A parametric integer programming algorithm for bilevel mixed integer programs

We consider discrete bilevel optimization problems where the follower solves an integer program with a fixed number of variables. Using recent results in parametric integer programming, we present polynomial time algorithms for pure and mixed integer bilevel problems. For the mixed integer case where the leader's variables are continuous, our algorithm also detects whether the infimum cost fails to be attained, a difficulty that has been identified but not directly addressed in the literature. In this case it yields a ``better than fully polynomial time'' approximation scheme with running time polynomial in the logarithm of the relative precision. For the pure integer case where the leader's variables are integer, and hence optimal solutions are guaranteed to exist, we present two algorithms which run in polynomial time when the total number of variables is fixed.Comment: 11 page

Establishing Nash equilibrium of the manufacturer-supplier game in supply chain management

We study a game model of multi-leader and one-follower in supply chain optimization where n suppliers compete to provide a single product for a manufacturer. We regard the selling price of each supplier as a pre-determined parameter and consider the case that suppliers compete on the basis of delivery frequency to the manufacturer. Each supplier’s profit depends not only on its own delivery frequency, but also on other suppliers’ frequencies through their impact on manufacturer’s purchase allocation to the suppliers. We first solve the follower’s (manufacturer’s) purchase allocation problem by deducing an explicit formula of its solution. We then formulate the n leaders’ (suppliers’) game as a generalized Nash game with shared constraints, which is theoretically difficult, but in our case could be solved numerically by converting to a regular variational inequality problem. For the special case that the selling prices of all suppliers are identical, we provide a sufficient and necessary condition for the existence and uniqueness of the Nash equilibrium. An explicit formula of the Nash equilibrium is obtained and its local uniqueness property is proved

Prevalence of Eimeria spp. infections and major histocompatibility complex class II DRA diversity in Mongolian Bactrian camels (Camelus bactrianus)

IntroductionThe two-humped Bactrian camel (Camelus bactrianus) is a large, even-toed ungulate native to the steppes of Central Asia. Domestic Bactrian camels are economically important in Mongolia and other Central Asian countries. These animals are used for transport, milk and meat production, and camel racing which is a great culture of nomads. Eimeriosis, also known as coccidiosis, is considered as an economically important parasitic diseases in Bactrian camels. There is still considerable lack of data concerning the spectrum of monoxenous Eimeria species, their epizootiology as well as their precise life cycles in Bactrian camels. This study was performed to determine the prevalence of Eimeria species in camelids from southern part of Mongolia.MethodsA total of 536 fresh camel fecal samples (n = 536) collected from herds located in five different Aimags (provinces) of Mongolia were examined. Eimeria spp. oocysts were isolated using the sugar flotation technique, and after sporulation, oocysts were identified by morphometric evaluation.ResultsWe identified the most common Eimeria species infecting Mongolian Bactrian camels: Eimeria cameli (22.3%), Eimeria rajasthani (37.3%) and Eimeria dromedarii (27.7%). Interestingly, mixed infections were detected in 24.8% (n = 133) of the samples, while 39.0% (n = 209) were negative for coccidian stages. To investigate the immunogenetic response of the Mongolian Bactrian camels to Eimeria spp. infection, we screened the genetic diversity in a functional important immune response gene of the major histocompatibility complex (MHC). We detected two polymorphic sites in the MHC class II DRA exon 2, which translated into one non-synonymous and one synonymous amino acid (aa) change.DiscussionThe resulting aa alleles were not significantly associated with any of the three detected Eimeria species infections, nor could we show heterozygote advantage in non-infected Mongolian Bactrian camels. Further investigations on molecular epidemiology, in vitro culture, pathogenicity and host–parasite interactions will be necessary to better understand the impact of eimeriosis in Bactrian camels

A genetic algorithm for the one-dimensional cutting stock problem with setups

This paper investigates the one-dimensional cutting stock problem considering two conflicting objective functions: minimization of both the number of objects and the number of different cutting patterns used. A new heuristic method based on the concepts of genetic algorithms is proposed to solve the problem. This heuristic is empirically analyzed by solving randomly generated instances and also practical instances from a chemical-fiber company. The computational results show that the method is efficient and obtains positive results when compared to other methods from the literature. © 2014 Brazilian Operations Research Society