A compact arc-based ILP formulation for the pickup and delivery problem with divisible pickups and deliveries

We consider the capacitated single vehicle one-to-one pickup and delivery problem with divisible pickups and deliveries (PDPDPD). In this problem, we do not make the standard assumption of one-to-one pickup and delivery problems that each location has only one transportation request. Instead we assume there are multiple requests per location that may be performed individually. This may result in multiple visits to a location. We provide a new compact arc-based ILP formulation for the PDPDPD by deriving time-consistency constraints that identify the order in which selected outgoing arcs from a node are actually traversed. The formulation can also easily be applied to the one-to-one PDP by restricting the number of times that a node can be visited. Numerical results on standard one-to-one PDP test instances from the literature show that our compact formulation is almost competitive with tailor-made solution methods for the one-to-one PDP. Moreover, we observe that significant cost savings up to 15% on average may be obtained by allowing divisible pickups and deliveries in one-to-one PDPs. It turns out that divisible pickups and deliveries are not only beneficial when the vehicle capacity is small, but also when this capacity is unrestrictive

Linear conic programming: genericity and stability

In het lineair conisch programmeren maximalizeren of minimalizeren we een lineaire functie over de intersectie van een affiene ruimte en een convexe kegel. Het conisch programmeren bevat lineaire programmeringsproblemen, semidefiniete programmeringsproblemen en copositieve programmeringsproblemen als subklassen. In deze thesis bestuderen we genericiteit en stabiliteit van eigenschappen van conische programmeringsproblemen. We noemen een eigenschap zwak generiek wanneer de eigenschap geldt voor bijna alle gevallen van een probleem. Numeriek gezien is stabiliteit wenselijk. Een eigenschap wordt beschouwd als zijnde stabiel voor een een specifiek geval van een probleem wanneer deze geldt ook bij kleine veranderingen van de data behorende bij dit geval. In deze thesis laten we zien dat de Slater condities zwak generiek en stabiel zijn. Het is bekend dat uniekheid van de optimale oplossing, niet-ontaardheid en strikte complementariteit zwak generiek zijn voor het conisch programmeren. We onderzoeken de stabiliteit van deze zwak generieke eigenschappen. Voor semidefiniete programmeringsproblemen laten we zien dat al deze zwak generieke eigenschappen stabiel zijn. Een andere interessante eigenschap is de orde van maximizers. Geometrisch is het gerelateerd aan de kromming van de toelaatbare verzameling rondom de oplossing. We karakteriseren eerste orde maximimale oplossingen in het conisch programmeren en geven noodzakelijke en voldoende voorwaarden voor hun stabiliteit. In het laatste deel van deze thesis beschouwen we copositieve problemen en enkele specifieke gevallen waar copositiviteit van een matrix efficiënt kan worden vastgesteld. In het bijzonder bewijzen we dat een matrix met exact één positieve eigenwaarde copositief is dan en slechts dan wanneer het een niet-negatieve matrix is

Dynamic Batching for Order Picking in Warehouses

Dynamic batch picking is characterized by combining product demand from multiple customer orders into one pick tour where new orders are continuously received. Using modern order-picking aids, updated picking instructions can be included in the current pick tours which allows pickers to be re-routed to pick for new orders even when they already started a pick tour. We develop a mathematical model for dynamic batch picking that minimizes the order throughput time of incoming customer orders. In case of new order arrivals, we can quickly re-optimize the model and determine new updated pick tours. This allows for short order throughput times and ensures that warehouse companies can set their order cut-off times as late as possible while still guaranteeing that orders can be delivered next day or in some cases even the same day

Coordinating technician allocation and maintenance routing for offshore wind farms

A maintenance activity at offshore wind farms requires a combination of technicians with different skills. At an operational level, it is important to fully utilize and coordinate technicians in order to increase efficiency of the short-term maintenance planning. In this paper, we investigate sharing of technicians between wind farms over multiple periods, while determining per period vessel routes for delivering and picking up technicians. The problem can be considered as a novel variant of the multi-period multi-commodity pick up and delivery problem. We develop an adaptive large neighborhood search heuristic which achieves high-quality, and often optimal, solutions on benchmark instances from the literature. The heuristic is used to explore the benefits of different sharing policies. By sharing technicians, both the flexibility of the daily planning is improved and the expected maintenance costs are reduced. In addition, the increased flexibility results in fewer vessel trips and increases the decision maker’s ability to cope with extreme scenarios encountered in the short-term maintenance planning

The effect of portable HEPA filter air cleaners on indoor PM2.5 concentrations and second hand tobacco smoke exposure among pregnant women in Ulaanbaatar, Mongolia: The UGAAR randomized controlled trial

Background Portable HEPA filter air cleaners can reduce indoor fine particulate matter (PM2.5), but their use has not been adequately evaluated in high pollution settings. We assessed air cleaner effectiveness in reducing indoor residential PM2.5 and second hand smoke (SHS) exposures among non-smoking pregnant women in Ulaanbaatar, Mongolia. Methods We randomized 540 participants to an intervention group receiving 1 or 2 HEPA filter air cleaners or a control group receiving no air cleaners. We followed 259 intervention and 253 control participants to the end of pregnancy. We measured one-week indoor residential PM2.5 concentrations in early (~11weeks gestation) and late (~31weeks gestation) pregnancy and collected outdoor PM2.5 data from centrally-located government monitors. We assessed blood cadmium in late pregnancy. Hair nicotine was quantified in a subset (n=125) to evaluate blood cadmium as a biomarker of SHS exposure. We evaluated air cleaner effectiveness using mixed effects and multiple linear regression models and used stratified models and interaction terms to evaluate potential modifiers of effectiveness. Results The overall geometric mean (GM) one-week outdoor PM2.5 concentration was 47.9?g/m3 (95% CI: 44.6, 51.6?g/m3), with highest concentrations in winter (118.0?g/m3; 110.4, 126.2?g/m3). One-week indoor and outdoor PM2.5 concentrations were correlated (r=0.69). Indoor PM2.5 concentrations were 29% (21, 37%) lower in intervention versus control apartments, with GMs of 17.3?g/m3 (15.8, 18.8?g/m3) and 24.5?g/m3 (22.2, 27.0?g/m3), respectively. Air cleaner effectiveness was greater when air cleaners were first deployed (40%; 31, 48%) than after approximately five months of use (15%; 0, 27%). Blood cadmium concentrations were 14% (4, 23%) lower among intervention participants, likely due to reduced SHS exposure. Conclusions Portable HEPA filter air cleaners can lower indoor PM2.5 concentrations and SHS exposures in highly polluted settings.Canadian Institute of Health Research (MOP 142380)Simon Fraser University, Faculty of Health Sciences (Mowafaghian Child Health Faculty Award

Genericity Results in Linear Conic Programming-A Tour d'Horizon

This paper is concerned with so-called generic properties of general linear conic programs. Many results have been obtained on this subject during the last two decades. For example, it is known that uniqueness, strict complementarity, and nondegeneracy of optimal solutions hold for almost all problem instances. Strong duality holds generically in a stronger sense, i.e., it holds for a generic subset of problem instances. In this paper, we survey known results and present new ones. In particular we give an easy proof of the fact that Slater’s condition holds generically in linear conic programming. We further discuss the problem of stability of uniqueness, nondegeneracy, and strict complementarity. We also comment on the fact that in general, a conic program cannot be treated as a smooth problem and that techniques from nonsmooth geometric measure theory are needed

A note on strict complementarity for the doubly non-negative cone

In this paper, we consider a closed convex cone given by the intersection of two cones and . We study faces and complementary faces of in terms of and . Based on complementary faces, the tangent spaces of can be characterized as well. Moreover, many numerical methods assume regularity conditions such as strict complementarity. We provide necessary and sufficient conditions for strict complementarity for the cone . All these results can be applied to the doubly non-negative cone. Finally, a numerically efficient procedure for checking strict complementarity of for the doubly non-negative cone is provided when X has exactly one zero eigenvalue

First order solutions in conic programming

We study the order of maximizers in linear conic programming (CP) as well as stability issues related to this. We do this by taking a semi-infinite view on conic programs: a linear conic problem can be formulated as a special instance of a linear semi-infinite program (SIP), for which characterizations of the stability of first order maximizers are well-known. However, conic problems are highly special SIPs, and therefore these general SIP-results are not valid for CP. We discuss the differences between CP and general SIP concerning the structure and results for stability of first order maximizers, and we present necessary and sufficient conditions for the stability of first order maximizers in CP

Dynamic Batching for Order Picking in Warehouses

Poster 2