, 40 12 (2006 6) 1) *.. I. (batch). (production planning). (downstream stage) (stockout).... (endangered). (utilization). *
40, 40 12 (EPQ; economic production quantity). (setup cost) (setup time) Bradley Conway(2003). 1980 (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).. 2. 32. 4. 5.
41 II. 1 2. 1 2. 2 1 (idle)., = 1, 2(demand rate), (production rate), 1 2,, 2 1,...,,. = =, (2.1) = =, = 1, 2. (2.2),,, = + + +..
42, 40 12,. Min. = + + + = + + + s.t. + + + 1 =. (2.3) (2.3). + 1... Min. = + +. (2.4) 1 (2.4) 2(second derivative) (2.4) (convex). (2.3)
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)
44, 40 12 = + +, =. (2.8) (2.8). 1 2.., = 1, 2. = = =,. (2.9) (2.1). =, = 1, 2. (2.10) (2.10). (2.5) (2.3) (2.10)
45.. 1 2.. step1: (2.5). + + + 1 =, = + + + 1 step2. step2: (2.10). =, =. 1 2. (upper bound) (lower bound). III. 1,,., = 1,,,,,,..,,. 2.
46, 40 12 = =, (3.1) = =, = 1,,. (3.2). Min. = { + } s.t. { + } 1 =, = 2,,. (3.3) (3.3). Min. = +. (3.4) (3.4), =1,,. =, =. (3.5)
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...
48, 40 12 (Di) (Pi) (hi) (Ci) 1 10,000 25,000 10 20 2 5,000 10,000 20 15. (Si) 1 (Qi*) (K) 1 2 3 1 1/600 252.26 0.9991 2 1/1200 126.13 1 1/600 333.33 1.0321 2 1/600 166.67 1 1/400 375.0 1.0487 2 1/800 187.5 2774.89 2883.33 2995.83 1(2.3) (2.5). 0.0009 2774.89. 2 3(2.3) (2.11) 0. 2 2993.33, 3 2995.83. (2.8), (2.10), (2.11) 1, 2, 3,. 258.2, =122.5, 2773.94 2774.89. 5..
49 (Di) (Pi) (hi) (Ci) 1 1,000 5,000 30 50 2 200 2,000 50 100 3 500 2,500 20 40 4 2,000 10,000 10 20 5 400 4,000 30 30 (3.3). (Si) 1 (Qi*) 1 0.002 90.8153 2 0.005 18.1631 1 3 0.003 0.9982 45.4077 5775.85 4 0.007 181.6306 5 0.001 36.3261 1 0.003 110 2 0.006 22 2 3 0.004 1.0422 55 5910.82 4 0.008 220 5 0.001 44 1(3.3) (3.5) 0.0018. 2(3.3) (3.9).
50, 40 12 V... Avi-Itzhak, B, W.L. Maxwell, and L.W. Miller (1965), Queueing with Alternating Priorities, Operations Research, Vol. 14, 306-318. Bradley, J.R. and R.W. Conway (2003), Managing Cyclic Inventories, Production and Operations Management, Vol. 12, No. 4, 464-479. 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, 50-55. Eisenberg, M. (1971), Two Queues with Changeover Times, Operations Research, Vol. 17, 386-401. Elmaghraby, S. (1978), The Economic Lot Scheduling Problem (ELSP): Review and Extensions, Management Science, vol. 24, No. 6, 587-598. Haessler, F. (1971), A note on Scheduling a Multi-Product Single-Machine System for an Infinite Planning Period, Management Science, Vol. 18, No. 4, 240-241. Parsons, R.J. (1966), Multiproduct Lot Size Determination When Certain Restrictions are Active, Journal of Industrial Engineering, Vol. 17, No. 7, 360-363. Sykes, J.S. (1970), Simplified Analysis of an Alternating Priority Queueing Model with Setup Times, Operations Research, Vol. 18, 1182-1192.
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