Proportionate flow shop: New complexity results and models with due date assignment

It is known that the proportionate flow shop minimum makespan $Fm/prpt/C_{\max }$ problem is solved optimally by any permutation job sequence. We show that the $Fm/prpt/C_{\max }$ problem is at least ordinary NP‐hard when missing operations are allowed and present some solvable cases. We then consider the standard proportionate flow shop problem (with no missing operations) and show that the solution algorithms for a class of single‐machine due date assignment problems can be extended/generalized to the corresponding proportionate flow shop problems. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 98–106, 2015     

The joint signature of coherent systems

We investigate the joint signature of $m$ coherent systems, under the assumption that the components have independent and identically distributed lifetimes. The joint signature, for a particular ordering of failure times, is an $m$‐dimensional matrix depending solely on the composition of the systems and independent of the underlying distribution function of the component lifetimes. The elements of the $m$‐dimensional matrix are formulated based on the joint signatures of numerous series of parallel systems. The number of the joint signatures involved is an exponential function of the number of the minimal cut sets of each original system and may, therefore, be significantly large. We prove that although this number is typically large, a great number of the joint signatures are repeated, or removed by negative signs. We determine the maximum number of different joint signatures based on the number of systems and components. It is independent of the number of the minimal cut sets of each system and is polynomial in the number of components. Moreover, we consider all permutations of failure times and demonstrate that the results for one permutation can be of use for the others. Our theorems are applied to various examples. The main conclusion is that the joint signature can be computed much faster than expected.     

Technical note: Finite-time regret analysis of Kiefer-Wolfowitz stochastic approximation algorithm and nonparametric multi-product dynamic pricing with unknown demand

We consider the problem of nonparametric multi-product dynamic pricing with unknown demand and show that the problem may be formulated as an online model-free stochastic program, which can be solved by the classical Kiefer-Wolfowitz stochastic approximation (KWSA) algorithm. We prove that the expected cumulative regret of the KWSA algorithm is bounded above by where κ₁, κ₂ are positive constants and T is the number of periods for any T = 1, 2, … . Therefore, the regret of the KWSA algorithm grows in the order of , which achieves the lower bounds known for parametric dynamic pricing problems and shows that the nonparametric problems are not necessarily more difficult to solve than the parametric ones. Numerical experiments further demonstrate the effectiveness and efficiency of our proposed KW pricing policy by comparing with some pricing policies in the literature.     

Success and failures of the Gripen offsets in the Visegrad Group countries

The Soviet-led Council for Mutual Economic Assistance member, Central European countries found themselves in a difficult political and economic situation after the collapse of the Soviet Union. Three post-Eastern Bloc countries formed the Visegrad Group to strengthen their ties to the West, but the need for foreign investment, job creation and technology transfer was urgent.

This is when military modernisation also came into the picture and the counter-trade—as known as offset—as a tool to help these economies. A trade practice which was meant to energise these economies via defence acquisitions linked economic programmes.

Two Visegrad Group member countries, Hungary and the Czech Republic decided to sign offset agreement with the defence firm SAAB to license Gripen fighter aircrafts. This study intends to analyse if these deals were able to help governments to reach their objectives or the two countries were unable to take advantage of the offset programmes.     

Two-agent scheduling with linear resource-dependent processing times

This paper considers a two-agent scheduling problem with linear resource-dependent processing times, in which each agent has a set of jobs that compete with that of the other agent for the use of a common processing machine, and each agent aims to minimize the weighted number of its tardy jobs. To meet the due date requirements of the jobs of the two agents, additional amounts of a common resource, which may be in discrete or continuous quantities, can be allocated to the processing of the jobs to compress their processing durations. The actual processing time of a job is a linear function of the amount of the resource allocated to it. The objective is to determine the optimal job sequence and resource allocation strategy so as to minimize the weighted number of tardy jobs of one agent, while keeping the weighted number of tardy jobs of the other agent, and the total resource consumption cost within their respective predetermined limits. It is shown that the problem is -hard in the ordinary sense, and there does not exist a polynomial-time approximation algorithm with performance ratio unless ; however it admits a relaxed fully polynomial time approximation scheme. A proximal bundle algorithm based on Lagrangian relaxation is also presented to solve the problem approximately. To speed up convergence and produce sharp bounds, enhancement strategies including the design of a Tabu search algorithm and integration of a Lagrangian recovery heuristic into the algorithm are devised. Extensive numerical studies are conducted to assess the effectiveness and efficiency of the proposed algorithms.