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The EOQ repair and waste disposal model with variable setup numbers. (English) Zbl 0947.90035
Summary: In a previous paper the author discussed an EOQ-model in which the stationary demand can be satisfied by newly made products and by repaired used products. In the modelled situation some share of the used products is collected and later repaired; the other products are disposed outside according to some waste disposal rate. In the present paper this model is extended to the case of variable setup numbers \(n\) and \(m\) for production and repair within some collection time interval. First, for a fixed waste disposal rate the cost optimal setup numbers and the minimum cost are determined. Secondly, the minimum cost is analysed as a function of this rate and it is shown to be convex for small and medium waste disposal rates and to be concave for large rates. Thirdly, the existence and generation of cost optimal waste disposal rates are discussed.

90B25 Reliability, availability, maintenance, inspection in operations research
Full Text: DOI
[1] Cho, D.J.; Parlar, M., A survey of maintenance models for mult-unit systems, European journal of operational research, 51, 1-23, (1991)
[2] Groenevelt, H.; Pintelon, L.; Seidmann, A., Production lot sizes with machine breakdowns, Management science, 38/1, 104-123, (1992) · Zbl 0759.90039
[3] Fandel, G., Effects of call-forward delivery systems on suppliers seriel per unit cost, (), 66-84
[4] Hahm, J.; Yano, C.A., The economic lot and delivery scheduling problem: the single item case, International journal of production economics, 28, 235-252, (1992)
[5] Heyman, D.P., Optimal disposal policies for a single-item inventory system with returns, Naval research logistics quarterly, 24, 385-405, (1977) · Zbl 0371.90034
[6] Hofmann, C., Abstimmung von produktions- und transportlosgrößen zwischen zulieferer und produzent. eine analyse auf der grundlage stationärer losgrößenmodelle, OR spektrum, 16/1, 9-20, (1994) · Zbl 0800.90391
[7] Kelle, P.; Silver, E.A., Purchasing policy of new containers considering the random returns of previously issued containers, IIE transactions, 21/4, 349-354, (1989)
[8] van der Laan, E.A., On inventory control models where items are remanufactured or disposed, (1993), Erasmus Universiteit Rotterdam, unpublished Master’s Thesis
[9] Muckstadt, J.A.; Isaac, M.H., An analysis of single item inventory systems with returns, Naval research logistics quarterly, 28, 237-254, (1981) · Zbl 0462.90021
[10] Müller-Merbach, H., Optimale losgrößen bei mehrstufiger fertigung, Zeitschrift wirtschaftliche fertigung, 60, 113-118, (1965)
[11] Mabini, M.C.; Pintelon, L.M.; Gelders, L.F., EOQ type formulations for controlling repairable inventories, International journal of production economics, 28, 21-33, (1992)
[12] Nahmias, S.; Rivera, H., A deterministic model for a repairable item inventory system with a finite repair rate, International journal of production research, 17, 215-221, (1979)
[13] Nahmias, S., Managing repairable inventory systems: A review, TIMS studies in management science, 16, 253-277, (1981)
[14] Porteus, E.L., Optimal lot sizing, process quality improvement and setup cost reduction, Operations research, 34/1, 137-144, (1986) · Zbl 0591.90043
[15] Porteus, E.L., Investing in new parameter values in the discounted EOQ model, Naval research logistics quarterly, 33, 39-48, (1986) · Zbl 0651.90016
[16] Richter, K., “An EOQ repair and waste disposal model”, in: Pre-prints of the Eighth International Working Seminar on Production Economics, Innsbruck 1994, Vol. 3, 83-91.
[17] Schrady, D.A., A deterministic inventory model for repairable items, Naval research logistics quarterly, 14/3, 391-398, (1967)
[18] Stadtler, H., Optimale lospolitiken für eine leichtmetallgießerei, OR spektrum, 14, 217-227, (1992)
[19] Simpson, V.P., Optimal solution structure for a repairable inventory problem, Operations research, 26, 270-281, (1978) · Zbl 0377.90040
[20] Taha, H.A.; Skeith, R.W., The economic lot sizes in multistage production systems, AIIE transactions, 2, 157-162, (1970)
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