Operations Research Letters最新文献

The change-making problem (CMP), introduced in 1970, is a classic problem in combinatorial optimisation. It was proven to be NP-hard in 1975, but it can be solved in pseudo-polynomial time by dynamic programming. In 1999, Heipcke presented a variant of the CMP which, at first glance, looks harder than the standard version. We show that, in fact, her variant can be solved in polynomial time.

We consider a lift-and-project approach for the cardinality-constrained Boolean quadric polytope. Some upper bounds for the distance between the polytope and its linear approximation are derived. Unsurprisingly, the distance converges to 0 when the number of variables increases sufficiently.

The principle of optimality is a fundamental aspect of dynamic programming, which states that the optimal solution to a dynamic optimization problem can be found by combining the optimal solutions to its sub-problems. While this principle is generally applicable, it is often only taught for problems with finite or countable state spaces in order to sidestep measure-theoretic complexities. Therefore, it cannot be applied to classic models such as inventory management and dynamic pricing models that have continuous state spaces, and students may not be aware of the possible challenges involved in studying dynamic programming models with general state spaces. To address this, we provide conditions and a self-contained simple proof that establish when the principle of optimality for discounted dynamic programming is valid. These conditions shed light on the difficulties that may arise in the general state space case. We provide examples from the literature that include the relatively involved case of universally measurable dynamic programming and the simple case of finite dynamic programming where our main result can be applied to show that the principle of optimality holds.

This paper studies independent retailers who can cooperate with transshipments. It is the first to prove that retailers can maximize their profits with no proactive transshipments by deploying only reactive transshipments, if and only if reactive transshipment prices are endogenous. Retailers seek mutually acceptable prices for reactive transshipments. A time and inventory-dependent price interval, if non-empty, includes all of the coordinating reactive transshipment prices that yield the centralized profit; if empty, reactive transshipment is unacceptable for one of the retailers.

We study a multilocation inventory system with unknown demand distribution using a nonparametric approach. The system consists of multiple distribution centers and customer locations, where products are shipped from the distribution centers to fulfill customer demands. We propose a novel algorithm, DMLI, for adaptive inventory management. Under specific conditions, we establish that the average expected T-period regret of DMLI converges to the optimal rate of $O(1/\sqrt{T})$.

We examine a technology firm's licensing choices, with or without a platform intermediary, in a market with two competing manufacturers. We analyze how market conditions influence the technology firm's decision, considering its ability to enhance product quality and network effects. We find that licensing through the platform intermediary is beneficial across a wider range of network effects when the gap in the manufacturers' capabilities narrows. Furthermore, this approach enables higher profitability with less effort in certain market conditions.

This paper addresses the challenge of integrating the compatibility criterion between candidates into the committee selection process under scoring rules. The compatibility between candidates is considered by assigning each committee a vector of weights based on this criterion. The goal is to choose a committee by taking into account both the compatibility between candidates and their performance based on scores. To achieve this, the paper defines a continuous weighted scoring function characterized by two crucial properties: linearity and independence of zero-weight members.

This paper investigates a bounded mixed batch scheduling problem with job release dates and rejection. The machine processes a batch containing several jobs that their number does not exceed the machine capacity. For the case with a certain release date, we present a polynomial-time exact algorithm. For the case with a constant number of release dates, a pseudo-polynomial-time exact algorithm is proposed. For the general problem, we provide a 2-approximation algorithm and a polynomial-time approximation scheme.

The primal separation problem for $\{0,1/2\}$-cuts is: Given a vertex $\hat{x}$ of the integer hull of a polytope P and some fractional point $x^{⁎}\in P$, does there exist a $\{0,1/2\}$-cut that is tight at $\hat{x}$ and violated by $x^{⁎}$? We present two cases for which primal separation is solvable in polynomial time. Furthermore, we show that the optimization problem over the $\{0,1/2\}$-closure can be solved in polynomial time up to a factor $(1+\epsilon )$, for any fixed $\epsilon >0$.

We derive error bounds for two-dimensional expected value functions that depend on the Vitali variation of the joint probability density function of the corresponding random vector. Contrary to bounds from the literature, our bounds are not restricted to underlying functions that are one-dimensional and periodic. In our proof, we first derive the bounds in a discrete setting, which requires us to characterize the extreme points of the set of all matrices that have zero-sum rows and columns and have an $L_1$-norm bounded by one. This result may be of independent interest.