تجزیه و تحلیل حساسیت از مدل شبیه سازی گسسته رویداد اتفاقی از عملیات برداشت محصول در یک سیستم کشت ایستای افزایش یافته

Greenhouse crop system design for maximum efficiency and quality of labour is an optimisation problem that benefits from model-based design evaluation. This study focussed on the harvest process of roses in a static system as a step in this direction. The objective was to identify parameters with strong influence on labour performance as well as the effect of uncertainty in input parameters on key performance indicators. Differential sensitivity was analysed and results were tested for model linearity and superposability and verified using the robust Monte Carlo analysis method since in the literature, performance and applicability of differential sensitivity analysis has been questioned for models with internal stochastic behaviour. Greenhouse section length and width, single rose cut time, and yield influence labour performance most, but greenhouse section dimensions and yield also affect the number of harvested stems directly. Throughput, i.e. harvested stems per second, being the preferred metric for labour performance, is most affected by single rose cut time, yield, number of harvest cycles per day, greenhouse length and operator transport velocity. The model is insensitive for σ of lognormal distributed stochastic variables describing the duration of low frequent operations in the harvest process, like loading and unloading rose nets. In uncertainty analysis, the coefficient of variation for the most important outputs, labour time and throughput, is around 5%. Total sensitivity as determined using differential sensitivity analysis and Monte Carlo analysis essentially agreed. The combination of both methods gives full insight into both individual and total sensitivity of key performance indicators.

Labour is a dominant cost factor in Dutch cut-rose production. Growers feel an economic need to decrease labour cost and control labour demand better. Crop production system design and labour management are the key processes for improving labour efficiency. These processes are commonly driven by system evolution and experience. Quantitative models for evaluation of new crop production system designs and new labour management strategies are not available. For this reason, the Greenhouse Work Simulation model (GWorkS) was developed. In Van 't Ooster et al., 2012 and Van 't Ooster et al., in press, this model was presented and validated for harvest in two crop production systems for cut rose, a mobile and a static rose production system. GWorkS is a stochastic discrete event model of crop operations in greenhouses. Its purpose is to support designers and growers in improving crop cultivation systems with respect to labour efficiency and quality of labour. For model-based design and evaluation of systems, it is required to evaluate 1) risks of model or system failure resulting from uncertainty, and 2) sensitivity of key performance indicators for individual parameters. Sensitivity analysis is the suitable technique for both (Macdonald & Strachan, 2001). The aims of this study were to identify 1) input parameters that must be chosen with care so as not to compromise the accuracy of the model prediction, as well as parameters for which accurate specification is less necessary, 2) features of the growing system to which labour demand is very sensitive and which could guide the designer and producer of a growing system to an improved system, and 3) impact of model limitations and sources of uncertainty on the model's ability to discriminate between alternative work scenarios. Delivering the aims of this study requires determination of individual sensitivity and uncertainty ranges of model output. Individual sensitivity describes effects of individual parameters on model output. Differential sensitivity analysis (DSA) is widely used to produce individual sensitivity (Lomas & Eppel, 1992). In this study, DSA is a one-at-a-time method varying just one parameter for each simulation while all other parameters remain fixed at their nominal values (Hamby, 1995). The change in a model output is a direct measure of the effect of the change in the single input parameter. However, in a stochastic model, this direct measure may be disturbed by random internal processes. For linear and superposable systems in the parameter space, DSA also produces total sensitivity by taking the length of the vector containing the individual sensitivities. This total sensitivity describes the output effect of perturbation of all parameters. If input perturbation equals the measured input uncertainty, then total sensitivity represents output uncertainty. When assumptions are met and when disturbance by internal random processes is excluded, DSA is an ideal and fast method for determining both parametric sensitivity and uncertainty. Gunawan, Cao, Petzold, and Doyle III (2005) and Kim, Debusschere, and Najm (2007) indicate that DSA does not directly apply to discrete stochastic dynamical systems and therefore its application in this study is not obvious since the GWorkS-rose model is a model of this type. It will however be shown with help of Monte Carlo analysis (MCA) that, in this case, application of DSA is appropriate. MCA is a more rigorous method for determining uncertainty, since no specific assumptions on the model are required. MCA involves simultaneous variation of all inputs. The variation of the inputs is random within a defined probability density function. The method fully accounts for interactions between inputs, for internal random processes and is not affected by the number of parameters (Macdonald & Strachan, 2001). MCA generates total sensitivity only (Lomas & Eppel, 1992). If both methods, DSA and MCA, agree with respect to total sensitivity, then DSA is a credible and fast method that can be used to determine individual sensitivity.

Sensitivity was determined at one operational point of the system, which was chosen from current practice in the Netherlands. It was considered as a point of departure for labour efficiency improvement. The sensitivity analysis therefore represents a local method, applied at 5 yield levels and two harvest cycles. The model is essentially linear, meaning that relative sensitivity coefficients are valid for a larger parameter space than the evaluated system operation point. Validity boundaries were however not determined in this study. The GWorkS-rose model is not extremely sensitive for any of the 22 tested input parameters. The highest sensitivity in labour time is slightly above 1. Individual sensitivities change with crop yield. Specific findings are summarised in Sections 4.1 and 4.3. Parameters for which the labour time or throughput sensitivity is greater than 0.1 must be chosen with care. Within this group, eight parameters were identified, namely 2 greenhouse parameters pj ∈ Pg, 4 operator parameters pj ∈ Po, 1 crop parameter pj ∈ Pc, and 1 management parameter pj ∈ Pm. These parameters are section length (LGh ∈ Pg) and width (nsp ∈ Pg), μ and σ in cutting performance ((μ(Tcr), σ(Tcr)) ∈ Po), trolley speed (vo ∈ Po), and anticipation distance before cutting Do ∈ Po, yield (Yn cf ∈ Pc), number of harvest cycles (nhc ∈ Pm). Moderate sensitivity was found for average performance in rose net handling. The model is insensitive for standard deviations (in the natural logarithm) in service times for low frequency rose net handling actions. Under the condition that cycle time is not affected by resources like the number of operators, throughput (stems s−1) is the preferred indicator of labour efficiency, as it accounts for yield effects. Focal points of designers and growers for labour efficiency improvement are 1) technical aids or system modifications to improve rose cutting performance, 2) ways to allow early and reliable anticipation for cutting the next rose, 3) evaluate whether a 2nd harvest cycle can be prevented, and 4) couple trolley speed with yield for Yn < 2 stems m−2. The main sources of model uncertainty are in parallel execution of actions and trolley speed. As a result, the coefficient of variation and the 99% uncertainty range is relatively large for accumulated transport time and overlap time. The uncertainty effect of these parameters in labour time, throughput and utilisation of the operator is acceptably small with CV < 5%.