A variant of \(L^{\natural}\)-convexity and its application to inventory models with batch ordering. (English) Zbl 1308.90005
Summary: Previous studies show that the concept of \(L^\natural\)-convexity. is helpful in characterizing the optimal policy for some inventory models with positive leadtimes. Such examples include the lost-sales inventory model by P. Zipkin [Oper. Res. 56, No. 4, 937–944 (2008; Zbl 1167.90369)]. On the structure of lost-sales inventory models and the inventory-pricing model by Z. Pang et al. [Oper. Res. 60, No. 3, 581–587 (2012; Zbl 1260.90023)]. However, when taking batch ordering into account, \(L^\natural\)-convexity does not work anymore.
In this paper, we extend \(L^\natural\)-convexity to a more general concept termed as \(Q\)-jump-\(L^\natural\)-convexity and apply it to batch ordering inventory models including a lost-sales inventory model and an inventory-pricing model with batch ordering and positive leadtimes. By utilizing this new concept, we can partially characterize the structure of the optimal policies for both the models. Moreover, we are able to evaluate the sensitivity of the optimal decisions with respect to system states.
In this paper, we extend \(L^\natural\)-convexity to a more general concept termed as \(Q\)-jump-\(L^\natural\)-convexity and apply it to batch ordering inventory models including a lost-sales inventory model and an inventory-pricing model with batch ordering and positive leadtimes. By utilizing this new concept, we can partially characterize the structure of the optimal policies for both the models. Moreover, we are able to evaluate the sensitivity of the optimal decisions with respect to system states.
MSC:
| 90B05 | Inventory, storage, reservoirs |
| 91B25 | Asset pricing models (MSC2010) |
| 52A40 | Inequalities and extremum problems involving convexity in convex geometry |
| 52C07 | Lattices and convex bodies in \(n\) dimensions (aspects of discrete geometry) |
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