Optimization-Based Available-To-Promise with Multi-Stage Resource Availability

Increasingly, customer service, rapid response to customer requirements, and flexibility to handle uncertainties in both demand and supply are becoming strategic differentiators in the marketplace. Organizations that want to achieve these benchmarks require sophisticated approaches to conduct order promising and fulfillment, especially in today’s high-mix low-volume production environment. Motivated by these challenges, the Available-to-Promise (ATP) function has migrated from a set of availability records in a Master Production Schedule (MPS) toward an advanced real-time decision support system to enhance decision responsiveness and quality in Assembly To Order (ATO) or Configuration To Order (CTO) environments. Advanced ATP models and systems must directly link customer orders with various forms of available resources, including both material and production capacity. In this paper, we describe a set of enhancements carried out to adapt previously published mixed-integer-programming (MIP) models to the specific requirements posed by an electronic product supply chain within Toshiba Corporation. This model can provide individual order delivery quantities and due dates, together with production schedules, for a batch of customer orders that arrive within a predefined batching interval. The model considers multi-resource availability including manufacturing orders, production capability and production capacity. In addition, the model also takes into account a variety of realistic order promising issues such as order splitting, model decomposition and resource expediting and de-expediting. We conclude this paper with comparison of our model execution results vs. actual historical performance of systems currently in place.     

Multicriteria order acceptance decision support in over-demanded job shops: A neural network approach

Order acceptance is an important issue in job shop production systems where demand exceeds capacity. In this paper, a neural network approach is developed for order acceptance decision support in job shops with machine and manpower capacity constraints. First, the order acceptance decision problem is formulated as a sequential multiple criteria decision problem. Then a neural network based preference model for order prioritization is described. The neural network based preference model is trained using preferential data derived from pairwise comparisons of a number of representative orders. An order acceptance decision rule based on the preference model is proposed. Finally, a numerical example is discussed to illustrate the use of the proposed neural network approach. The proposed neural network approach is shown to be a viable method for multicriteria order acceptance decision support in over-demanded job shops.     

A decision support system for order acceptance/rejection in hybrid MTS/MTO production systems

In this paper, we present a novel decision support system for order acceptance/rejection in a hybrid Make-to-Stock/Make-to-Order production environment. The proposed decision support system is comprised of five steps. At the first step, the customers are prioritized based on a fuzzy TOPSIS method. Rough-cut capacity and rough-cut inventory are calculated in the second step and in case of unavailability in capacity and materials, some undesirable orders are rejected. Also, proper decisions are made about non-rejected orders. At the next step, prices and delivery dates of the non-rejected orders are determined by running a mixed-integer mathematical programming model. At the fourth step, a set of guidelines are proposed to help the organization negotiate over price and due date with the customers. In the next step, if the customer accepts the offered price and delivery date, the order is accepted and later considered in the production schedule of the shop floor, otherwise the order is rejected. Finally, numerical experiments are conducted to show the tractability of the applied mathematical programming model.     

An integrated production and inventory model to dampen upstream demand variability in the supply chain

We consider a two-echelon supply chain: a single retailer holds a finished goods inventory to meet an i.i.d. customer demand, and a single manufacturer produces the retailer’s replenishment orders on a make-to-order basis. In this setting the retailer’s order decision has a direct impact on the manufacturer’s production. It is a well known phenomenon that inventory control policies at the retailer level often propagate customer demand variability towards the manufacturer, sometimes even in an amplified form (known as the bullwhip effect). The manufacturer, however, prefers to smooth production, and thus he prefers a smooth order pattern from the retailer. At first sight a decrease in order variability comes at the cost of an increased variance of the retailer’s inventory levels, inflating the retailer’s safety stock requirements. However, integrating the impact of the retailer’s order decision on the manufacturer’s production leads to new insights. A smooth order pattern generates shorter and less variable (production/replenishment) lead times, introducing a compensating effect on the retailer’s safety stock. We show that by including the impact of the order decision on lead times, the order pattern can be smoothed to a considerable extent without increasing stock levels. This leads to a situation where both parties are better off.     

Strategic capacity planning for light emitting diode (LED) supply chains across Taiwan and China

This paper describes a mixed-integer programming (MIP) model formulated for strategic capacity planning for light emitting diode (LED) makers of Taiwan, major companies in the global LED market. These firms have complex supply chains across Taiwan and China, and the region’s unique political and economic environment has created not only competitive advantages but also challenges in supply chain management: government regulations require that customer orders be accepted from Taiwan or China according to customer attributes; when conducting manufacturing, Taiwanese firms may need to transfer orders across national borders for reasons such as manufacturing technology (the required technology is available only at certain manufacturing facilities) or more efficient capacity utilization; and there are operations to be performed with specific processing requirements to follow, posing substantial challenges for planners. Motivated by the significance of these firms in the global market, we develop a MIP model with novel features to support their strategic capacity planning, covering demand and manufacturing-related decisions, including order acceptance and transfer, manufacturing starts, capacity expansion, and logistics. We illustrate the model’s performance using modified industry data in a numerical example; we also describe the potential impacts the model may create in industry applications.     

Supplier selection in make-to-order environment with risks

The problem of allocation of orders for parts among part suppliers in a customer driven supply chain with operational risk is formulated as a stochastic single- or bi-objective mixed integer program. Given a set of customer orders for products, the decision maker needs to decide from which supplier to purchase parts required for each customer order to minimize total cost and to mitigate the impact of delay risk. The selection of suppliers and the allocation of orders is based on price and quality of purchased parts and reliability of on time delivery. To control the risk of delayed supplies, the two popular percentile measures of risk are applied: value-at-risk and conditional value-at-risk. The proposed approach is capable of optimizing the supply portfolio by calculating value-at-risk of cost per part and minimizing mean worst-case cost per part simultaneously. Numerical examples are presented and some computational results are reported.     

Order planning for networked make-to-order enterprises—a case study

From the general trend towards global markets and a growing customer orientation, new concepts and forms of organisation are emerging, such as distributed or networked enterprises. One key requirement of these new paradigms is the availability of models and tools to support order negotiation with the optimisation of manufacturing routes and logistics and ensuring the co-ordination of all participating entities. We address the problem of planning an incoming customer order to be produced in a distributed (multi-site) and multi-stage production system. In particular, we have used as a case study the industry of semiconductors (in the business area of application specific integrated circuits). The problem is tackled in a hierarchical model, in two levels: there is a global network planning procedure, and a set of local capacity models associated to the different production units reflecting their particular features. An approach based on simulated annealing is presented, as well as a specially designed constructive heuristic, that takes into account many of the real world constraints and complexities. The general performance of the simulated annealing algorithm is assessed through some preliminary computational experiments. Finally, some concluding remarks and current directions of research are presented.     

Reinforcement learning versus heuristics for order acceptance on a single resource

Order Acceptance (OA) is one of the main functions in business control. Accepting an order when capacity is available could disable the system to accept more profitable orders in the future with opportunity losses as a consequence. Uncertain information is also an important issue here. We use Markov decision models and learning methods from Artificial Intelligence to find decision policies under uncertainty. Reinforcement Learning (RL) is quite a new approach in OA. It is shown here that RL works well compared with heuristics. It is demonstrated that employing an RL trained agent is a robust, flexible approach that in addition can be used to support the detection of good heuristics.     

Optimization of production allocation and transportation of customer orders for a leading forest products company

A leading manufacturer of forest products with several production facilities located in geographical proximity to each other has recently acquired a number of new production plants in other regions/countries to increase its production capacity and expand its national and international markets. With the addition of this new capacity, the company wanted to know how to best allocate customer orders to its various mills to minimize the total cost of production and transportation. We developed mixed-integer programming models to jointly optimize production allocation and transportation of customer orders on a weekly basis. The models were run with real order files and the test results indicated the potential for significant cost savings over the company’s current practices. The company further customized the models, integrated them into their IT system and implemented them successfully. Besides the actual cost savings for the company, the whole process from the initial step of analyzing the problem, to developing, testing, customizing, integrating and finally implementing the models provided enhanced intelligence to sales staff.     

Semiconductor lot allocation using robust optimization

In this work, the problem of allocating a set of production lots to satisfy customer orders is considered. This research is of relevance to lot-to-order matching problems in semiconductor supply chain settings. We consider that lot-splitting is not allowed during the allocation process due to standard practices. Furthermore, lot-sizes are regarded as uncertain planning data when making the allocation decisions due to potential yield loss. In order to minimize the total penalties of demand un-fulfillment and over-fulfillment, a robust mixed-integer optimization approach is adopted to model is proposed the problem of allocating a set of work-in-process lots to customer orders, where lot-sizes are modeled using ellipsoidal uncertainty sets. To solve the optimization problem efficiently we apply the techniques of branch-and-price and Benders decomposition. The advantages of our model are that it can represent uncertainty in a straightforward manner with little distributional assumptions, and it can produce solutions that effectively hedge against the uncertainty in the lot-sizes using very reasonable amounts of computational effort.     

A multi-stage supply chain network design problem with in-house production and partial product outsourcing

We propose a mixed-integer linear programming model for a novel multi-stage supply chain network design problem. Our model integrates location and capacity choices for plants and warehouses with supplier and transportation mode selection, and the distribution of multiple products through the network. The aim is to identify the network configuration with the least total cost subject to side constraints related to resource availability, technological conditions, and customer service level requirements. In addition to in-house manufacturing, end products may also be purchased from external sources and consolidated in warehouses. Therefore, our model identifies the best mix between in-house production and product outsourcing. To measure the impact of this strategy, we further present two additional formulations for alternative network design approaches that do not include partial product outsourcing. Several classes of valid inequalities tailored to the problems at hand are also proposed. We test our models on randomly generated instances and analyze the trade-offs achieved by integrating partial outsourcing into the design of a supply chain network against a pure in-house manufacturing strategy, and the extent to which it may not be economically attractive to provide full demand coverage.     

Capacity planning with congestion effects

Important operational performance measures for a successful firm include not only price and quality, but also fast and on time delivery of customer orders. Capacity is a key issue in determining the lead time from customer order to delivery. However, capacity planning models seldom consider the impact of capacity levels on lead time performance. An important characteristic of this paper is the incorporation of congestion effects and their impact on lead time in making capacity acquisition decisions. It is especially important in a make-to-order environment, where customer orders arrive randomly and lead to high variability and congestion. This work was motivated by our observations of such tradeoffs at firms in several industries. We present a model to make equipment choice decisions in a multi-product, multi-machine, and single-stage production environment with congestion effects. The model is a nonlinear integer program. We present a heuristic solution procedure for this problem, which is based on a lower bound for the formulation that can be solved efficiently. The computational study shows that the solution procedure is quite effective in solving industry size problems. We illustrate the application of the model using data from a chemical-testing laboratory. We also discuss various extensions of the model.     

Manufacturing delivery performance for supply chain management

This paper considers single-stage make-to-order production systems. We focus on (1) modeling the appropriate expected costs under a variety of modeling assumptions and (2) characterizing the optimal policies. Our approach to solving the problem is to derive the distribution of actual completion times of the process for individual orders and to compare it to the corresponding quoted due dates in order to obtain the expected total costs. We then show the convexity of the objective cost function for determining the decision variable(s), the planned customer order leadtime.     

A branch and price solution approach for order acceptance and capacity planning in make-to-order operations

Make-to-order (MTO) operations have to effectively manage their capacity to make long-term sustainable profits. This objective can be met by selectively accepting available customer orders and simultaneously planning for capacity. We model a MTO operation of a job-shop with multiple resources having regular and non-regular capacity. The MTO firm has a set of customer orders at time zero with fixed due-dates. The process route, processing times, and sales price for each order are given. Since orders compete for limited resources, the firm can only accept some orders. In this paper a Mixed-Integer Linear Program (MILP) is proposed to aid an operational manager to decide which orders to accept and how to allocate resources such that the overall profit is maximized. A branch-and-price (B&P) algorithm is devised to solve the MILP effectively. The MILP is first decomposed into a master problem and several sub-problems using Dantzig-Wolfe decomposition. Each sub-problem is represented as a network flow problem and an exact procedure is proposed to solve the sub-problems efficiently. We also propose an approximate B&P scheme, Lagrangian bounds, and approximations to fathom nodes in the branch-and-bound tree. Computational analysis shows that the proposed B&P algorithm can solve large problem instances with relatively short time.     

Analytical models for supplier selection and order quantity allocation

In the literature, decision models and techniques for supplier selection do not often consider inventory management of the items being purchased as part of the analysis. In this article, two mixed integer nonlinear programming models are proposed to select the best set of suppliers and determine the proper allocation of order quantities while minimizing the annual ordering, inventory holding, and purchasing costs under suppliers’ capacity and quality constraints. The first model allows independent order quantities for each supplier while the second model restricts all order quantities to be of equal size, as it would be required in a multi-stage (supply chain) inventory model. Illustrative examples are used to highlight the advantages of the proposed models over a previous model introduced in the literature.     

Fuzzy linear programming models for NPD using a four-phase QFD activity process based on the means-end chain concept

Quality function deployment (QFD) is a customer-driven approach in processing new product development (NPD) to maximize customer satisfaction. Determining the fulfillment levels of the “hows”, including design requirements (DRs), part characteristics (PCs), process parameters (PPs) and production requirements (PRs), is an important decision problem during the four-phase QFD activity process for new product development. Unlike previous studies, which have only focused on determining DRs, this paper considers the close link between the four phases using the means-end chain (MEC) concept to build up a set of fuzzy linear programming models to determine the contribution levels of each “how” for customer satisfaction. In addition, to tackle the risk problem in NPD processes, this paper incorporates risk analysis, which is treated as the constraint in the models, into the QFD process. To deal with the vague nature of product development processes, fuzzy approaches are used for both QFD and risk analysis. A numerical example is used to demonstrate the applicability of the proposed model.     

Simultaneous price and due date settings for multiple customer classes

Extending the model of [Eur. J. Oper. Res. 116 (2) (1999) 305] that, under contingent capacity, simultaneously optimizes the bidding price and due date for each incoming order, we propose a bidding model with multiple customer segments classified based on parameters of willingness to pay, sensitivity to short delivery time, quality level requirement, and intensity of competition. The winning probability function was also modified to be of more practical and robust model in reflecting stochastic nature of customer's decision. Two sequencing rules, namely the early-due-date (EDD) for time-critical orders and first-come-first-serve (FCFS) for regular orders, were applied to determine the sequencing position of each incoming order, and a simplified pattern search algorithm was used to improve the efficiency in searching for optimal price and due date. The simulation results show that, in general, our proposed model and method can significantly increase the marginal revenue to the firm.     

Production and availability policies through the Markov Decision Process and myopic methods for contractual and selective orders

In this paper, we consider a supply chain with one manufacturer, one retailer, and some online customers. In addition to supplying the retailer, manufacturers may selectively take orders from individuals online. Through the Markov Decision Process, we explore the optimal production and availability policy for a manufacturer to determine whether to produce one more unit of products and whether to indicate “in stock” or “out of stock” on website. We measure the benefits and influences of adding online customers with and without the retailer’s inventory information sharing. We also simulate the production and availability policy via a myopic method, which can be implemented easily in the real world. Prediction of simple switching functions for the production and availability is proposed. We find the information sharing, production capacity and unit profit from online orders are the primary factors influencing manufacturer profits and optimal policy. The manufacturer might reserve 50% production capacity for contractual orders from the retailer and devote the remaining capacity to selective orders from spontaneous online customers.     

Exploiting timely demand information to reduce inventories

Electronic Data Interchange (EDI) and related technologies are making it less expensive to frequently transmit demand information up the supply chain from the point of sale. However, little is known about how the various participants in the supply chain might exploit more timely demand information. This research is intended to be an opening contribution to the analytical study of timely demand information. We study a simple two-level system composed of a supplier (or component plant) and a single customer (or final assembly plant). The two factories use a standard periodic base-stock policy for one particular item, but the equal-length production cycles of the two factories do not necessarily coincide. Both participants hold inventories to buffer the effects of uncertain orders and uncertain deliveries. The supplier is in turn supplied by a source with infinite capacity. Final demand occurs only at the final assembly plant, which communicates demand over its order cycle to the component plant. If the component plant begins a production cycle between orders from the final assembly plant, it is uninformed about some number of days' demand which has been observed at the customer but not yet communicated. Any technology, such as EDI, that makes it cheaper for the customer to communicate demand as it occurs allows the supplier to base its decisions on more accurate information. With more accurate demand information the supplier could reduce inventories, or improve the reliability of its deliveries to its customer, or both. The customer, in turn, could reduce its inventories if its supplier were more reliable. We examine the changes brought about by the exchange of timely demand information in inventories and service levels at both the supplier and customer. Our results show that inventory-related benefits are particularly sensitive to demand variability, the service level provided by the supplier, and the degree to which the order and production cycles are out of phase.     

Supply chain scheduling with receiving deadlines and non-linear penalty

We study the operations scheduling problem with delivery deadlines in a three-stage supply chain process consisting of (1) heterogeneous suppliers, (2) capacitated processing centres (PCs), and (3) a network of business customers. The suppliers make and ship semi-finished products to the PCs where products are finalized and packaged before they are shipped to customers. Each business customer has an order quantity to fulfil and a specified delivery date, and the customer network has a required service level so that if the total quantity delivered to the network falls below a given targeted fill rate, a non-linear penalty will apply. Since the PCs are capacitated and both shipping and production operations are non-instantaneous, not all the customer orders may be fulfilled on time. The optimization problem is therefore to select a subset of customers whose orders can be fulfilled on time and a subset of suppliers to ensure the supplies to minimize the total cost, which includes processing cost, shipping cost, cost of unfilled orders (if any), and a non-linear penalty if the target service level is not met. The general version of this problem is difficult because of its combinatorial nature. In this paper, we solve a special case of this problem when the number of PCs equals one, and develop a dynamic programming-based algorithm that identifies the optimal subset of customer orders to be fulfilled under each given utilization level of the PC capacity. We then construct a cost function of a recursive form, and prove that the resulting search algorithm always converges to the optimal solution within pseudo-polynomial time. Two numerical examples are presented to test the computational performance of the proposed algorithm.