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1 , (2006 6) 1) *.. I. (batch). (production planning). (downstream stage) (stockout).... (endangered). (utilization). *

2 40, (EPQ; economic production quantity). (setup cost) (setup time) Bradley Conway(2003) (JIT; just-in-time production). (work-in-process inventory).. (cycle policy). (cycle) (deterministic) (stochastic) ( Sykes 1970, Elmaghraby 1978). (Avi-Itzhak et. al., 1965, Sykes, 1970). (Eisenberg 1971, Elmaghraby 1978, Bradley Conway 2003).. (iterative method), (dynamic programming), (ILP; integer linear programming) (Doll Whybark 1973, Elmaghraby 1978, Haessler 1971, Parsons 1966)

3 41 II (idle)., = 1, 2(demand rate), (production rate), 1 2,, 2 1,...,,. = =, (2.1) = =, = 1, 2. (2.2),,, =

4 42, 40 12,. Min. = = s.t =. (2.3) (2.3) Min. = + +. (2.4) 1 (2.4) 2(second derivative) (2.4) (convex). (2.3)

5 43 (symmetry). 1(first derivative) 1 2. (2.3) (joint) (Hessian). =, =. (2.5) (2.5) (2.3), =1.2., = 1,2. (2.6) (2.3) (Bradley Conway, 2003).., = 1, 2,. =, = 1, 2. (2.7)

6 44, = + +, =. (2.8) (2.8) , = 1, 2. = = =,. (2.9) (2.1). =, = 1, 2. (2.10) (2.10). (2.5) (2.3) (2.10)

7 step1: (2.5) =, = step2. step2: (2.10). =, = (upper bound) (lower bound). III. 1,,., = 1,,,,,,..,,. 2.

8 46, = =, (3.1) = =, = 1,,. (3.2). Min. = { + } s.t. { + } 1 =, = 2,,. (3.3) (3.3). Min. = +. (3.4) (3.4), =1,,. =, =. (3.5)

9 47 (3.5)(3,3), = 1,,,. = = = =, (3.6), (3.7), (3.8). (3.9), =1,,,. step1: (3.5), =1,,. { + } 1 =, =1,,, { + } 1 step2. step2: (3.9), =1,,. =. IV...

10 48, (Di) (Pi) (hi) (Ci) 1 10,000 25, ,000 10, (Si) 1 (Qi*) (K) / / / / / / (2.3) (2.5) (2.3) (2.11) , (2.8), (2.10), (2.11) 1, 2, 3, , =122.5,

11 49 (Di) (Pi) (hi) (Ci) 1 1,000 5, , , ,000 10, , (3.3). (Si) 1 (Qi*) (3.3) (3.5) (3.3) (3.9).

12 50, V... Avi-Itzhak, B, W.L. Maxwell, and L.W. Miller (1965), Queueing with Alternating Priorities, Operations Research, Vol. 14, Bradley, J.R. and R.W. Conway (2003), Managing Cyclic Inventories, Production and Operations Management, Vol. 12, No. 4, Doll, C.L. and D.C. Whybark (1973), An Iterative Procedure for the Single-Machine Multi-Product Lor Scheduling Problem, Management Science, Vol. 20, No. 1, Eisenberg, M. (1971), Two Queues with Changeover Times, Operations Research, Vol. 17, Elmaghraby, S. (1978), The Economic Lot Scheduling Problem (ELSP): Review and Extensions, Management Science, vol. 24, No. 6, Haessler, F. (1971), A note on Scheduling a Multi-Product Single-Machine System for an Infinite Planning Period, Management Science, Vol. 18, No. 4, Parsons, R.J. (1966), Multiproduct Lot Size Determination When Certain Restrictions are Active, Journal of Industrial Engineering, Vol. 17, No. 7, Sykes, J.S. (1970), Simplified Analysis of an Alternating Priority Queueing Model with Setup Times, Operations Research, Vol. 18,

13 51 An EPQ Model for Multi-Product with Setup Times 1)Sung-Chul Kim* In this paper, we developed an EPQ model for multi-product applying cycle time. Products are produced by a single machine based on cycle policy and we considered both the setup costs and setup times. The results can be easily understood and implemented. Keywords: production planning, economic order quantity, cycle policy, setup cost, setup time, cycle time *Professor, Department of Business Administration, Duksung Women s University, Seoul

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Buy one get one with discount Promotional Strategy Kyong-Kuk Kim, Chi-Ghun Lee and Sunggyun Park ISysE Department, FEG 002079 Contents Introduction Literature Review Model Solution Further research 2 ISysE