Application of Triplet Notation and Dynamic Programming to Single-Line, Multi-Product Dairy Production Scheduling

Introduction

The application of optimal methods for production scheduling in the dairy industry has been limited. The predominate need that has been addressed is the need to forecast supply. As the dairy industry implements advanced production equipment technologies and demand forecasting becomes stronger, dairies may begin to push back on suppliers and enable efficient production schedules. This paper addresses this emerging area of application.

Raw milk is initially processed into two variations, skim, and whole. One percent and two percent milk are the result of blending appropriate ratios of skim and whole milk. Therefore, a single filling line may simultaneously produce all four varieties of milk (Mans, 2007). Other product families such as orange juice, carnival drinks, and buttermilk are also processed using the same filling line although separate storage tanks are used for each product family.

Product is piped into one of two bowls for filling. Between batches of different product families, the equipment must be cleaned. Less extended cleaning can also be required between products within the same product family.

A primary goal of this scheduling approach is to facilitate the transition of the dairy operation from a push system to a pull system. Order due dates will act as constraints in the problem formulation and ultimately guide the order of production. Customers have standing due dates each week for their orders and these dates must be met. Additionally the scheduling approach will reduce inventory held. In the past excess inventory was carried when it was uncertain as to whether an order could be slotted into the production schedule.

A very limited amount of research has been completed in this area. We begin with presentation of literature both directly and indirectly addressing the dairy industry. Chemical industry scheduling models and other type of food processing scheduling models offer insight into appealing approaches to the dairy problem. We then formulate the scheduling problem using triplet notation where the first leg of the triplet represents a production run and the second leg of the triplet represents a cleaning cycle. Constraints are relaxed using Lagrange relaxation and the problem is them solved using dynamic programming.