Production Planning Based on DEA Profit Efficiency Models

Introduction

Data envelopment analysis (DEA) has been applied as efficiency evaluation and ranking tool in many areas, such as nations’ ranking in the Olympic Games, colleges and universities evaluation, bank industry, production plan and other areas. If products supply or service supply exceeds the market demand in an industry, it will lead to low profit, even loss, the quality of products varies from different levels of corporations, and disorderly competition among the industry. For instance, in 2012, steel industry of China lost 8.249 billion, a 7.39 percent increase year-on-year, due to the excess production capacity. A lot of firms set up in the photovoltaic industry resulted in far diversity among products from distinct firms. Furthermore, in China, overcapacity brought about disorderly competition, low operating efficiency, and other issues in cement, rare earth, shipbuilding industries. In America, at the beginning of this century, internet bubble burst brought about overcapacity to the computer, electronic equipment, and high-tech industries. International financial crisis in 2008 caused overcapacity in many industries. Facing the varied market, if a company does not predict the market demand in next year before setting the production plan, excess production capacity or idle production capacity will lead to a bad performance. The appropriate production plan is the basic step to gain profit.

There are tons of approaches to make production plan. Karlin (1960) developed a dynamic inventory model with linear purchasing cost functions in different conditions, facing various demand distributions in diverse stages. They showed monotonicity results with production and inventory capacity limits in the stochastic case. Beckmann (1961) proposed models to find the optimal strategy for adjusting the rate of production to stock under the assumption that production of a product was continuous and subjected to the direct cost of production, with a known demand distribution. Their results revealed the relationship between stock level and the rate of production. Veinott (1964) sought the optimal production levels restricted by the minimizing production and inventory carrying costs, the production, and inventory capacity limits. Veinott (1965) put forward models to analyse multi-periods of equal length of the single product and non-stationary inventory problem, with the optimal stock ordering policy and several classes of product demand independently in each period. Sobel (1970) developed models for optimal production policies of a single product with stochastic demand. Kunreuther and Morton (1973) proposed an algorithm to find all seasonal demand to be met from regular production under the general assumptions for the production and production smoothing, holding the certain cost functions. Their results complemented the findings of Modigliani and Hohn (1955), besides, they provided insight into the nature of the optimal policy for stochastic planning problems.