Managing Material Flow and Batching

Production scheduling, production quality control and inventory management in the food industry lead to a focus on the flow of materials through the production facility. Many important decisions depend on accurate and timely information regarding the amount and quality of materials that are undergoing some step in the manufacturing sequence. This information is used by the manager to determine product costs, procurement, or harvest requirements, and to project output product amounts and to assist in setting prices. Product safety, good product qualities, and product profitability require that the manufacturing sequence conform to the requirements of the food as material and that the processing facilities be managed efficiently. Because of the typical low margin per sale, the throughput for such facilities must be large. This means that small improvements in efficiency will have important consequences for profitability. In many food production facilities, the manufacturing sequence is further complicated because either the technology or the economics require batch processing. Although the ideal may be "continuous processing," the technology may not be available as in the manufacture of cheddar cheese, the blending of processed cheese, or the processing of low-acid foods. In other cases, the continuous technology is too expensive or otherwise infeasible to be adopted as in the retort processing of low-acid foods. This leads to complications in achieving target productions, especially in cases where batches of intermediate materials are used in multiple products. The decision making surrounding procurement, production scheduling, and quality control is strongly connected to the technology of the food being processed. This technology once again determines the manufacturing sequence and constrains the amount of throughput.

The flow of materials in canning requires that incoming vegetables be washed, sorted by grades, placed in a container that is partially filled with brine, then retort processed before being cooled, labeled, and placed in cases. Although not all of these steps are used in every manufacturing sequence, brining and retort processing are both batch-processing steps. The flow of materials provides a structure to organize information regarding this manufacturing sequence. Such information can be fed forward to control subsequent steps in the processing. For example, the size of peas (as well as the variety of peas and the formulation of the brining solution) will affect the time and temperature settings for the subsequent retort processing. Amounts of materials and corresponding costs may be kept in this same flow of materials structure as well as information required by government regulation or company policy.

Using a flow of materials structure provides great organizational advantage. Although it is possible to do the arithmetic and track the resources by hand for a few products, with many products that use many intermediate products the mass of detail that accumulates is soon overwhelming. Using the flow of materials as a structure provides more than organizational convenience, however. The development of the so-called Gozinto matrices can be done from the flow of materials structure (10,11), and their connection to materials requirements planning (MRP) means that accurate projections of materials use, costs, and inventory amounts can be conveniently made. Although the time phasing of inventory and production is not as impor tant a problem in the food industry as it is in fabrication industries, tracking the use of intermediate products, product costing, and batching are.

A Gozinto matrix is created through a procedure that organizes production information into a lower triangular, invertible matrix. The rows and columns of this matrix correspond to products and inputs to products, organized so that no row corresponding to an input to a product occurs above the row corresponding to the product in the matrix. This means that the bottom rows in the matrix correspond to ingredients purchased or harvested from outside the production facility, whereas the top rows correspond to the output products of the facility. The rows in between correspond to intermediate products that may find there way into many output products. More details may be found in Mize and coworkers (11).

Inverting this matrix and doing some elementary matrix algebra provides a means of anticipating and tracking inventories and production. For specified target production, the precise input needs of each ingredient or intermediate product may be determined. Inventories would be kept to a minimum if we could procure or manufacture exactly these quantities of input materials. But getting exactly the quantity of intermediate products required is complicated by batch processing and by the use of batch output in multiple products. The amount of brine needed for a target number of cases of canned vegetables is rarely a whole number of batches of brine. More likely, the target will require 12.37 batches of brine, or some other in between number. Is it better in these cases to make 12 batches or 13 batches or to make partial batches (ie, 0.37 batches)?

If we make more batches than the target, we will have excess quantity of batch output, which must be stored or discarded, or used in excess production of final product, which then must be stored. If we make less than the target production, we may not meet demand (causing stock outs) and opportunity costs associated with lost sales. If we make partial batches, we face the same labor and fixed costs associated with full batches but get less output. Furthermore, partial batches often imply important technological changes-especially in the food industry—since batch inputs may not scale linearly. Salt and spices are good examples of inputs for which it is not good enough to simply cut the amounts in half when the batch is half the size. If this technological information is not available, product quality will vary when the batch is rescaled.

In these circumstances, what is the best the production manager can do? If the costs just described are understood and can be estimated, an optimization model can be built and used to determine how many batches of input are best for target production amounts. The difficult part is the construction of an objective measure, which simultaneously takes into account the costs of the different alternatives as well as potential revenues from the products. Measuring profits for a production run will require determining the revenue from each of the products made and subtracting ingredient costs, batching costs, and the costs from overproduction and underproduction. The resulting detailed model can be found in Chung (12). For purposes of this review suffice it to say that it is possible and profitable to apply optimization in batching situations. The goal of the model is to find not only a product mix but also a batch mix that maximize the penaltied profits.

Although other models are possible, this example shows how such a model might be constructed. Such models may require that certain values be integers but still may be solved by computer methods. The result will be optimal choices regarding the number of batches produced that reflect the costs and revenues that the production facility faces, rather than the intuition of the manager.

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