The present paper extends prior researches on data envelopment (DEA)-based production planning in a centralized decision-making environment. In such an environment, the production planning problem involves the participation of all individual units, each contributing in part to the total production. The production planning problem involves determining the number of products to be produced by all individual units in the next season when demand changes can be forecasted. The current study is concerned with optimal production planning in a centralized decision-making environment. The approach proposed in this paper takes the size of operational units into consideration and the production level for each unit becomes proportional to the ability of the units. The applicability of the proposed approach in real applications is illustrated empirically using two real cases.
Data envelopment analysis (DEA) was introduced in 1978 when Charnes, Cooper and Rhodes (CCR approach) demonstrated how to change a fractional linear measure of efficiency into a linear programming format. In DEA, decision making units (DMUs) could be assessed on the basis of multiple inputs and outputs. Since the first DEA model developed, many other DEA models and applications have been developed and extended (see Cooper et al., 2004, Amirteimoori and Emrouznejad, 2011 and Amirteimoori, in press).
An important application of DEA, from both a practical organizational standpoint and a cost research perspective, is the problem of production planning. The production planning problem is common to many production systems and typically implies assigning required products to the available resources. Many contributions to this theory have been made in the last two decades from various perspectives; see, for instances, Kim and Kim (2001), Sharma, 2007a and Sharma, 2007b, Chazal et al. (2008), Pastor et al. (2009), Sharma (2008) and Sharma, 2009a and Sharma, 2009b.
Kim and Kim (2001) proposed an iterative approach to finding the capacity-feasible production plan. An extended formulation of the LP model was proposed, in order to consider the workload profile of the production quantity and the actual amount of the capacity to be allocated to the requirements for each producer.
Chazal et al. (2008) studied the production planning and inventory management problem based on the assumption that the firm under consideration performs in continuous time on a finite period in order to dynamically maximize its instantaneous profit. Pastor et al. (2009) presented a case of production planning in a woodturning company, where it met the demand at a minimum cost while being subjected to a series of principal conditions.
Using the DEA technique in production planning is not new. As far as we are aware, four DEA-based approaches have been published in the literature: Golany (1988), Beasley (2003), Korhonen and Syrjanen (2004) and Du et al. (2010). Golany (1988), for instance, presented an interactive linear programming procedure to set up goals for desired outputs. Their procedure is based on the empirical production functions generated by DEA and is then adjusted by new information provided by the decision maker in each iteration.
Beasley (2003) proposed nonlinear resource allocation models to jointly decide on the input and output amounts to each DMU for the next period while maximizing the average efficiency of all DMUs. Korhonen and Syrjanen (2004) developed a DEA-based interactive approach to a resource allocation problem that typically appears in a centralized decision making environment. Du et al. (2010) look at the production planning problem, from the productivity and efficiency perspective, using DEA. They have proposed two planning ideas in a centralized decision-making environment when demand changes can be forecasted.
The current paper is concerned with the production planning problem in a centralized decision making environment. It has been assumed that both, supplies for the inputs and demands for the outputs, can be forecast in the next production season. With the forecasted demands for the outputs and supplies for the inputs, the paper develops a DEA-based production planning approach to determine the most favorable production plans. We axiomatically assume that output productions can be increased in the next production season when input usages are increased. The approach proposed in this paper takes the size of the operational units into consideration and the production levels for each unit become proportional to the ability of the units. The term “ability” in our study means that the planned production is proportional to the input usages and output productions from a size point of view. In other word, the approach should not set a huge production plan for DMUs with small inputs and outputs. We will define two magnitude sizes for each DMU: a size on the input side and a size on the output side. These definitions will be used to determine a practicable production plan in the next production season.
The rest of the paper is organized as follows: the following section provides a background of the subject. The proposed production planning model is given in Section 3. Then, a simple example is given to illustrate the proposed approach. Section 5 applies the approach to a real data set consisting of 14 Iranian gas companies. Finally, we conclude with the result.
Because of the uncertain nature of the future, there is a need to provide robust and flexible procedures in order to examine alternative courses of action and their implications. Production planning using DEA has been studied widely in the last decade. The current paper has addressed decision processes in which all operational units fall under the supervision of a central decision maker, which requires production planning in the next production season when demand changes can be forecasted. It has been assumed that all of the individual units are able to modify their input usages and output productions in the next season. Two magnitude sizes on the input and output sides have been defined for each operational unit and the approach took the size of each unit into consideration. Nevertheless, the obtained production plan for each unit is proportional to the size of each unit. This guarantees the practicability of the proposed approach.
