* Corresponding author. Tel.: # 1 215 895 1449; fax: # 1 215 895 2891; e-mail: banerjea@duvm.ocs.drexel.edu. Int. J. Production Economics 59 (1999) 251 — 259 Production lot sizing with variable production rate and explicit idle capacity cost Somkiat Eiamkanchanalai, Avijit Banerjee*  Faculty of Commerce and Accountancy, Chulalongkorn University, Bangkok 10330, Thailand  Department of Decision Sciences, College of Business and Administration, Drexel University, Philadelphia, PA 19104, USA Abstract This paper develops a model for simultaneously determining the optimal run length and the rate of production for a single item. As opposed to traditional approaches, the item’s output rate is treated as a decision variable. It is assumed that the production cost per unit is a quadratic function of the production rate, in an effort to capture the effect of increased unit cost as a result of deviating from the “nominal” rate of output, for which the system was designed. In addition a linear function is incorporated in the proposed model to represent the desirability or undesirability, as the case may be, of unused capacity. The iterative solution procedure developed is illustrated through a numerical example and extensive sensitivity analysis is performed for examining the major tradeoffs involved.  1999 Elsevier Science B.V. All rights reserved. Keywords: Inventory model; Production lot sizing 1. Introduction Since the development of the economic order quantity (EOQ) concept more than eight decades ago, a substantial amount of research has been conducted in the area of inventory lot sizing. One of the earliest embellishments of the classical EOQ model has been the incorporation of a finite production rate, resulting in the more general economic lot size, or alternately, the optimal pro- duction run length (PRL), formula (see, for example, [1]). Subsequent studies in this regard has focused on modifying the PRL concept under a variety of real world conditions, including the presence of inflationary factors, uncertainty, mul- tiple production stages, multiplicity of products to be produced, etc. [2]. In other words, the literature pertaining to production batching has a relatively long and rich history. In spite of this history, however, an important aspect of the production run length problem has received relatively scant attention from researchers. With a few recent exceptions, most of the studies in this area assume that the production rate of an item of interest is a fixed parameter — determined by the current level of resources deployed. In reality, for 0925-5273/99/$ - see front matter  1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 5 - 5 2 7 3 ( 9 8 ) 0 0 1 0 2 - 9