Optimal Delivery Schedule Research Articles

Consecutive Daily Versus Every Other Day Stereotactic Body Radiation Therapy Scheduling for Stage I Non-small Cell Lung Cancer

The optimal delivery schedule for stereotactic body radiation therapy (SBRT) in treating stage I non-small cell lung cancer (NSCLC) is unknown. This study used the National Cancer Database to examine daily versus every other day (QOD) SBRT scheduling, including trends over time and association with survival. The National Cancer Database was used to retrospectively identify patients with stage I NSCLC treated with 3-, 4-, or 5-fraction of SBRT between 2004 and 2016. Survival analysis was performed using the Kaplan-Meier method and Cox regression modeling. Of 15,269 patients, 3927 (25.7%) received SBRT daily, and 11,342 (74.3%) received treatment QOD. The use of QOD treatment increased from 63.2% in 2007 to 78.3% in 2016, and 5-fraction SBRT increased from 3.7% in 2004 to 51.4% in 2016 (both P < .0001). QOD 5-fraction became the most prevalent scheduling from 2012 to 2016 (28.5% in 2012 to 41.6% in 2016). Factors significantly associated with daily SBRT scheduling included number of fractions, race, lower income, lower comorbidities, and treatment at academic/research programs (all P ≤ .01).Median survival for daily SBRT was 37.9 months versus 38.4 months for QOD (P = .4). On multivariable analysis, no difference was found in overall survival between daily versus QOD scheduling (adjusted hazard ratio [aHR], 0.99; 95% confidence interval [CI], 0.94-1.04; P = .55). Five-fraction SBRT was associated with worse survival versus 3 fractions (aHR, 1.09; 95% CI, 1.03-1.15; P = .002). With 3-fraction SBRT, QOD treatment was associated with improved survival versus daily treatment (aHR, 0.91; 95% CI, 0.84-0.98; P = .02). With 5-fraction SBRT, QOD treatment was associated with worse survival versus daily treatment (aHR, 1.11; 95% CI, 1.02-1.22; P = .02). QOD SBRT schedules were more frequently used to treat stage I NSCLC than daily regimens by a factor of 3:1, and QOD 5-fraction SBRT became the most common dose schedule after 2012. Three-fraction QOD SBRT was associated with improved survival versus daily, whereas 5-fraction QOD SBRT was associated with worse survival versus daily.

The generator distribution problem for base stations during emergency power outage: A branch-and-price-and-cut approach

Motivated by the need for uninterrupted service provision in the telecommunications industry, this paper presents a novel problem concerning the transportation of diesel generators during an unplanned power outage. Given a set of base stations, each equipped with a capacitated back-up battery pack, the problem consists in finding an optimal delivery and pick-up schedule that minimises corresponding costs. The problem is significantly complicated by the fact that the delivery quantity is a decision variable, and the pick-up times depend on the delivery time, delivery quantity and constraints related to battery-charging requirements. To address the issue, we develop problem-specific pick-up time functions that can be effectively incorporated into the proposed algorithm. The problem is formulated as an arc-based model and a set-packing model. To solve it to optimality, we design a tailored branch-and-price-and-cut algorithm, including novel customised dominance criteria in the labelling algorithm and adopting heuristics that exploit the problem features and effectively improve the algorithmic performance. The efficacy of the proposed algorithm is validated based on the extensive computational study and compared with a commercial solver. The proposed acceleration techniques are found to be potent with regard to computational times, and useful managerial insights are provided as part of sensitivity analyses.

Design for Optimally Routing and Scheduling a Tow Train for Just-in-Time Material Supply of Mixed-Model Assembly Lines

With the increase in product varieties, the combination of supermarkets and tow trains is being adopted by more automobile manufacturers for part feeding, especially in mixed-flow assembly lines. This paper focuses on the routing, scheduling, and loading problems of a single towed train that transports parts from one supermarket to the workstation buffer in a mixed-flow assembly line and aims to optimize the loading of the tow train, the optimal delivery schedule and route, and the appropriate departure time to minimize shipping and line inventory costs. To enable part feeding in line with the just-in-time (JIT) principle, a new mixed-integer mathematical model from nonlinearity to linearity and a novel artificial immune genetic algorithm-based heuristic are proposed. Both methods can provide reasonable solutions compared by minimizing the route length and inventory level in terms of speed, and the genetic algorithm shows better performance on a large scale.

Combining Unimanual and Bimanual Therapies for Children with Hemiparesis: Is There an Optimal Delivery Schedule?

Constraint-induced movement therapy (CIMT) and bimanual therapy (BT) are among the most effective hand therapies for children with unilateral cerebral palsy (uCP). Since they train different aspects of hand use, they likely have synergistic effects. The aim of this study was to examine the efficacy of different combinations of mCIMT and BT in an intensive occupational therapy program for children with uCP. Children (n = 35) participated in intensive modified CIMT (mCIMT) and BT, 6 weeks, 5 days/week, 6 h/day. During the first 2 weeks, children wore a mitt over the less-affected hand and engaged in functional and play activities with the affected hand. Starting in week 3, bimanual play and functional activities were added progressively, 1 hour/week. This intervention was compared to two different schedules of block interventions: (1) 3 weeks of mCIMT followed by 3 weeks of BT, and (2) 3 weeks of BT followed by 3 weeks of mCIMT. Hand function was tested before, after, and two months after therapy with the Assisting Hand Assessment (AHA), Pediatric Evaluation of Disability Inventory (PEDI), and Canadian Occupational Performance Measure (COPM). All three groups of children improved in functional independence (PEDI; p < 0.031), goal performance (COPM Performance; p < 0.0001) and satisfaction (COPM Satisfaction; p < 0.0001), which persisted two months post-intervention. All groups showed similar amounts of improvement, indicating that the delivery schedule for mCIMT and BT does not significantly impact the outcomes.

Optimizing the delivery schedule of equipment in a project environment considering resource leveling of storage space and its constraint: a case study

PurposeThe present work seeks to determine the optimal delivery schedule of equipment at a project site in the backdrop of limited storage space, at a minimum cost, and without disturbing the overall project schedule. In addition, the optimized delivery schedule helps in minimizing the fluctuating requirements of space at the project site across the entire project lifespan.Design/methodology/approachThe study is carried out at a Steel plant operating in a constrained space but undergoing a production capacity expansion. The problem motivated us to explore the possibility of postponing the delivery dates of certain equipment closer to the erection dates without compromising on the project schedule. Given the versatility of linear programming models in dealing with such schedule optimization problems, the authors formulated the above problem as a Zero-One Integer Linear Programming problem.FindingsThe model is implemented for all the new equipment arriving for two major units – the Hot Strip Mill (HSM) and the Blast Furnace (BF). It generates an optimized delivery schedule by delaying the delivery of some equipment by a certain number of periods, without compromising the overall project schedule and at a minimum storage cost. The average space utilization increases by 25.85 and 14.79% in HSM and BF units respectively. The fluctuations in space requirements are reduced substantially in both units.Originality/valueThe study shows a timeline in the form of a Gantt chart for the delivery of equipment, storage of equipment across different periods, and the number of periods for which the delivery of certain equipment needs to be postponed. The study uses linearly increasing storage costs with the increase in the number of periods for storage of the equipment in the temporary shed.HighlightsDetermined the optimal delivery schedule of the equipment in a project environment in the backdrop of limited storage space in the project site.Formulated the above problem as a Zero-One Integer Linear Programming (ILP) problem.The average space utilization has increased by 25.85 and 14.79% in HSM and BF units respectively.The optimized delivery schedule helps in reducing the fluctuations in space requirements substantially across the entire lifespan of the project.The timeline of delivery of equipment, storage of equipment across different periods and periods of postponement of the equipment are shown in the form of a Gantt Chart.

Extension of Particle Swarm Optimization algorithm for solving two-level time minimization transportation problem

A time minimization transportation problem deals with the resource efficiency to minimize time taken by the transport systems to deliver the commodity from sources to destinations. In this paper, a two-level time minimization transportation problem has been considered that categorizes the source–destination links into Level-I and Level-II with respect to the higher and lower level priority. The optimal delivery schedule of Level-I is followed up with the same for the Level-II cells. The paper proposes a solution procedure consisting of new algorithms that have been hybridized within the Particle Swarm Optimization to solve the problem making efficient use of resources. The solution procedure provides a methodical approach to the transport enterprises.This procedure does away with the rigid constraints, such as the location and number of non-zero allocations, required to be met by the traditional techniques of solving the transportation problem. The procedure generates pairs of Level-I and Level-II times at each iteration and the best pair(s) amongst these is/are marked out as the optimal solution of the problem. The solution procedure is explained through a numerical illustration.

The Saving Matrix Method for Improving Distribution Efficiency

The delivery route for the Bandung 40400 Mail Processing Center is determined based on the estimation using the zoning system, and this may trigger delays. This happens because of each vehicle can only deliver to one distribution center at a time. This makes the load factor level of vehicle utilization below 20%. This study aims to obtain the optimal route and delivery schedule to improve distribution efficiency and increase the load factor of vehicle capacity utilization. This quantitative research method uses the Saving Matrix algorithm on all distribution channels. The results obtained indicate that the optimal delivery routes are 5 to 6 cluster. This saves mileage of up to 144 km per route per day and saves distribution costs of up to Rp. 39,146.50 for one delivery. In addition, there was an increase in the load factor of 18.37% for dropping 1 and 16.49% for dropping 2. By using the proposed route, a resume of the delivery schedule is obtained with clearer departure and arrival times and saving times up to 275 minutes. Furthermore, the expansion of the scope of research and comparing the level of effectiveness between distribution centers in various regions can be carried out as a follow-up study.&#x0D; Keywords—Saving matrix algorithm; Delivery routes; Load factor; Scheduling

Rationale, design, and methods for the development of a youth adapted Brief Tobacco Intervention plus automated text messaging for high school students

BackgroundTobacco use is increasing among youth in the U.S. The current study seeks to develop and pilot test a universal group-based Youth Brief Tobacco Intervention (Y-BTI) plus mobile phone automated text messaging (ATM) for 9th grade students to both prevent initiation among non-users and promote cessation among current users. MethodsThis study will use a sequential, multi-method research design beginning with mixed methods formative work with 9th grade students to adapt the existing young adult Brief Tobacco Intervention (BTI) for youth and develop automated text messages. The formative work with students will identify salient themes and strategies for the interventions and optimal delivery schedules for the ATM intervention. The second phase of the study evaluates the Y-BTI and ATM through a pilot cluster randomized controlled trial that compares four treatment combinations: (1) Y-BTI + ATM, (2) Y-BTI alone, (3) ATM alone, or (4) standard of care. The Y-BTI is a single session, group-based intervention delivered in schools. The ATM intervention will provide comparable content to the Y-BTI but be delivered via text messaging 3–5 times per week for four weeks. ConclusionIn order to curb the rise of tobacco use among youth, interventions that are easily implemented and disseminated need to be developed. We aim to build upon previous research by showing that a universal group-based Y-BTI and ATM are effective in reducing tobacco use among a 9th graders by preventing initiation among tobacco naïve youth and promoting cessation among current users.

Simultaneous cooperation of Refrigerated Ground Vehicle (RGV) and Unmanned Aerial Vehicle (UAV) for rapid delivery with perishable food

With the growth of e-commerce, various types of last-mile delivery services have emerged to meet customer needs. Among the most notable of these are “rapid delivery” and “perishable food delivery” services. Owing to their advantages, the use of unmanned aerial vehicles (UAVs), which are both fast and inexpensive, has received considerable interest for rapid delivery. However, because of the inherent limitations of UAVs, they are used in conjunction with other ground vehicles. In contrast, maintaining freshness during delivery of perishable food is crucial for customer satisfaction and hygiene. Consequently, the cooperative operation of refrigerated ground vehicles (RGVs) with UAVs is necessary for rapid and fresh delivery services. RGVs can focus on the delivery of perishable foods and large-sized general products in such an operation, whereas UAVs can focus on small-sized general goods. In this study, the cooperative operation of RGVs and UAVs was investigated for the rapid delivery of perishable food. Mixed integer linear programming (MILP) was developed to derive optimal delivery schedules for RGVs and UAVs with the objective of minimizing the maximum service completion time of delivery vehicles. Additionally, an RGV-UAV route generating algorithm (R-U RGA) was presented to efficiently derive optimal, near-optimal, or qualified vehicle schedules when the MILP fails to derive optimal schedules in a reasonable time. The validity of the proposed MILP model was verified through a case study. The usefulness of the R-U RGA was confirmed through numerical experiments conducted on instances of various sizes. Additionally, numerical tests were performed to compare the benefits of the RGV-only delivery system and the proposed cooperative delivery system. These tests conducted in terms of economic, environmental, and service factors; they quantitatively elucidate the tradeoffs between the two systems.

Consecutive Daily vs. Every Other Day SBRT Scheduling for Stage I NSCLC

<h3>Purpose/Objective(s)</h3> The optimal delivery schedule for stereotactic body radiation therapy (SBRT) in treating Stage I non-small cell lung cancer (NSCLC) is unknown. This study utilized the National Cancer Database (NCDB) to examine daily vs. every other day (QOD) SBRT scheduling in the United States, including trends over time and association with survival. <h3>Materials/Methods</h3> The NCDB was used to identify patients with Stage I NSCLC treated with 3, 4, or 5 fraction SBRT between 2004-2016. Daily scheduling was defined as completing SBRT in 3, 4, or 5 days, respectively. QOD scheduling for 3, 4, and 5 fractions was defined as SBRT completion in 5-9, 8-12, and 10-14 days, respectively. Survival analysis was performed using the Kaplan-Meier method and Cox regression modeling. The multivariate model included age, gender, race, insurance status, median income, Charlson-Deyo comorbidity score, clinical T stage, histology, and facility type. <h3>Results</h3> Of 15,269 patients who met study criteria, 3,927 (25.7%) received SBRT daily, and 11,342 (74.3%) received treatment QOD. A total of 4,993 (32.7%), 4,278 (28.0%), and 5,998 (39.3%) patients received 3, 4, and 5 fractions, respectively. The most common dose fractionations were 10 Gy x 5 (26.7%), 12 Gy x 4 (18.4%), and 18 Gy x 3 (17.3%). Factors significantly associated with daily SBRT scheduling included lower income (<i>P</i> < 0.0001), lower comorbidities (<i>P</i> = 0.0019), and treatment at academic/research programs (<i>P</i> < 0.0001). The use of daily SBRT scheduling decreased from a peak of 36.8% in 2007 to 21.7% in 2016, while QOD treatment increased from a nadir of 63.2% in 2007 to 78.3% in 2016 (both <i>P</i> < 0.0001). The use of 3-fraction SBRT decreased over time from 81.5% in 2004 to 23.4% in 2016, while 5-fraction SBRT increased from 3.7% in 2004 to 51.4% in 2016 (both <i>P</i> < 0.0001); there was no significant change in use of 4-fraction regimens (<i>P</i> = 0.6). The most common treatment schedule was 3 fractions QOD from 2004-2011 (25.5-70.4%), while more recently 5 fractions QOD was most prevalent from 2012-2016 (rising from 28.5% in 2012 to 41.6% in 2016). Median follow-up was 28.9 months, and median survival was 38.3 months. Median survival for patients who received daily SBRT was 37.9 months vs. 38.4 months for QOD (<i>P</i> = 0.4). On multivariate analysis, no difference was found in overall survival between daily vs. QOD scheduling (hazard ratio [HR] 0.99 [95% confidence interval 0.94-1.04]; <i>P</i> = 0.6). With 3-fraction SBRT, QOD treatment was associated with improved survival vs. daily treatment (HR 0.91 [0.84-0.98]; <i>P</i> = 0.02). With 5-fraction SBRT, QOD treatment was associated with worse survival vs. daily treatment (HR 1.11 [1.02-1.22]; <i>P</i> = 0.02). <h3>Conclusion</h3> In this NCDB analysis, QOD SBRT schedules were more frequently used to treat Stage I NSCLC than daily regimens by a factor of 3:1. QOD scheduling increased over time, as did 5-fraction treatments, with 5-fraction QOD becoming the most common dose schedule after 2012. No clear association was found between daily vs. QOD scheduling and overall survival.

A Short-Term Planning Framework for the Operation of Tanker-Based Water Distribution Systems in Urban Areas

Tanker-based distribution systems have been prevalent in developing countries to supply clean and pure water in different regions. To efficiently operate such tanker service systems, a large fleet of tanker trucks are required to transport water among several water sources, water treatment plants and consumers spanning across the regions. This requires tighter coordination between water suppliers, treatment plant operations, and user groups to use available water resources in a sustainable manner, along with the assurance of water quality and timely delivery. This paper proposes a novel formulation to assist decision-making for optimizing tanker-based water distribution systems and treatment operations, with an overall objective of minimizing the total operating cost such that all of the constraints related to the water demand, supply operations, and environmental and social aspects are honored while supplying water to a maximum number of users. The problem is formulated and solved as a mixed integer linear programming (MILP) optimization framework and captures all of the nuances related to (i) water availability limitations and quality constraints from different sources, (ii) maintaining water quality as it transports via tankers, (iii) water demands for various end-use purposes, and (iv) transportation across a water supply chain. The proposed novel framework is applied to a realistic urban model to find the optimal tanker delivery schedule, ensuring appropriate treatment and timely delivery of water. The results of the case study conducted on a representative-scale problem also elucidate several aspects of treatment plant operation and consumer demand fulfillment for the efficient planning and management of tanker-based water distribution systems.

A Matheuristic Algorithm for the Inventory Routing Problem

This work addresses a challenging inventory routing problem that arises from a practical application faced by air-product companies, including Air Liquide. Given its computational complexity and industrial importance, this problem (denoted as IRP-Challenge2016) was presented as the topic of the French Operational Research and Decision Support Society/European Operational Research Society (ROADEF/EURO) Challenge 2016. The IRP-Challenge2016 seeks an optimal delivery schedule to minimize the unit distribution cost, while satisfying various hard constraints. It involves a single product, a heterogeneous fleet, heterogeneous drivers, multiperiods, a deterministic consumption forecast, and time-window constraints. We present a new mathematical formulation of the problem and introduce a matheuristic algorithm that integrates a local search-based metaheuristic with mathematical programming. Our algorithm combines mixed integer programming and linear programming as slave methods to optimize timing and delivery and embeds these procedures within a multineighborhood search metaheuristic to adjust routes. The method extends and enhances a preliminary version of our algorithm, which ranked third in the final round of the ROADEF/EURO Challenge 2016. Computational results for 20 challenge benchmark instances demonstrate the value of the proposed algorithm in terms of both effectiveness and efficiency with respect to the results reported in the competition. We additionally analyze several key components of our matheuristic to gain an insight into its operation.

GAME MODEL FOR ONLINE AND OFFLINE RETAILERS UNDER BUY-ONLINE AND PICK-UP-IN-STORE MODE WITH DELIVERY COST AND RANDOM DEMAND

Online retailers are increasingly adding buy-online and pick-up-in-store (BOPS) modes to order fulfilment. In this paper, we study a system of BOPS by developing a stochastic Nash equilibrium model with incentive compatibility constraints, where the online retailer seeks optimal online sale prices and an optimal delivery schedule in an order cycle, and the offline retailer pursues a maximal rate of sharing the profit owing to the consignment from the online retailer. By an expectation method and optimality conditions, the equilibrium model is first transformed into a system of constrained nonlinear equations. Then, by a case study and sensitivity analysis, the model is validated and the following practical insights are revealed. (I) Our method can reliably provide an equilibrium strategy for the online and offline retailers under BOPS mode, including the optimal online selling price, the optimal delivery schedule, the optimal inventory and the optimal allocation of profits. (II) Different model parameters, such as operational cost, price sensitivity coefficient, cross-sale factor, opportunity loss ratio and loss ratio of unsold goods, generate distinct impacts on the equilibrium solution and the profits of the BOPS system. (III) Optimization of the delivery schedule can generate greater consumer surplus, and makes the offline retailer share less sale profit from the online retailer, even if the total profit of the BOPS system becomes higher. (IV) Inventory subsidy is an indispensable factor to improve the applicability of the game model in BOPS mode.

Mathematical Investigation on the Sustainability of UAV Logistics

Unmanned aerial vehicles (UAVs) are expected to make groundbreaking changes in the logistics industry. Leading logistics companies have been developing and testing their usage of UAVs recently as an environmentally friendly and cost-effective option. In this paper, we investigate how much the UAV delivery service is environmentally friendly compared to the traditional ground vehicle (GV) delivery service. Since there are fuel (battery) and loadable weight restrictions in the UAV delivery, multi-hopping of UAV is necessary, which may cause a large consumption of electrical energy. We present a two-phase approach. In Phase I, a new vehicle routing model to obtain optimal delivery schedules for both UAV-alone and GV-alone delivery systems is proposed, which considers each system’s restrictions, such as the max loadable weight and fuel replenishment. In Phase II, CO2 emissions are computed as a sustainability measure based on the travelling distance of the optimal route obtained from Phase I, along with various GV travel-speeds. A case study finds that the UAV-alone delivery system is much more CO2 efficient in all ranges of the GV speeds investigated.

Delivery Lot Size Optimization and Schedule of Shipment in Distribution Centre

This paper describes the optimal delivery lot sizes and plan delivery schedules from distribution center to manufacturer with a Distribution Requirement Planning (DRP). A company that produces nails has a problem that the planning and scheduling of goods distribution is not coordinated well. the demand for each product is out of control resulting in shortages or excesses as well as delays in distribution at each Distribution Center (DC). The purpose of this research is to analyze the distribution needs by using the Distribution Resources Planning (DRP) method to avoid delays in distributing products to each DC. Distribution analysis using the DRP method is used to get when and how many products will be sent for each DC. This method starts with calculating demand forecasting for the next 12 months. After obtaining the request results for the next 12 months, then the EOQ is calculated and the safety stock profit of each DC. With DRP method the optimal delivery quantity in DC Aceh 51.180 kgs, DC Padang 65.830 kgs, DC Pekanbaru 54.100 kgs, DC Palembang 67.225 kgs, and DC Medan 42.950 kgs. Using the optimal quantity delivery, frequency of shipment decreased until 51,5% and inventory cost decreased until 20,4%.

Optimal Delivery Scheduling and Charging of EVs in the Navigation of a City Map

This paper presents a mixed integer linear programming model to optimize the costs of maintenance and extra hours for scheduling a fleet of battery electric vehicles (BEVs) so that the products are delivered to prespecified delivery points along a route. On this route, each BEV must have an efficient charging strategy at the prespecified charging points. The proposed model considers the average speed of the BEVs, the battery states of charge, and a set of deliveries allocated to each BEV. The charging points are located on urban roads and differ according to their charging rate (fast or ultra-fast). Constraints that guarantee the performance of the fleet’s batteries are also taken into consideration. Uncertainties in the navigation of urban roads are modeled using the probability of delay due to the presence of traffic signals, schools, and public works. The routes and the intersections of these routes are modeled as a predefined graph. The results and the evaluation of the model, with and without considering the extra hours, show the effectiveness of this type of transport technology. The models were implemented in AMPL and solved using the commercial solver CPLEX.

Implementation of a Decision Support System for Improving Irrigation Water Delivery: Case Study

AbstractDecision support systems (DSSs) for irrigation system management have many benefits, which include water savings and the development of optimal water delivery schedules, while maintaining f...

INTEGRATED STEPWISE APPROACH FOR OPTIMAL WATER ALLOCATION IN IRRIGATION CANALS

ABSTRACTOptimal water management in irrigation networks should be an integrated approach which includes both canal and field systems. Integrated optimal water management of irrigation networks requires consideration of both optimal allocation of water among different crops at field level, and optimal water delivery scheduling at the canal level, which is often neglected. In this study, an integrated stepwise approach has been presented for considering both farm‐ and canal‐level optimization problems. Three modules are proposed for the optimization model. In the first module, crop–water production functions for different crops are produced, and optimal seasonal allocation of available water among several crops is determined using an LP algorithm. The objective function of this module is to maximize total net benefit of all crops. The second module takes the optimal allocated water to each crop from the first module, and determines its optimal distribution through the growing season for each crop, such that the total yield at the end of the season is maximized. Taking into account the output of the second module, and cultivated area of each crop, the water requirement volume for each secondary canal is computed. The third module determines optimal water delivery scheduling among outlets of the secondary canal using a genetic algorithm (GA). The objective of the third module is to minimize canal flow, and to maximize delivery adequacy and beneficial water delivery duration. The decision variables are delivery discharge to each outlet, the number of outlets grouped in a block which receive water sequentially, and the sequence of water delivery to the outlets in each block. The proposed approach was applied on the K canal of the Moghan Irrigation Network in the north‐west of Iran. The optimal water delivery scheduling of a secondary canal, based on the optimal water allocation among several crops, and intra‐seasonal irrigation scheduling are presented, which shows the utility of the integrated approach. Copyright © 2013 John Wiley &amp; Sons, Ltd.

Scheduling and lot sizing models for the single-vendor multi-buyer problem under consignment stock partnership

We consider a centralized supply chain composed of a single vendor serving multiple buyers and operating under consignment stock arrangement. Solving the general problem is hard as it requires finding optimal delivery schedule to the buyers and optimal production lot sizes. We first provide a nonlinear mixed integer programming formulation for the general scheduling and lot sizing problem. We show that the problem is NP-hard in general. We reformulate the problem under the assumption of ‘zero-switch rule’. We also provide a simple sequence independent lower bound to the solution of the general model. We then propose a heuristic procedure to generate a near-optimal delivery schedule. We assess the cost performance of that heuristic by conducting sensitivity analysis on the key model parameters. The results show that the proposed heuristic promises substantial supply-chain cost savings that increase as the number of buyers increases.

Combining vehicle routing and packing for optimal delivery schedules of water tanks

This article describes a decision-support system that was developed in 2011 and is currently in production use. The purpose of the system is to assist planners in constructing delivery schedules of water tanks to often remote areas in Australia. A delivery schedule consists of a number of delivery trips by trucks. An optimal delivery schedule minimises cost to deliver a given total sales value of delivered products. To construct an optimal delivery schedule, trucks need to be optimally packed with water tanks and accessories to be delivered to a set of delivery locations. This packing problem, which involves many packing and loading constraints, is intertwined with the transport problem of minimising distance travelled by road. Such a decision-support system that optimises multi-component operational problems is of great importance for an organisation; it supports what-if analysis for operational and strategic decisions and trade-off analysis to handle multi-objective optimisation problems; it is capable of handling and analysing variances; it is easy to modify – constraints, business rules, and various assumptions can be re-configured by a client. Construction of such decision-support systems requires the use of heuristic methods rather than linear/integer programming.