The order picking process is often the single largest expense in a distribution centre (DC). The DC considered in this paper uses a picking line configuration to perform order picking. The number of pickers in a picking line, and the initial arrangement of stock-keeping units (SKUs), are two important factors that affect the total completion time of the picking lines. In this paper, the picking line configuration is simulated with an agent-based approach to describe the behaviour of an individual picker. The simulation is then used to analyse the effect of the number of pickers and the SKU arrangement. Verification and validation of this model shows that the model represents the real-world picking line to a satisfactory degree. Marginal analysis (MA) was chosen to determine a 'good' number of pickers by means of the simulation model. A look-up table is presented to provide decision support for the choice of a 'good' number of pickers to improve completion times of the picking line, for the properties of a specific picking line. The initial SKU arrangement on a picking line is shown to be a factor that can affect the level of picker congestion and the total completion time. The greedy ranking and partitioning (GRP) and organ pipe arrangement (OPA) techniques from the literature, as well as the historical SKU arrangements used by the retailer under consideration, were compared with the proposed classroom discipline heuristic (CDH) for SKU arrangement. It was found that the CDH provides an more even spread of SKUs that are picked most frequently, thus decreasing congestion and total completion time.
A real life order picking system consisting of a set of unidirectional picking lines is investigated. Batches of stock keeping units (SKUs) are processed in waves defined as a set of SKUs and their corresponding store requirements. Each wave is processed independently on one of the parallel picking lines as pickers walk in a clockwise direction picking stock. Once all the orders for a wave are completed a new mutually exclusive set of SKUs are brought to the picking line for a new wave. SKUs which differ only in size classification, for example small, medium and large shirts, are grouped together into distributions (DBNs) and must be picked in the same wave. The assignment of DBNs to available picking lines for a single day of picking is considered in this paper. Different assignments of DBNs to picking lines are evaluated using three measures, namely total walking distance, the number of resulting small cartons and work balance. Several approaches to assign DBNs to picking lines have been investigated in literature. All of these approaches seek to minimise walking distance only and include mathematical formulations and greedy heuristics. Four different correlation measure are introduced in this paper to reduce the number of small cartons produced and reduce walking distance simultaneously. These correlation measures are used in a greedy insertion algorithm. The correlation measures were compared to historical assignments as well as a greedy approach which is known to address walking distances effectively. Using correlation measures to assign DBNs to picking lines reduces the total walking distance of pickers by 20% compared to the historical assignments. This is similar to the greedy approach which only considers walking distance as an objective, however, using correlations reduced the number of small cartons produced by the greedy approach.
In this article a mathematical model is presented to assist management decisions on an integrated crop and livestock farm. Risk is incorporated into the model as the negative deviation of the actual gross income from the expected value of an activity's gross income. The model includes crop production (permitting and optimising a crop rotation system), dairy production and wool sheep production. Relevant data from a farm in the Swartland region of the Western Cape were used to test and validate the model. The results show that the adoption of crop rotation is superior in terms of gross margin to that generated from a mono-crop strategy. Empirical results also indicate that the complex interrelationships involved in a mixed crop-livestock farm operation play a major role in determining optimal farm plans. These complex interrelationships favour the introduction of crop rotation in the crop production activities of the farm under investigation. Solutions of the model with risk indicate that the crop rotation strategy and animal production levels are sensitive to different risk levels, and that the incorporation of risk greatly affects the level of land allocation to crop rotation and animal production level of the farm. Finally, the results suggest that the introduction of crop rotation is of paramount importance in improving the profitability and sustainability of the farm, thus the inclusion of forage crops such as medics into the integrated crop-livestock production is beneficial for sustained profitability.
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