A Redesigned Benders Decomposition Approach for Large-Scale In-Transit Freight Consolidation Operations

The growth in online shopping and third party logistics has caused a revival of interest in finding optimal solutions to the large scale in-transit freight consolidation problem. Given the shipment date, size, origin, destination, and due dates of multiple shipments distributed over space and time, the problem requires determining when to consolidate some of these shipments into one shipment at an intermediate consolidation point so as to minimize shipping costs while satisfying the due date constraints. In this paper, we develop a mixed-integer programming formulation for a multi-period freight consolidation problem that involves multiple products, suppliers, and potential consolidation points. Benders decomposition is then used to replace a large number of integer freight-consolidation variables by a small number of continuous variables that reduces the size of the problem without impacting optimality. Our results show that Benders decomposition provides a significant scale-up in the performance of the solver. We demonstrate our approach using a large-scale case with more than 27.5 million variables and 9.2 million constraints

Optimal Timing, Pricing and Advertisement Decisions for a New Product Diffusion in a Dual-Market Setting

In this study, we introduce an optimization model for synchronized main market entry timing, pricing, and advertisement spending for a new product in a dual-market setting. It has been established that newly introduced products in the marketplace encounter early adopters before they are accepted by main adopters. Typically, this transient is critical in determining the product's success in the market. Many new products go through a chasm and may not survive the transition to the main market. Product managers use pricing and advertising to help their products cross the chasm and successfully diffuse to the main market. The past experiences have indicated that another critical factor determining the diffusion is the time of entry to the main market. In such cases, the firm introduces the product to the early adopters before entering the main market, and the gradual growth in the former market serves as an effective bridge to the latter. We propose a mathematical model that maximizes total profit across the product's life cycle by making optimal decisions on product pricing pre-main market entry, main market entry timing, pricing post-main market entry, and advertisement spending in main market. The demand mapping is built by extending the Bass Diffusion framework. We employ an integer non-linear programming model to solve this problem. By carrying out computational experiments, we investigate the impact of the influence of the early adopters on the main market and the gap between the price sensitivities in two markets on the optimal decisions and the overall diffusion process

Inventory Control with Advance Ordering and Expedited Replenishments

We study a finite horizon multi-stage inventory control problem where demand is stochastic and nonstationary. The demand distribution across periods is a function of a demand signal which is random at the beginning of the planning horizon. The firm has the option of contracting its supplies in advance of realization of the market signal to benefit from price discounts. It is also possible for the firm to replenish its inventories during the selling season by paying higher spot market prices after the market signal is observed. Our research is motivated by applications in cruise line industry where contracts are made before the final number of bookings is realized. Based on the finalized bookings and consumption rates, additional purchases can be made at intermediate stops with higher prices. We investigate optimal combination of advance contracting and expedited replenishment policies under such settings. [PUBLICATION ABSTRACT

Minimizing total weighted tardiness and overtime costs for single machine preemptive scheduling

•We study the single machine preemptive scheduling problem with both regular and overtime modes.•The objective is to minimize the total tardiness and overtime costs.•We propose a heuristic solution methodology for the problem.•The efficiency of the heuristic is tested with upper bounds generated by the mathematical model. This paper studies the scheduling of a finite set of jobs on a single resource that operates under both regular and overtime capacity modes. Jobs, which can be preempted, have associated release and due dates. Limited overtime capacity can be utilized to reduce tardiness. However, since overtime is costly, justification of the overtime use depends on the trade-off between the tardiness and the overtime costs. The overall objective is to minimize the total cost of tardiness and overtime. To achieve this objective, we develop a holistic method composed of three-stages. We first provide a heuristic based on an effective priority rule for the base case where no overtime capacity is considered. This heuristic is later employed in the first-stage to produce a compact non-delay schedule built based on the assumption that overtime capacity incurs no additional cost. In the second stage, the overtime usage is reduced by shifting workload and generating a full-delay schedule without altering the tardiness of jobs produced in the first stage. The third stage improves the total costs by altering the tardiness of jobs in return for savings in overtime utilization. Using computational tests, we compare the performance of our heuristics to the upper bounds generated by the exact mixed-integer programming formulation. The results show that the proposed method is efficient in obtaining solutions that are considerably better than the generated upper bounds in significantly short times and as such, it can be quite useful as an effective solution approach especially for large size problems

Contingency Inventory Reservation for Low-Probability High-Impact Events

This article investigates reservation contracts for contingency inventory management between two buyers and a single supplier under a game theoretic framework. Two channel structures are considered in this context. In the first setting, the buyers simultaneously move to offer reservation fees to the supplier, who in turn, decides on the inventory amount she wants to carry for each buyer. In the second setting, the supplier moves first and offers nonrefundable-deductible reservation fees for the buyers, who respond with their respective reservation quantities. By reserving through a shared supplier, the buyers enable a contingency inventory pool which alleviates overage risk for the supplier and enables availability of products after low-probability high-impact events. Conditions for successful implementation of contingency reservation contracts are investigated. The results obtained for both channel structures were contrasted. It is shown that in a market where the buyers have more negotiation power, reservation contracts are more likely to achieve inventory buildup under relatively lower event probabilities

Design of predictable production scheduling model using control theoretic approach

As one of the most important planning and operational issues in manufacturing systems, production scheduling generally deals with allocating a set of resources over time to perform a set of tasks. Recently, control theoretic approaches based on nonlinear dynamics of continuous variables have been proposed to solve production scheduling problems as an alternative to traditional production scheduling methods that deal with decision-making components in discrete nature. The major goal of this paper is to improve predictability and performance of an existing scheduling model that employs the control theoretic approach, called distributed arrival time controller (DATC), to manage arrival times of parts using an integral controller. In this paper, we first review and investigate unique dynamic characteristics of the DATC in regards to convergence and chattering of arrival times. We then propose a new arrival time controller for the DATC that can improve predictability and performance in production scheduling. We call the new mechanism the double integral arrival-time controller (DIAC). We analyse unique characteristics of the DIAC such as oscillatory trajectory of arrival times, their oscillation frequency, and sequence visiting mechanism. In addition, we compare scheduling performance of the DIAC to the existing DATC model through computational experiments. The results show that the proposed system can be used as a mathematical and simulation model for designing adaptable manufacturing systems in the future

Physician Scheduling for Emergency Telemedicine

The use of technology in the health sector has increased over the years with the aim of providing efficient and quality services to save lives. Physician staffing and scheduling is a major managerial challenge for sustaining effective care in telemedicine especially in the context of emergency medicine. Motivated by an industry project with a telemedicine company that serves to multiple hospitals, this research focuses on the provision of telemedicine for stroke patients. The company operates 24/7 where the physicians perform their work remotely for patients typically located in the emergency wards in hospitals. Since stroke is a state of emergency, the telemedicine system must respond to an arriving case with a physician who is credentialed in the hospital where the patient is treated within a very short time window and as such, queuing the patient is not an option when there is no available on-shift physician. In such cases, the system must invoke the off-shift physicians, which is referred to as a "blast", an option that is required but not preferred by the telemedicine company due to high costs. A novel integer programming model is proposed for physician scheduling, which aims to minimize total costs under a chance constraint that limits the blast probabilities and other tactical constraints that are unique to this setting

Overhaul planning and exchange scheduling for maintenance services with rotable inventory and limited processing capacity

Maintenance, repair and overhauling (MRO) of high cost equipment used in many industries are typically subject to regulations set by local governments or international agencies. For example in the aviation industry, critical equipment must be overhauled at certain intervals for continuing permission of use. As such, the overhaul must be completed by strict deadlines. Since the overhaul is typically a long process, MRO companies may implement exchange programs where they carry so called rotable inventory for exchanging expensive modules that require overhaul so that the equipment can continue its services with minimal interruption. The extracted module is overhauled in a capacitated facility and rotated back to the inventory for a future exchange. Since both the rotable inventory and the overhaul process capacity are limited, it may be necessary to carry out some of the exchanges earlier than their deadlines. Early exchanges results in a decrease in the maintenance cycle time of the equipment, which is not desirable for the equipment user. In this paper, we propose an integer programming model so as to minimize total earliness by generating optimal overhaul start times for rotables on parallel processing lines and exchange timetables for orders. We show that the LP relaxation of the proposed model has the integrality property. We develop a practical exact solution algorithm for the model based on a full-delay scheduling approach with backward allocation. The proposed procedure is demonstrated through both a numerical study and a case study from the airline MRO service industry. (C) 2016 Elsevier Ltd. All rights reserved.This research was partially supported by the Science Fellowships & Grant Programs Department of The Scientific & Technological Research Council of Turkey (TUBITAK), BIDEB #2221. We are grateful to two anonymous referees whose comments have significantly contributed to improvement of our paper