X-Y Band and Modified ( s, S ) Policy

Chen Shaoxiang and M. Lambrecht
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Chen Shaoxiang: Department of Applied Economic Sciences, K. U. Leuven, Belgium
M. Lambrecht: Department of Applied Economic Sciences, K. U. Leuven, Belgium

Operations Research, 1996, vol. 44, issue 6, 1013-1019

Abstract: This paper considers the stochastic, single-item, periodic review inventory problem. Most importantly we assume a finite production capacity per period and a production cost function containing a fixed (as well as a variable) component. With stationary data, a convex expected holding and shortage cost function, we show that generally the modified ( s , S ) policy is not optimal to the finite horizon problems. The optimal policy does, however, show a systematic pattern which we call the X-Y band structure. This X-Y band policy is interpreted as follows: whenever the inventory level drops below X , order up to capacity; when the inventory level is above Y , do nothing; if the inventory level is between X and Y , however, the ordering pattern is different from problem to problem. Although the X and Y bounds may change from period to period, we prove the existence of a pair of finite X and Y values that can apply for all the periods (i.e., bounds on individual bounds). One calculation for such X and Y bounds that are tight in some cases is also provided. By exploring the X-Y band structure, we can drastically reduce the computation effort for finding the optimal policies.

Keywords: inventory/production; policies; review/lead times; production/scheduling; planning; dynamic programming/optimal control; Markov infinite slate (search for similar items in EconPapers)
Date: 1996
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Citations: View citations in EconPapers (21)

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