Multi-Plant Production and Transportation Planning Based on Data Envelopment Analysis

By Fang, Liu; Gongbing, Bi et al. | Canadian Social Science, May 1, 2014 | Go to article overview

Multi-Plant Production and Transportation Planning Based on Data Envelopment Analysis


Fang, Liu, Gongbing, Bi, Jingjing, Ding, Canadian Social Science


Abstract

This paper proposes a methodology for developing a coordinated aggregate production plan for manufacturers producing multiple products at multiple plants simultaneously, in a centralized environment via data envelopment analysis (DEA).

Based on demand forecast of the planning horizon, the central decision maker (DM) specifies the optimal combination of input resources required by the optimal output targets for each plant to keep the supply and demand in balance, and the accompanying transportation trips and volumes among distribution centers (DCs) or warehouse facilities. In this paper, we focus on an integrated production-transportation problem since production and transportation are two fundamental ingredients in the whole operation chain. We deal with multiple products manufactured in multiple plants.

The proposed mixed integer DEA models minimize both production costs and transportation costs. The capacity constraint for each plant is enforced by using the production possibility set theory. Finally, we validate our models by a numerical example and sensitivity analysis.

Key words: Integrated production-transportation planning; Data envelopment analysis

INTRODUCTION

We consider an integrated production and transportation planning problem: how to optimally determine aggregate production planning and transportation trips among distribution centers (DCs) and the corresponding transportation volumes, where production and transportation plan are considered simultaneously.

The production decisions concerns how to allocate input resources and set output targets among different production units, while the transportation decisions work out how to transport superfluous outputs for one DC to other under-supply DCs when all these DCs are accommodated by the corresponding production unit. We are interested in making an integral decision to minimize the aggregate costs including production costs, here mainly referring to the costs of input resources, and transportation costs to satisfy each DC's market demand.

In supply chain management, it concerns efficient policies related to purchasing raw materials from suppliers according to order or market forecast, transforming them into finished goods considering production capacity, and delivering them to end customer. Traditionally, the activities are optimized separately due to the intractability of large model. It is obvious that such pattem neglects the internal relation in the chain compared with optimizing these steps simultaneously since optimization of each step separately does not necessarily lead to the optimization of all steps in an integrated manner. That is especially true when we deal with multi-plant and multi-DC under a centralized environment, where mutual cooperation is permitted and often required as long as such decision is cost-efficient for each DC to meet its demand.

Consequently, the coordinated operations of the main stages will lead to remarkable cost reductions for the company. For example, in a research of Libbey-OwensFord Company (Martin et al., 1993), integrated approach saves nearly $2,000,000 compared with separated operations in annual cost. Another production-distribution study for Procter&Gamble (P&G) company (Camm et al., 1997) shows that integrated planning cuts down almost 20% of total cost. Integrated production and planning has become a new branch of supply chain management (Hugos, 2011; Papageorgiu, 2009).

Our model differs from previous works in the technique to characterize production function. We assume no a priori information on production technology. In particular, this paper introduces data envelopment analysis (DEA), a nonparametric method to describe production process, into integrated production-transportation problem, which is a different approach compared to the previous works in this field. There have been many papers covering the integrated production-transportation problem in a tactical level, some of which include the management of inventory especially in multi-period situations. …

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