Using PuLP this Python template solves a capacity planning problem using linear programming. 

Linear optimization in Python for oil pump capacity planning

In the exemplary case study solved by this Python model a new oil field is prepared. For this, oil pumps must be purchased. Different pump types have different production capacities and purchasing prices.

The problem is to minimize purchasing expenses while at least securing required production volumes.

Another constraint is the available surface area of the oil field. Above figure displays an exemplary oil field in Texas.

KPIs traced by the linear capacity planning Python model

The optimization model considers the following KPIs:

• Purchasing expenses
• Production output
• Surface area occupied on the oil field

Who will benefit from this linear programming template?

Linear programming is a fundamental mathematical programming technique, applied not only in capacity planning. For example, logistics networks can be optimized with linear programming as well. It is also used for e.g. marketing campaign planning, pricing, and much more.

Hence, getting familiar with linear programming and owning a Python template for implementing a linear optimization program in Python, can be beneficial to a wide group of users. This includes students, analysts, and managers – in manufacturing, logistics, purchasing, accounting, controlling, and marketing.

More about linear optimization in Python and other programming languages

If you are interested in linear programming, capacity planning, and mathematical optimization, here are some related articles that might help in getting you started:

• Optimization via master production scheduling
• Price and inventory optimization
• Integer programming
• Linear programming in Julia
• Linear program with Google ortools in Python

In detail this downloadable SimPy simulation framework comprises:

• SimPy object-oriented modeling library for modeling poultry supply chain
• Example model implementing exemplary poultry supply chain 
• Conceptual model description
• Configuration file
• Integrated statistics generation

To learn more about the various different simulation methods you can e.g. read this simulation method introduction.

Poultry supply chain elements included in the model

The framework comprises the following supply chain entity models: 

• Egg supplier
• Hatchery
• Brooder
• Farmer coops
• Slaughterhouse
• Meat processing

Information flow assumed by the simulation framework

The exemplary poultry supply chain model included by this virtual product implements/assumes a PUSH controlled supply chain. The egg supplier is the source of the material flow, and the meat processor is the sink. Egg shipments from the egg supplier are supplied to the hatchery upon order placement by the hatchery, using a s,S-based inventory control logic. From there on material flow is PUSH based, all the way to the slaugtherhouse’s finished product stock (carcasses). Meat processing, facilitating the sink in this example model, pulls its demand from the slaughterhouses’ inventory. For more details read the conceptual supply chain description (part of the product).

Relevant poultry  growth assumptions and constraints

This framework focuses on supply chain simulation. It thus makes some simplifying assumptions. For example, chicken growth dynamics are not modelled in detail. Instead  the model assumes process dwell times and chicken start and end weights for relevant processes.

This applies to the following processes:

• Broodery. The framework, via its configuration files, allows for brooding time specification. It is assumed that all hatched undergo the same brooding time. It is furthermore assumes, that all chicken have the same weight when exiting the broodery.
• Farm coops. The framework allows two different population types to be modelled. For example, hens and toms. Coop dwell is the same for all chicken and all populations of the same type. Dwell times in the coop can however be different for the two different population types. This allows to reflect e.g. faster growth of one population type over another. All chicken, regardless of their type, are assumed to have the same weight at the end of their coop dwell time. This is the “slaughter-ready weight”.

KPIs calculated by this framework

This framework calculates and tracks the number of units in a process or in stock (inventory). The same is true for final demand at the end customer (meat processing facility). 

Modelling demand and inventory becomes unit neutral in this way. That allows for straight forward specifcation of mortality rates (referred to as “scrap” as per production industry terminology) and unsuccessful hatching ratios (failure ratios). Morever, chicken weights at the various stages of the supply chain can thereby easily be assumed and multiplied with the quanitites. The same is true for costs, e.g. purchasing costs, feeding costs (per period and chicken unit), holding costs, processing costs, etc. 

It must be clearly understood that a cost model is not part of this simulation model. But since stocks and flows are measured in the same unit (“number of chicken”, “number of eggs”, “number of carcasses”) a cost model can flexibly and easily be applied on top of the simulation results generated by this framework.

Exemplary model output 

Here are some exemplary statistics and statistics visualizations generated by the SimPy framework comprised by this virtual product: