Optimal and Heuristic Decision Strategies for Integrated Production and Marketing Planning

In this study we examine the effects of integrating production and marketing decisions for a short- to medium-range planning horizon in a profit maximizing firm. We formulate two models for determining price, marketing expenditure, demand or production volume, and lot size for a single product with stable demand when economies of scale are present. The full integration (FI) model simultaneously determines all the decisions involved, while the partial integration (PI) model separates the lot sizing decision from the others, as happens frequently in practice. Geometric programming (GP) techniques and marginal analysis are used to compare FI and PI, and obtain important managerial implications regarding the two models.     

A Heuristic Algorithm for the Capacitated Multiple Supplier Inventory Grouping Problem

This paper presents and solves a model for the multiple supplier inventory grouping problem, which involves the minimization of logistics costs for a firm that has multiple suppliers with capacity limitations. The costs included in the model are purchasing, transportation, ordering, and inventory holding, while the firm's objective is to determine the optimal flows and groups of commodities from each supplier. We present an algorithm, which combines subgradient optimization and a primal heuristic, to quickly solve the multiple supplier inventory grouping problem. Our algorithm is tested extensively on problems of various sizes and structures, and its performance is compared to that of OSL, a state-of-the-art integer programming code. The computational results indicate that our approach is extremely efficient for solving the multiple supplier inventory grouping problem.     

Master Scheduling in Assemble-To-Order Environments: A Capacitated Multiobjective Lot-Sizing Model

Basic characteristics of an assemble-to-order environment make effective master scheduling extremely difficult. Limited resource capacities and dynamic customer end-item demand contribute to the complexity of the master production scheduling problem. To gain flexibility and responsiveness within this system, the master production schedule (MPS) focuses at the component level. This research proposes a master scheduling technique for manufactured components which combines a multiobjective capacitated multi-item/multi-stage lot-sizing model with an interactive multiple objective optimization solution procedure. To evaluate the model's performance as a realistic and practical master scheduling tool, this study focuses on the National Cash Register (NCR) electronics manufacturing facility in Columbia, South Carolina.     

Inventory Positioning/Partitioning for Backorders Optimization for a Class of Multi-Echelon Inventory Problems*

Inventory management has undergone significant philosophical changes in recent decades such as the advent of the zero inventory concept. However, as attractive as the concept of minimal inventories may be, it is often unrealistic in application. Attention to basic features of inventory control systems such as order quantities, base stock levels, and reorder points remain crucial to ensure customer service at minimal cost. A nonlinear optimization model for determining base stock levels in a multi-echelon inventory network is presented. Lagrangian relaxation results in (1) newsboy-style relations that provide the optimal solutions, and (2) instantaneous shadow prices for the budget constraint. Sensitivity analysis of this model will facilitate making decisions concerning the desired investment in inventory for the entire system. This model may be solved on standard nonlinear programming software and is generalizable to problems in both production and distribution settings.     

Determining Order Quantity and Selling Price by Geometric Programming: Optimal Solution,Bounds, and Sensitivity*

This paper presents a geometric programming (GP) approach to finding a profit-maximizing selling price and order quantity for a retailer. Demand is treated as a nonlinear function of price with a constant elasticity. The proposed GP approach finds optimal solutions for both no-quantity discounts and continuous quantity discounts cases. This approach is superior to the traditional approaches of solving a system of nonlinear equations. Since the profit function is not concave, the traditional approaches may require an exhaustive search, especially for the continuous discounts schedule case. By applying readily available theories in GP, we easily can find global optimal solutions for both cases. More importantly, the GP approach provides lower and upper bounds on the optimal profit level and sensitivity results which are unavailable from the traditional approaches. These bounding and sensitivity results are further utilized to provide additional important managerial implications on pricing and lot-sizing policies.     

Labor Utilization Effects of Labor Scheduling Flexibility Alternatives in a Tour Scheduling Environment

This study used a factorial experimental design and a new modeling methodology to investigate the impact of a number of labor scheduling flexibility alternatives and labor requirements characteristics on labor utilization within a tour scheduling environment. Break-placement flexibility and shift-length flexibility were found to be extremely effective in improving labor utilization for all labor requirement distributions used. Flexibility with respect to the number of days included in a tour schedule resulted in substantial improvement in labor utilization for all labor requirements distributions exhibiting daily and/or weekly variation. Surprisingly, virtually no improvement in labor utilization was achieved for any labor requirement distribution by the removal of requirements for consecutive days off. In addition, almost no improvement was found by allowing the shift start time to vary across the working days included in tours. High labor requirement amplitude was found to have a strong adverse effect on labor utilization while longer operational days were associated with improved labor utilization for all labor requirement distributions. We discuss the implications of these results for service operations management and provide suggestions for future research.     

Vendor Selection with Bundling*

Product bundling has become increasingly prevalent not only in consumer goods but also in the industrial sector. We study a purchasing problem in which a buyer must obtain necessary numbers of various stock items from a variety of vendors who charge different prices, have limited capacities and different levels of quality, and offer bundled products at discounted prices. We examine relationships among different bundling scenarios and show that the most general scenario is one in which free items are given to the buyer when sufficient quantities are purchased. We develop a mixed integer linear program that finds the purchasing strategy for the buyer that minimizes the total purchase cost. We present computational results which indicate that the problem is very tractable to solve optimally on a personal computer with standard optimization software. Finally, three extensions of the model are discussed.     

An Industrial Ocean-Cargo Shipping Problem

This paper reports the modeling and solution of an industrial ocean-cargo shipping problem. The problem involves the delivery of bulk products from an overseas port to transshipment ports on the Atlantic Coast, and then over land to customers. The decisions made include the number and the size of ships to charter in each time period during the planning horizon, the number and location of transshipment ports to use, and transportation from ports to customers. The complexity of this problem is compounded by the cost structure, which includes fixed charges in both ship charters and port operations. Such a large scale, dynamic, and stochastic problem is reduced to a solvable stationary, deterministic, and cyclical model. The process of modeling the problem and the solution of the resultant mixed integer program are described in detail. Recommendations from this study have been implemented.     

A Mathematical Programming Approach to Production Decisions in the Emerging Aquaculture Industry

The creation of new food sources is an important advancement in the search for solutions to food shortages in both developing and underdeveloped countries. Aquaculture, the production of aquatic animals under controlled conditions, offers exciting new possibilities for alternative protein sources in a wide variety of locales. This paper presents a mathematical programming model designed to aid the manager of an aquaculture facility in production scheduling and the evaluation of new technologies in this rapidly changing environment.     

The Impact of Learning and Labor Attrition on Worker Flexibility in Dual Resource Constrained Job Shops

This study investigates the impact of worker learning, worker flexibility, and labor attrition on the system performance of a dual resource constrained (DRC) job-shop. The effects of learning and labor attrition have not been previously addressed in DRC literature. Results from the study, consistent with previous literature, show that the greatest benefits are achieved when inter-departmental worker flexibility is incrementally introduced into the system. In addition, the learning environment, which depends on the initial processing time of jobs and the learning rates of workers, is shown to impact the acquisition of flexibility. The study also shows that the impact of labor attrition on system performance under certain shop conditions may be significant.     

Optimal Delivery Time Quotation and Order Sequencing

This paper examines the problem of quoting a common delivery time for several orders. The decision maker responsible for the quote must trade off the cost associated with a long delivery time against the cost of tardy orders that might be induced by a short delivery time. First, an aggregate cost model is investigated where it is assumed that some cost is incurred if the quoted delivery time exceeds a given threshold and the cost of order tardiness is dependent on the order. Both exact and heuristic solution procedures are proposed for this model. Finally, for the situation where the costs cannot be quantified, a bicriteria formulation of the problem is pursued and the set of nondominated solutions is identified.     

A Hierarchical Production Planning and Scheduling Model

A hierarchical production planning and scheduling system is developed that integrates planning decisions into a unified and consistent framework. A three-tiered approach is used to address long-term inventory control, short-term production planning, and daily scheduling tasks. A product grouping scheme introduces uniformity into the solution process and simplifies overall model complexity. Results of the model implementation are reported.     

A Game-Theoretic Approach to Quantity Discount Problems*

The traditional quantity discount problem is analyzed from the perspective of game theory, including both noncooperative and cooperative models. For the noncooperative case, the Stackelberg equilibrium is derived. For the cooperative case, the Pareto Optimality criteria are used to find a group of optimal strategies. Both scenarios are illustrated through an example which quantifies the benefits resulting from cooperation between the buyer and the seller for game-theoretic solutions using geometric programming.     

SCHEDULING PARALLEL PROCESSORS WITH SETUP COSTS AND RESOURCE LIMITATIONS

An integer linear programming model is presented for the scheduling of n products on m identical machines. The particular problem studied is one that occurs frequently in the fiberglass and textile industries. The model incorporates setup costs, lost production costs, and overtime costs. Due to the structure of the model, integer solutions can be obtained by explicitly restricting only a small number of the integer variables. This allows those responsible for scheduling to solve realistically sized problems in an efficient manner. Computational results are provided for a set of generated test problems.     

Standard Container Size Discounts and the Single-Period Inventory Problem*

This paper analyzes the problem of choosing the optimal order quantity and its associated number of standard containers making up the order for single-period inventory models under standard container size discounts. A range is determined that contains the optimal order quantity. Two algorithms are presented. The first algorithm solves the general case in which there is no restriction on the types of containers included in an order. The second algorithm solves a more restricted policy that requires the buyer to accept the order with successively smaller container sizes.     

The Value of Supplier Information to Improve Management of a Retailer's Inventory

The distribution of lead time demand is essential for determining reorder points in inventory systems. Usually, the distribution of lead time demand is approximated directly. However, in some cases it may be worthwhile to take the demand per unit time and lead time into account, particularly when specific information is available. This paper deals with the situation where a supplier, who produces on order in fixed production cycles, provides information on the status of the coming production run. The retailer can use this information to gain insight into the lead-time process. A fixed order (s_vQ) strategy is presented, with a set of reorder points s_v depending on the time t until the first possible delivery, which is determined by the information of the supplier. A Markov model that analyzes a given (s_vQ) strategy is used to quantify the value of the information provided by the supplier. Some numerical examples show that the approach may lead to considerable cost savings compared to the traditional approach that uses only one single reorder point, based on a two-moments approximation. Using this numerical insight, the pros and cons of a more frequent exchange of information between retailers and suppliers can be balanced.     

An Integrative,Experiential Approach to Production Management Education

This paper addresses the important relationship between production and operations management (POM) and information technology. An approach to POM education is presented in which information technology is used to create an experiential learning environment that integrates the topics taught in POM courses. Results of an implementation of the proposed approach are presented and implications are discussed for POM education.     

A Generalized Loss Function for Process Optimization

The use of loss functions for measuring the undesirability associated with failure to achieve target values for manufacturing product characteristics is widespread in industry. This study presents a generalization of one of the most commonly used loss functions and compares the two functions based on five theoretical criteria. A simulation involving multiple probability distributions for a single product characteristic is used to compare the performance of the loss functions. An example from the manufacture of helicopter transmission gears is used to empirically demonstrate the superiority of the generalized loss function over the conventional loss function.     

A Model for Master Production Scheduling in Uncertain Environments

In uncertain environments, the master production schedule (MPS) is usually developed using a rolling schedule. When utilizing a rolling schedule, the MPS is replanned periodically and a portion of the MPS is frozen in each planning cycle. The cost performance of a rolling schedule depends on three decisions: the choice of the replanning interval (R), which determines how often the MPS should be replanned; the choice of the frozen interval (F), which determines how many periods the MPS should be frozen in each planning cycle; and the choice of the forecast window (T), which is the time interval over which the MPS is determined using newly updated forecast data. This paper uses an analytical approach to study the master production scheduling process in uncertain environments without capacity constraints, where the MPS is developed using a rolling schedule. It focuses on the choices of F, R, and T for the MPS. A conceptual framework that includes all important MPS time intervals is described. The effects of F, R, and T on system costs, which include the forecast error, MPS change, setup, and inventory holding costs, are also explored. Finally, a mathematical model for the MPS is presented. This model approximates the average system cost as a function of F, R, T, and several environmental factors. It can be used to estimate the associated system costs for any combination of F, R, and T.     

Vendor Selection with Bundling: A Comment*

In a recent article by Rosenthal, Zydiak, and Chaudhry (1995), a mixed integer linear programming model was introduced to solve the vendor selection problem for the case in which the vendor can sell items individually or as part of a bundle. Each vendor offered only one type of bundle, and the buyer could purchase at most one bundle per vendor. The model employed n(m+ 1) binary variables, where n is the number of vendors and m is the number of products they sell. The existing model can lead to a purchasing paradox: it may force the buyer to pay more to receive less. We suggest a reformulation of the same problem that (i) eliminates this paradox and reveals a more cost-effective purchasing strategy; (ii) uses only n integer variables and significantly reduces the computational workload; and (iii) permits the buyer to purchase more than one bundle per vendor.