In my research work, I want to construct mathematical programming model for a supply chain network problem. I have assumed production cost to be linear in nature. Is this assumption correct or should I change this assumption. Please suggest with valid description.
Production cost is composed by several items. First there is a fixed cost to pay to design the system, and start production, and then it might be a slightly decreasing cost per unit produced, as you will have - in the long run - the benefit of a working system for a long time. There is also one or more constraints because of capacity limitations in the production, as well as maintenance costs due to repeated repairs or replacements of worn-out or safety-regulated components that need to be replaced, and hence no production during those shutdowns. During shut-downs you of course do not make any profit. Further, depending of the type of repair, you might consider opportunistic maintenance - which means that one replaces more than the broken ones in order to have a high rate of production.
Generally it can be approximated to be linear. However, in some cases nonlinearity should be considered.
Please check the following:
https://www.sciencedirect.com/science/article/abs/pii/S037722171300266X
https://saylordotorg.github.io/text_managerial-accounting/s09-04-the-relevant-range-and-nonline.html
Hello
I completely agree with Michael Patriksson.
However, we can add any others internal costs: materials stock carrying costs (or holding costs), semi-finished products warehousing costs, handling costs between different stages. in the same factory, and perhaps transportation costs between different production places (several factories not necessary located in the same district).
Bye
Indeed, there is no limit to how complex it can get, but best is to start small, and try to obtain real data from the enterprise; without real data it all would become just a game.
Distinguished Syed Aqib Khalil, without coming into conflict with the answers of other colleagues, in which you can see how complex the estimation of production costs and logistics costs can be, I agree with the first sentence of Noha A. Mostafa, “Generally it can be approximated to be linear”.
Remember that in Operations Research, the model is as important as the use we make of it. Therefore, managing costs as linear will be useful if the cost component is not the heart of your model.
If costs are very relevant in your model, I would recommend that you review the Activity Based Costing (ABC), technique to which we mention in the work that is in Research Gate and whose link I copy below.
I hope these comments are of some use and many successes in your research.
Best regards,
José Hernández.
https://www.researchgate.net/publication/304038357_LOGISTIC_FLOWS_THROUGH_THE_FUNCTIONS_OF_THE_COST_MANAGER
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