Ana Muriel

Effective Zero-Inventory-Ordering Policies for the Single-Warehouse Multiretailer Problem with Piecewise Linear Cost Structures

We analyze the problem faced by companies that rely on TL (Truckload) and LTL (Less than Truckload) carriers for the distribution of products across their supply chain. Our goal is to design simple inventory policies and transportation strategies to satisfy time varying demands over a finite horizon, while minimizing system wide cost by taking advantage of quantity discounts in the transportation cost structures. For this purpose, we study the cost effectiveness of restricting the inventory policies to the class of zero-inventory-ordering (ZIO) policies in a single-warehouse multiretailer scenario in which the warehouse serves as a cross-dock facility. In particular, we demonstrate that there exists a ZIO inventory policy whose total inventory and transportation cost is no more than 4/3 (5.6/4.6 if transportation costs are stationary) times the optimal cost. However, finding the best ZIO policy is an NP hard problem as well. Thus, we propose two algorithms to find an effective ZIO policy: An exact algorithm whose running time is polynomial for any fixed number of retailers, and a linear-programming-based heuristic whose effectiveness is demonstrated in a series of computational experiments. Finally, we extend the worst-case results developed in this paper to systems in which the warehouse does hold inventory.

Managing Flexible Capacity in a Make-to-Order Environment

Flexible capacity has been shown to be very effective to hedge against forecast errors at the investment stage. In a make-to-order environment, this flexibility can also be used to hedge against variability in customer orders in the short term. For that purpose, production levels must be adjusted each period to match current demands, to give priority to the higher margin product, or to satisfy the closest customer. However, this will result in swings in production, inducing larger order variability at upstream suppliers and significantly higher component inventory levels at the manufacturer. Through a stylized two-plant, two-product capacitated manufacturing setting, we show that the performance of the system depends heavily on the allocation mechanism used to assign products to the available capacity. Although managers would be inclined to give priority to higher-margin products or to satisfy customers from their closest production site, these practices lead to greater swings in production, result in higher operational costs, and may reduce profits.

On the Effectiveness of Zero-Inventory-Ordering Policies for the Economic Lot-Sizing Model with a Class of Piecewise Linear Cost Structures

We consider an economic lot-sizing problem with a special class of piecewise linear ordering costs, which we refer to as the class of modified all-unit discount cost functions. Such an ordering cost function represents transportation costs charged by many less-than truckload carriers. We show that even special cases of the lot-sizing problem are NP-hard and therefore analyze the effectiveness of easily implementable policies. In particular, we demonstrate that there exists a zero-inventory-ordering(ZIO) policy, i.e., a policy in which an order is placed only when the inventory level drops to zero, whose total inventory and ordering cost is no more than 4/3 times the optimal cost. Furthermore, if the ordering cost function does not vary over time, then the cost of the best ZIO policy is no more than 5/6 4/6 times the optimal cost. These results hold for any transportation and holding cost functions that satisfy the following properties: (i) they are non decreasing functions, and (ii) the associated cost per unit is non increasing. Finally, we report on a numerical study that shows the effectiveness of ZIO policies on a set of test problems.

Supply Chain Design and Planning – Applications of Optimization Techniques for Strategic and Tactical Models

Publisher Summary This chapter describes the optimization models that effectively address the coordination of various decisions concerning the planning and design of the supply chain, and are the promising foundations for the development of Decision Support Systems in this field. The chapter focuses on three different problem areas: (1) production/distribution systems, (2) pricing to improve supply chain performance, and (3) logistics network design. In the production/distribution systems, the models that are designed to determine the appropriate production, inventory, and transportation policies for a set of manufacturing plants, warehouses, and retailers, are reviewed. The chapter extends dynamic pricing techniques to a more general supply chain setting with nonperishable inventory. Specifically, the pricing, production, and inventory decisions are considered simultaneously in a finite and an infinite horizon single product environment. The objective is to maximize the profit under conditions of periodically varying inventory holding and production costs, and price sensitive, stochastic demand.

Impact of Partial Manufacturing Flexibility on Production Variability

As manufacturers in various industries evolve toward predominantly make-to-order production to better serve their customers needs, increasing product mix flexibility emerges as a necessary strategy to provide adequate market responsiveness. However, the implications of increased flexibility on overall system performance are widely unknown. We develop analytical models and an optimization-based simulation tool to study the impact of increasing flexibility on shortages, production variability, component inventories, and order variability induced at upstream suppliers in general multiplant multiproduct make-to-order manufacturing systems. Our results show that 1. Partial flexibility leads to a considerable increase in production variability, and consequently in higher component inventory levels and upstream order variability. Although a modest increase in flexibility yields most of the sales benefits, production variability is reduced as more flexibility is added to the system. Consequently, investments in additional flexibility may be justified when component inventories are expensive, or simply by the benefits associated with the smoother production. 2. The performance of flexible systems is highly dependent on the capacity allocation policies implemented. Policies that evenly distribute product demands to the available plants lead to consistently better performance because they avoid the misplacement of inventories by replicating the performance of a single-plant system. These insights and the simulation tool can be used by practitioners to guide the design of their flexible production systems, trading off the initial capital outlay versus the sales benefits and the expected operational costs.

Parallel Machine Scheduling, Linear Programming, and Parameter List Scheduling Heuristics

In this paper we consider a class of parallel machine scheduling problems and their associated set-partitioning formulations. We show that the tightness of the linear programming relaxation of these formulations is directly related to the performance of a class of heuristics called parameter list scheduling heuristics. This makes it possible to characterize the worst possible gap between optimal solutions for the scheduling problems and the corresponding linear programming relaxations. In the case of the classical parallel machine weighted completion time model we also show that the solution to the linear programming relaxation of the set-partitioning formulation is asymptotically optimal under mild assumptions on the distribution of job weights and processing times. Finally, we extend most of the results to the time-discretized formulation of machine scheduling problems.

Dynamic allocation of same-day requests in multi-physician primary care practices in the presence of prescheduled appointments

Appointments in primary care are of two types: 1) prescheduled appointments, which are booked in advance of a given workday; and 2) same-day appointments, which are booked as calls come during the workday. The challenge for practices is to provide preferred time slots for prescheduled appointments and yet see as many same-day patients as possible during regular work hours. It is also important, to the extent possible, to match same-day patients with their own providers (so as to maximize continuity of care). In this paper, we present a mathematical framework (a stochastic dynamic program) for same-day patient allocation in multi-physician practices in which calls for same-day appointments come in dynamically over a workday. Allocation decisions have to be made in the presence of prescheduled appointments and without complete demand information. The objective is to maximize a weighted measure that includes the number of same-day patients seen during regular work hours as well as the continuity provided to these patients. Our experimental design is motivated by empirical data we collected at a 3-provider family medicine practice in Massachusetts. Our results show that the location of prescheduled appointments – i.e. where in the day these appointments are booked – has a significant impact on the number of same-day patients a practice can see during regular work hours, as well as the continuity the practice is able to provide. We find that a 2-Blocks policy which books prescheduled appointments in two clusters – early morning and early afternoon – works very well. We also provide a simple, easily implementable policy for schedulers to assign incoming same-day requests to appointment slots. Our results show that this policy provides near-optimal same-day assignments in a variety of settings.

Capacitated multicommodity network flow problems with piecewise linear concave costs

Lagrangian techniques have been commonly used to solve the capacitated multi-commodity network flow problem with piecewise linear concave costs. In this paper, we show that the resulting lower bounds are no better than those obtained by the linear programming relaxation and focus on developing algorithms based on the latter. For that purpose, we characterize structural properties of the optimal solution of the linear programming relaxation and propose a heuristic solution approach that uses these properties to transform the fractional solution into an integer one. Our computational experiments show the effectiveness of the algorithm.

Guidelines for scheduling in primary care under different patient types and stochastic nurse and provider service times

Scheduling in primary care is challenging because of the diversity of patient cases (acute versus chronic), mix of appointments (pre-scheduled versus same-day), and uncertain time spent with providers and non-provider staff (nurses/medical assistants). In this paper, we present an empirically driven stochastic integer programming model that schedules and sequences patient appointments during a work day session. The objective is to minimize a weighted measure of provider idle time and patient wait time. Key model features include: an empirically based classification scheme to accommodate different chronic and acute conditions seen in a primary care practice; adequate coordination of patient time with a nurse and a provider; and strategies for introducing slack in the schedule to counter the effects of variability in service time with providers and nurses. In our computational experiments we characterize, for each patient type in our classification, where empty slots should be positioned in the schedule to reduce waiting time. Our results also demonstrate that the optimal start times for a variety of patient-centered heuristic sequences consistently follow a pattern that results in easy to implement guidelines. Moreover, these heuristic sequences and appointment times perform significantly better than the practices schedule. Finally, we also compare schedules suggested by our two-service-stage model (nurse and provider) with those that only consider the provider stage and find that the performance of the provider-only model is 21% worse than that of the two-service-stage model.

Impact of Manufacturing Flexibility on Supply Chain Performance in the Automotive Industry

The basis of competition in the automotive industry is changing. While product innovation and styling remain the most important areas of competition, an almost equally fierce battle is now developing in the areas of customization and order fulfillment (Stalk, Stephenson and King [35]). Currently, all models of vehicle distribution are fundamentally inventory-driven and do not promote customized ordering. However, several vehicle manufacturers — most notably Ford and General Motors — have recently launched initiatives to transform their companies from predominantly make-to-stock to predominantly make-to-order producers. This will enable vehicle manufacturers and their dealers not only to dramatically reduce their finished goods inventory but also respond to challenges and threats from third party Internet companies.