Optimising carcase cuts in the red meat industry
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Problem Moderators: Winston L. Sweatman, Massey University; Kevin White, University of South Australia
New measurement technologies are being introduced to the red meat industry. Previously carcases have been sorted by weight, breed, and an estimate of fat thickness. Now there is opportunity to gather more accurate information on the lean meat, fat and bone in individual carcases before they are processed.
In the case of lambs, each carcase is divided into five primal regions. Four of these are processed on production lines in the boning room, resulting in saleable cuts of meat.
The meat workers handling the carcases need to be given a cutting plan for each carcase, and they should have continuity in their tasks. They cannot be constantly changing between different cutting patterns. There is a high throughput of carcases and the decision process for handling them needs to be timely.
Optimisation opportunities arise in matching the available carcases to the orders for different cuts. For example, some cuts are more suitable for large lambs, while others suit small lambs. For some cuts of meat it is desirable to leave on a thicker layer of fat to enhance the cooked product, whereas for others the fat must be trimmed and disposed of at a lower price.
The cuts are usually produced in a succession of stages. Preliminary cuts may be further processed into multiple further cuts. In this process, the fulfilment of an order may result in saleable byproducts, and a market is required for these. Also a carcase, once started, must be completely processed.
A further issue is the labour cost involved. Some cutting patterns require more time, or the involvement of one of the more highly-skilled meat workers. The production of cuts needs to be feasible for the workforce available.
Carcases are hung on racks in a chilling room for a period before they are processed. There is some opportunity to sort the carcases as they go into the chiller, and this opportunity can be used to facilitate subsequent access to the carcases for processing in an efficient order.
The MISG group identified the following key features of the problem:
- Orders for saleable products (cuts)
- Carcases (with different weights and fat scores)
- Profit per cut (depending on both the carcase and market)—this may be negative
- Carcases must be completely processed
- Production line sequencing must minimise cutting pattern changes.
The overall goal is to maximise the gross margin.
An initial integer programming model was constructed to optimally match individual carcases to cutting patterns that would appropriately fill a set of orders. Using real data, this model could be solved in reasonable time (about eight minutes) for 95 carcases. Relaxing the integrality constraints enabled quick solution for a 996-carcase case study. The solution contained only five fractional values (all of them multiples of 0.5) out of a total of 3278 non-zero variables.
An improved integer programming model considered carcase types rather than individual carcases. The weight and fat score of each carcase determines which of 205 types it belongs to. The relaxation of this model was solved for 3699 carcases in less than a minute, producing only nine fractional values (all multiples of 0.5) in its solution.
Having decided on the cutting pattern for each region of each carcase, there is the issue of how to order the carcases on the racks in order to have continuity in the boning room. It is desirable to have runs of carcases with the same cutting pattern, for each region of the carcase. The MISG group considered modelling this by grouping carcases according to their superpattern (a superpattern is a cutting prescription for all regions of the carcase). These groups can then be sequenced in order to minimise disruptive costs of pattern changes.
During the week the group found and studied a number of papers and reports in the literature. These included considerations not only of the efficient processing of carcases but also of cutting patterns for timber. Some of these papers will be discussed in the full report.