International Journul qf Production Economics, 33 (1994) 257-264 Elsevier 257 An economic manufacturing quantity model with learning effects* T.C.E. Cheng Department of’ Management, Hong Kong Polytechnic, Hung Horn, Koaloon, Hong Kong (Received 13 July 1993; accepted 30 July 1993) Abstract This paper considers the calculation of economic manufacturing quantity (EMQ) under the influence of learning. The size of each order is assumed to be large enough to allow the manufacturing learning phenomenon to manifest itself. The set-up cost is also assumed to decline as a result of learning over the life of the product. These two types of learning phenomena are incorporated in the classical EMQ model to compute the optimal manufacturing quantities and number of orders. The special case of equal manufacturing quantities is then considered. After the theoretical treatment, several numerical examples are solved to study the effect ofassuming equal manufacturing quantities on the optimal solutions. The results indicate that the assumption of equal manufacturing quantities not only simplifies the process of determining the optimal solutions but also provides close approximations to the optimal solutions. 1. Introduction The classical economic manufacturing quantity (EMQ) model seeks to determine the optimal manufacturing size in batch produc- tion. Over the past 30 years, there has been a proliferation of research on optimal manu- facturing sizing for the purposes of inventory management. Surveys of these research results have been undertaken by Whitin [l], Clark [2] and Urgeletti Tinarelli [3], among others. Two important assumptions of the classical EMQ model are that the set-up and unit vari- able manufacturing costs are constant and in- dependent of manufacturing quantities [4]. These assumptions are normally valid for items produced by machines which exhibit small variations between operations [S]. Even Correspondence to: T.C.E. Cheng, Department of Management, Hong Kong Polytechnic, Hung Horn, Kowloon, Hong Kong. for manual operations, these assumptions may be appropriate under conditions of stable pro- duction, loose standards and short production run with limited product life [6]. However, under certain circumstances, both set-up and unit variable manufacturing costs exhibit a significant declining trend over time. This decreasing cost behaviour is observed when operations are performed with high human content, coupled with long production runs over an extended period of product life. The steady decline in cost is attributable to the learning curve effect. This effect was first dis- covered by Wright [7] in the aircraft industry; it was subsequently empirically found to exist in many industries in both the manufacturing and service sectors [S]. Some attempts to develop an EMQ model which takes into consideration the effect of learning on manufacturing size have been re- ported in the literature. Keachie and Fontana [6] were among the first researchers to apply the learning curve to the EMQ model. They 0925-5273/94/$07.00 0 1994 Elsevier Science B.V. All rights reserved. SSDI 0925-5273(93)E0074-6