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Sales promotions are important in the fast-moving consumer goods (FMCG) industry due to the significant spending on promotions and the fact that a large proportion of FMCG products are sold on promotion. This paper considers the problem of planning sales promotions for an FMCG product in a grocery retail setting. The category manager has to solve the promotion optimization problem (POP) for each product, i.e., how to select a posted price for each period in a finite horizon so as to maximize the retailer’s profit. Through our collaboration with Oracle Retail, we developed an optimization formulation for the POP that can be used by category managers in a grocery environment. Our formulation incorporates business rules that are relevant, in practice. We propose general classes of demand functions (including multiplicative and additive), which incorporate the post-promotion dip effect, and can be estimated from sales data. In general, the POP formulation has a nonlinear objective and is NP-hard. We then propose a linear integer programming (IP) approximation of the POP. We show that the IP has an integral feasible region, and hence can be solved efficiently as a linear program (LP). We develop performance guarantees for the profit of the LP solution relative to the optimal profit. Using sales data from a grocery retailer, we first show that our demand models can be estimated with high accuracy, and then demonstrate that using the LP promotion schedule could potentially increase the profit by 3%, with a potential profit increase of 5% if some business constraints were to be relaxed. The online appendix is available at https://doi.org/10.1287/opre.2016.1573

Abstract. We propose the DISCO algorithm for graph realization in R d , given sparse and noisy short-range inter-vertex distances as inputs. Our divide-and-conquer algorithm works as follows. When a group has a sufficiently small number of vertices, the basis step is to form a graph realization by solving a semidefinite program. The recursive step is to break a large group of vertices into two smaller groups with overlapping vertices. These two groups are solved recursively, and the sub-configurations are stitched together, using the overlapping atoms, to form a configurations for the larger group. At intermediate stages, the configurations are improved by gradient descent refinement. The algorithm is applied to the problem of determining protein molecule structure. Tests are performed on molecules taken from the Protein Data Bank database. Given 20-30% of the interatom distances less than 6Å that are corrupted by a high level of noise, DISCO is able to reliably and efficiently reconstruct the conformation of large molecules. In particular, given 30% of distances with 20% multiplicative noise, a 13000-atom conformation problem is solved within an hour with an RMSD of 1.6Å. Introduction.A graph realization problem is to assign coordinates to vertices in a graph, with the restriction that distances between certain pairs of vertices are specified to lie in given intervals. Two practical instances of the graph realization problem are the molecular conformation and sensor network localization problems.The molecular conformation problem is to determine the structure of a protein molecule based on pairwise distances between atoms. Determining protein conformations is central to biology, because knowledge of the protein structure aids in the understanding of protein functions, which would lead to further applications in pharmaceutical and medicine. In this problem, the distance constraints are obtained from knowledge of the sequence of constituent amino acids; minimum separation distances (MSDs) derived from van der Waals interactions; and nuclear magnetic resonance (NMR) spectroscopy experiments. We take note of two important characteristics of molecular conformation problems: the number of atoms may go up to tens of thousands, and the distance data may be very sparse and highly noisy.The sensor network localization problem is to determine the location of wireless sensors in a network. In this problem, there are two classes of objects: anchors (whose locations are known a priori) and sensors (whose locations are unknown and to be determined). In practical situations, the anchors and sensors are able to communicate with one another, if they are not too far apart (say within radio range), to estimate the distance between them.While the two problems are very similar, the key difference between molecular conformation and sensor network localization is that the former is anchor-free, whereas in the latter the positions of the anchor nodes are known a priori.Recently, semidefinite programming (SDP) relaxation techniques have...

In many low‐ and middle‐income countries, including Zambia, stockouts of life‐saving medicines threaten the advancement of the Sustainable Development Goals (SDGs); it is therefore vital to reduce stockouts through the use of improved inventory control policies. The associated medicine distribution problem is challenging because it involves seasonality and uncertainty in both demand and lead times, heterogeneous delivery locations, and lost demand. Besides service level and inventory costs, equity across delivery locations must also be considered. This empirical study is based on an independently validated simulation model constructed from extensive field data, and addresses the lack of rigorous recommendations of inventory policies in this context. It compares the current base‐stock and other policies proposed in the practitioner's literature with an optimization‐based policy adapted from research on industrial settings. Although the optimization‐based policy may need more implementation efforts, it generally outperforms the other evaluated policies. Our results also suggest that the prevalent proportional inventory rationing rules may lead to substantial service level discrepancies between facilities. Finally, the performance metrics of service level and distribution equity can be at odds, prompting non‐trivial design trade‐offs and considerations. This work motivated the development of a digital distribution information system involving smartphones with barcode scanners deployed in 60 health centers, posts, and district hospitals in Zambia until 2018.

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