystyle \sum _{i=1}^{N}{t}_{i}{Y}_{i}}\le T,$$

(11.2)

where ${Y}_{i}=0\rm\rm{or}\rm{Y}_{i}=1$, T is the total sensing time available, N represents the potential sensors, G _i is the information gain for sensor i, and t _i is the time needed by sensor i.

The stochastic optimal control model of fresh produce flows in the handling system reflecting the structure of tracking and testing for contaminations along the supply chain is used to determine the aggregate tracking cost, cost of seller risks or Type I error and the cost of buyer risks or Type II error, and a risk premium to quantify efficiency gains (Saha 1993; Wilson and Dahl 2006). Tests can be conducted at different stages (from the farm to the POE) or nodes in Fig. 11.1 and at varying sampling intensities to determine the success effectiveness of current inspection policies and procedures. Optimal control models can determine optimal testing and sampling strategies (where to test and inspection frequency/intensity) that maximizes the expected utility of the certainty equivalent (CE) (Nganje et al. 2009).

Estimating the CE of wealth requires assumption of the firm’s risk preference. The approach presented by Saha (1993) is adopted, where an expo power utility function is used to maximize the expected utility of the certainty equivalent. The objective is:

$$ \text{Max}EU({W}_{\text{CE}})=E(\lambda -{\text{e}}^{(-\Phi N{R}^{\eta })})$$

(11.3)

$$ \text{s}\text{.a}.\text{ {1em}}{X}_{j}\in {Y}_{j},$$

where U is utility; W _CE is the certainty equivalent of the vertically integrated firm in fresh produce supply chain; λ is parameter determining positiveness of the function; E is expectation; e is the exponential function; Φ and η are parameters, which affect the absolute and relative risk aversion of the utility function; X _j is the decision variable vectors of the model (whose elements are T _j and S _j , representing where to test and how intensive to test); Y _j is the opportunity set of the model; and NR is the net revenue function (revenue minus system cost). The probability of X _j to determine a Type II error at the optimal sampling decision and intensity is given by a binomial probability distribution. An attractive feature of the binomial probability distribution is that acceptable probability of success could be used to derive the optimal sampling policy (whether or not to test at a particular node and at what intensity).

The advantage of using this utility function in the stochastic simulation model is that it is flexible and allows for changes in absolute and relative risk aversion. The parameters of the utility function λ, Φ, and η are fixed and set to 2, 0.01, and 0.5, respectively, following with an initial wealth of 500. In this model, the total system or aggregate cost is estimated. Stages along fresh produce supply chain where testing can be implemented include the farm, transport from farm to packinghouse, packinghouse, transport from packinghouse to warehouse, warehouse, transport from warehouse to retail stores, and retail stores. Costs for tests conducted at each stage can be estimated separately. The total system cost (C) for a particular tracking strategy is defined as:

$$ C={\displaystyle \sum _{j=1}^{n}Tj\cdot \text{TC}j\cdot Sj\cdot Vj+\text{QL}j+C-\text{TPAT}/\text{FAST}},$$

(11.4)

where j is the stage for each economic agent where tests are conducted; T _j is binary variable indicating test/no test at stage j; TC _j is the cost of testing per unit ($/test) at stage j; S _j is the sampling intensity at stage j; V _j is the size of lots at stage j; QL _j is the volume diverted multiplied by quality loss cost per unit at stage j; and C-TPAT/FAST is the cost of participating C-TPAT/FAST program.

The advantage of optimal control model over alternative valuation models is that a risk premium or efficiency gain can be estimated with multiple stochastic variables or risk factors in the model (Nganje et al. 2009). As noted in the paper written by Nganje et al. (2009), the risk premium is the incentive or efficiency gains required by the vertically integrated firm in the import supply chain to offset potential risks from intentional or unintentional food contamination when they implement alternative policies and programs. It is a measure of the value of risk reduction of alternative risk reduction measures. In this chapter, the risk premium is derived for C-TPAT/FAST inspection procedures as the expected returns of the base case strategy (random testing) less the certainty equivalent of the C-TPAT/FAST procedure. The risk premium is defined as:

$$ \pi ={\text{EV}}_{\text{BCM}}-{\text{CE}}_{\text{C - TPAT/FAST}},$$

(11.5)

where π is the risk premium of the vertically integrated firm participating the C-TPAT/FAST program; EV_BCM is the expected value of the base case model with random testing only and no IG; and CE_C-TPAT is the certainty equivalent of the firm joining the C-TPAT/FAST program, which is derived from (11.3).