Integration of Lot Sizing and Flow Shop Scheduling with Lot Streaming

Navid Mortezaei,Norzima Zulkifli

doi:10.1155/2013/216595

Abstract

We will develop a mathematical model for the integration of lot sizing and flow shop scheduling with lot streaming. We will develop a mixed-integer linear model for multiple products lot sizing and lot streaming problems. Mixed-integer programming formulation is presented which will enable the user to find optimal production quantities, optimal inventory levels, optimal sublot sizes, and optimal sequence simultaneously. We will use numerical example to show practicality of the proposed model. We test eight different lot streaming problems: (1) consistent sublots with intermingling, (2) consistent sublots and no intermingling between sublots of the products (without intermingling), (3) equal sublots with intermingling, (4) equal sublots without intermingling, (5) no-wait consistent sublots with intermingling, (6) no-wait equal sublots with intermingling, (7) no-wait consistent sublots without intermingling, and (8) no-wait equal sublots without intermingling. We showed that the best makespan can be achieved through the consistent sublots with intermingling case.

Highlights

In the manufacturing industries, the commonly used planning and scheduling decision-making strategy generally follows a hierarchical approach, in which the planning problem is solved first to define the production targets, and the scheduling problem is solved next to meet these targets [1]
We showed that the best makespan can be achieved through the consistent sublots with intermingling case
We summarize some works of research regarding integration of lot sizing and flow shop scheduling as follows

Summary

Introduction

The commonly used planning and scheduling decision-making strategy generally follows a hierarchical approach, in which the planning problem is solved first to define the production targets, and the scheduling problem is solved next to meet these targets [1]. An integrated cost model including setup time dependency and order backlog was developed to handle both procurement lot sizing and production scheduling simultaneously. They proposed a genetic algorithm (GA) based heuristic to create an optimal or near-optimal solution for the flow line assembly problem under the setup-dependent environment [6]. Yan and Zhang claimed that none of the existing literature involves a monolithic optimization model for production planning and scheduling in a multistage system They formulated a monolithic optimization model for a three-stage manufacturing system that includes a job shop, a parallel flow shop, and a single machine shop.

Integrated Model for Lot Sizing and Scheduling with Lot Streaming

Numerical Example

Findings

Conclusion