arXiv subjects

John E Beasley

Publications and source records attributed to John E Beasley.

7 recordsLinked to original sources

arXiv2026

Subset second-order stochastic dominance for enhanced indexation with diversification enforced by sector constraints

In this paper we apply second-order stochastic dominance (SSD) to the problem of enhanced indexation with asset subset (sector) constraints. The problem we consider is how to construct a portfolio that is designed to outperform a given market index whilst having regard to the proportion of the portfolio invested in distinct market sectors. In our approach, subset SSD, the portfolio associated with each sector is treated in a SSD manner. In other words in subset SSD we actively try to find sector portfolios that SSD dominate their respective sector indices. However the proportion of the overall portfolio invested in each sector is not pre-specified, rather it is decided via optimisation. Our subset SSD approach involves the numeric solution of a multivariate second-order stochastic dominance problem. Computational results are given for our approach as applied to the S&P500 over the period 3rd October 2018 to 29th December 2023. This period, over 5 years, includes the Covid pandemic, which had a significant effect on stock prices. The S&P500 data that we have used is made publicly available for the benefit of future researchers. Our computational results indicate that the scaled version of our subset SSD approach outperforms the S&P500. Our approach also outperforms the standard SSD based approach to the problem. Our results show, that for the S&P500 data considered, including sector constraints improves out-of-sample performance, irrespective of the SSD approach adopted. Results are also given for Fama-French data involving 49 industry portfolios and these confirm the effectiveness of our subset SSD approach.

q-fin.CP↗

arXiv2026

Enhanced indexation using both equity assets and index options

In this paper we consider how we can include index options in enhanced indexation. We present the concept of an \enquote{option strategy} which enables us to treat options as an artificial asset. An option strategy for a known set of options is a specified set of rules which detail how these options are to be traded (i.e.~bought, rolled over, sold) depending upon market conditions. We consider option strategies in the context of enhanced indexation, but we discuss how they have much wider applicability in terms of portfolio optimisation. We use an enhanced indexation approach based on second-order stochastic dominance. We consider index options for the S\&P~500, using a dataset of daily stock prices over the period 2017-2025 that has been manually adjusted to account for survivorship bias. This dataset is made publicly available for use by future researchers. Our computational results indicate that introducing option strategies in an enhanced indexation setting offers clear benefits in terms of improved out-of-sample performance. This applies whether we use equities or an exchange-traded fund as part of the enhanced indexation portfolio.

q-fin.CP↗

arXiv2023

A heuristic for the non-unicost set covering problem using local branching

In this paper we present a heuristic for the non-unicost set covering problem using local branching. Local branching eliminates the need to define a problem specific search neighbourhood for any particular (zero-one) optimisation problem. It does this by incorporating a generalised Hamming distance neighbourhood into the problem, and this leads naturally to an appropriate neighbourhood search procedure. We apply our approach to the non-unicost set covering problem. Computational results are presented for 65 test problems that have been widely considered in the literature. Our results indicate that our heuristic is better than six of the eight other heuristics we examined, slightly worse than that of one heuristic, but that there is a single heuristic that out-performs all others. We believe that the work described here illustrates that the potential for using local branching, operating as a stand-alone matheuristic, has not been fully exploited in the literature.

math.OC↗

arXiv2023

A two stage approach for order and rack allocation with order backlog in a mobile rack environment

In this paper we investigate a problem associated with operating a robotic mobile fulfilment system (RMFS). This is the problem of allocating orders and mobile storage racks to pickers. We present a two-stage formulation of the problem. In our two-stage approach we, in the first-stage, deal with the orders which must be definitely fulfilled (picked), where the racks chosen to fulfil these first-stage orders are chosen so as to (collectively) contain sufficient product to satisfy all orders. In the second-stage we restrict attention to those racks chosen in the first-stage solution in terms of allocating second-stage orders. We present three different strategies for first-stage order selection; one of these strategies minimises the requirement to make decisions as to the rack sequence (i.e. the sequence in which racks are presented to each picker). We present a heuristic procedure to reduce the number of racks that need to be considered. Extensive computational results are presented for test problems that are made publicly available; including test problems that are significantly larger than previous problems considered in the literature.

math.OC↗

arXiv2020

Order allocation, rack allocation and rack sequencing for pickers in a mobile rack environment

In this paper we investigate the problem of simultaneously allocating orders and mobile storage racks to static pickers. Here storage racks are allocated to pickers to enable them to pick all of the products for the orders that have been allocated to them. Problems of the type considered here arise in facilities operating as robotic mobile fulfilment systems. We present a formulation of the problem of allocating orders and racks to pickers as an integer program and discuss the complexity of the problem. We present two heuristics (matheuristics) for the problem, one using partial integer optimisation, that are directly based upon our formulation. We also consider the problem of how to sequence the racks for presentation at each individual picker and formulate this problem as an integer program. We prove that, subject to certain conditions being satisfied, a feasible rack sequence for all orders can be produced by focusing on just a subset of the orders to be dealt with by the picker. Computational results are presented, both for order and rack allocation, and for rack sequencing, for randomly generated test problems (that are made publicly available) involving up to 500 products, 150 orders, 150 racks and 10 pickers.

math.OC↗

arXiv2020

Order batching using an approximation for the distance travelled by pickers

In this paper we investigate the problem of order batching for picker routing. Our approach is applicable to warehouses (storage areas) arranged in the standard rectangular grid layout, so with parallel aisles and two or more cross-aisles. The motivation underlying our work is online grocery shopping in which orders may be composed of dozens of items. The approach presented directly addresses order batching, but uses a distance approximation to influence the batching of orders without directly addressing the routing problem. We present a basic formulation based on deciding the orders to be batched together so as to optimise an objective that approximates the picker routing distance travelled. We extend our formulation by improving the approximation for cases where we have more than one block in the warehouse. We present constraints to remove symmetry in order to lessen the computational effort required, as well as constraints that significantly improve the value of the linear programming relaxation of our formulation. A heuristic algorithm based on partial integer optimisation of our mathematical formulation is also presented. Once order batching has been decided we optimally route each individual picker using a previous approach presented in the literature. Extensive computational results for publicly available test problems involving up to 75 orders are given for both single and multiple block warehouse configurations.

math.OC↗

arXiv2017

Optimally solving the joint order batching and picker routing problem

In this work we investigate the problem of order batching and picker routing in storage areas. These are labour and capital intensive problems, often responsible for a substantial share of warehouse operating costs. In particular, we consider the case of online grocery shopping in which orders may be composed of dozens of items. We present a formulation for the problem based on an exponential number of connectivity constraints and we introduce a significant number of valid inequalities based on the standard layout of warehouses, composed of parallel aisles and two or more cross-aisles. The proposed inequalities are highly effective and greatly improve computational results. Instances involving up to 20 orders are solved to proven optimality when we jointly consider order batching and picker routing. Instances involving up to 5000 orders are considered where order batching is done heuristically, but picker routing is done optimally.

math.OC↗