The capacity planning problem in make-to-order enterprises

This paper addresses the short-term capacity planning problem in a make-to-order (MTO) operation environment. A mathematical model is presented to aid an operations manager in an MTO environment to select a set of potential customer orders to maximize the operational profit such that all the selected orders are fulfilled by their deadline. With a given capacity limit on each source for each resource type, solving this model leads to an optimal capacity plan as required for the selected orders over a given (finite) planning horizon. The proposed model considers regular time, overtime, and outsourcing as the sources for each resource type. By applying this model to a small MTO operation, this paper demonstrates a contrast between maximal capacity utilization and optimal operational profit.     

Optimizing the supply chain configuration for make-to-order manufacturing

We consider a make-to-order (MTO) manufacturer who has won multiple contracts with specified quantities to be delivered by certain due dates. Before production starts, the company must configure its supply chain and make sourcing decisions. It also needs to plan the starting time for each production task under limited availability of resources such as machines and workforce. We develop a model for simultaneously optimizing such sourcing and planning decisions while exploiting their tradeoffs. The resulting multi-mode resource-constrained project scheduling problem (MMRCPSP) with a nonlinear objective function is NP-complete. To efficiently solve it, a hybrid Benders decomposition (HBD) algorithm combining the strengths of both mathematical programming and constraint programming is developed. The HBD exploits the structure of the model formulation and decomposes it into a relaxed master problem handled by mixed-integer nonlinear programming (MINLP), and a scheduling feasibility sub-problem handled by constraint programming (CP). Cuts are iteratively generated by solving the feasibility sub-problem and added back to the relaxed master problem, until an optimal solution is found or infeasibility is proved. Computational experiments are conducted to examine performance of the model and algorithm. Insights about optimal configuration of MTO supply chains are drawn and discussed.     

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.     

A robust optimization model for multi-site production planning problem in an uncertain environment

This paper addresses the multi-site production planning problem for a multinational lingerie company in Hong Kong subject to production import/export quotas imposed by regulatory requirements of different nations, the use of manufacturing factories/locations with regard to customers’ preferences, as well as production capacity, workforce level, storage space and resource conditions at the factories. In this paper, a robust optimization model is developed to solve multi-site production planning problem with uncertainty data, in which the total costs consisting of production cost, labor cost, inventory cost, and workforce changing cost are minimized. By adjusting penalty parameters, production management can determine an optimal medium-term production strategy including the production loading plan and workforce level while considering different economic growth scenarios. The robustness and effectiveness of the developed model are demonstrated by numerical results. The trade-off between solution robustness and model robustness is also analyzed.     

The use of a premium-payment scheme in a supply chain involving capacity acquisition

We study a practice whereby a downstream firm makes to his supplier a premium-payment for a certain quantity of products. We show that the adoption of this practice can induce the supplier to build bigger capacity. The higher capacity level enables the supplier to satisfy a larger portion of demands from the downstream firm, and this leads to higher payoffs for both parties in the supply chain. With the assistance of an under-capacity penalty imposed on the supplier, this premium-payment scheme can help lure the parties into taking the channel-optimal actions. Our numerical examples help reveal various features of the scheme.     

A procurement model using capacity reservation

In this paper we model a scenario where a buyer reserves capacity from one or more suppliers in the presence of demand uncertainty. We explicitly derive suppliers’ capacity reservation price, which is a function of their capacity, amount of capacity reserved by the buyer and other parameters. The buyer operates in a “built-to-order” environment and needs to decide how much capacity to reserve and from how many suppliers. For a strategy of equal allocation of capacity among the selected suppliers we develop closed form solutions and show that the model is robust to the number of suppliers from whom capacity is procured through reservation. When the parameters of demand distribution changes the supply base is likely to remain more or less the same. Our analysis further shows that increasing the number of pre-qualified suppliers does not provide significant advantages to the buyer. On the other hand, a pre-qualified supply base with greater capacity heterogeneity will benefit the buyer.     

Make-or-buy service capacity decision in a supply chain providing after-sales service

We consider a supply chain comprising a manufacturer and a retailer. The manufacturer supplies a product to the retailer, while the retailer sells the product bundled with after-sales service to consumers in a fully competitive market. The sales volume is affected by the retailer’s service-level commitment. The retailer can build service capacity in-house at a deterministic price before service demand is realized, or buy the service from an outsourcing market at an uncertain price after service demand realization. We find that the outsourcing market encourages the retailer to make a higher level of service commitment, while prompting the manufacturer to reduce the wholesale price, resulting in more demand realization. We analyze how the expected cost of the service in the outsourcing market and the retailer’s risk attitude affect the decisions of both parties. We derive the conditions under which the retailer is willing to build service capacity in-house and under which it will buy the service from the outsourcing market. Moreover, we find that the manufacturer’s sharing with the retailer the cost to build service capacity improves the profits of both parties.     

An instrument for measuring supply chain flexibility for the textile and clothing companies

Supply chain flexibility (SCF) represents the capability of firms to respond to unanticipated changes in customer needs and competitor actions. Given the growing research interest in flexibility strategies, the development of a valid and reliable instrument to measure organizational responses toward environmental uncertainties or risks is imperative. However, no systematic and scientific research has been conducted to develop such an instrument. The present study adopts a comprehensive and rigorous procedure to develop a multifaceted scale for SCF through an empirical investigation. The results of a confirmatory factor analysis suggest that SCF can be operationalized as a second-order factor model comprising four dimensions, namely: sourcing flexibility, operating system flexibility, distribution flexibility, and information system flexibility. A series of goodness-of-fit indices further demonstrates that this scale is internally consistent, reliable, and valid. The various findings suggested in the present study provide a more succinct picture of SCF, and the well-validated scale could be used as a basis for further research and theoretical groundwork in the field of supply chain management.     

Interactive group decision-making using a fuzzy linguistic approach for evaluating the flexibility in a supply chain

With global competition rapidly intensifying and shifting to the supply chain level, the supply chain flexibility has become increasingly important. However, the literature addressing supply chain flexibility remains limited. This study thus builds a group decision-making structure model of flexibility in supply chain management development. This study presents a framework for evaluating supply chain flexibility comprising two parts, an evaluation hierarchy with flexibility dimensions and related metrics, and an evaluation scheme that uses a three-stage process to evaluate supply chain flexibility. This study then proposes an algorithm for determining the degree of supply chain flexibility using a fuzzy linguistic approach. Evaluations of the degree of supply chain flexibility can identify the need to improve supply chain flexibility, and identify specific dimensions of supply chain flexibility as the best directions for improvement. The results of this study are more objective and unbiased for two reasons. First, the results are generated by group decision-making with interactive consensus analysis. Second, the fuzzy linguistic approach used in this study has more advantage to preserve no loss of information than other methods. Additionally, this study presents an example using a case study to illustrate the availability of the proposed methods and compare it with other methods.     

Integer programming approach to reactive scheduling in make-to-order manufacturing

New algorithms based on mixed integer programming formulations are proposed for reactive scheduling in a dynamic, make-to-order manufacturing environment. The problem objective is to update a long-term production schedule subject to service level and inventory constraints, whenever the customer orders are modified or new orders arrive. Different rescheduling policies are proposed, from a total reschedule of all remaining and unmodified customer orders to a non-reschedule of all such orders. In addition, a medium restrictive policy is considered for rescheduling only a subset of remaining customer orders awaiting material supplies. Numerical examples modeled after a real-world scheduling/rescheduling of customer orders in the electronics industry are presented and some results of computational experiments are reported.     

Supply capacity acquisition and allocation with uncertain customer demands

We study a class of capacity acquisition and assignment problems with stochastic customer demands often found in operations planning contexts. In this setting, a supplier utilizes a set of distinct facilities to satisfy the demands of different customers or markets. Our model simultaneously assigns customers to each facility and determines the best capacity level to operate or install at each facility. We propose a branch-and-price solution approach for this new class of stochastic assignment and capacity planning problems. For problem instances in which capacity levels must fall between some pre-specified limits, we offer a tailored solution approach that reduces solution time by nearly 80% over an alternative approach using a combination of commercial nonlinear optimization solvers. We have also developed a heuristic solution approach that consistently provides optimal or near-optimal solutions, where solutions within 0.01% of optimality are found on average without requiring a nonlinear optimization solver.     

Coordination mechanism for capacity reservation by considering production time,production rate and order quantity

In this paper we study the coordination of a dyadic supply chain producing a high-tech product by contracts. The product has a short life cycle and the buyer faces stochastic demands during the selling period. We consider the production time, which causes the inventory costs on supplier’s side. As the supplier builds production capacity in advance, the production rate is limited to the capacity created during the production time. In addition, we take into account the inventory cost and operational cost for the buyer. We examine the model under both full information and partial information updating situations, and propose a coordinating contract for each case. Our analysis includes the study of members’ decisions under both forced and voluntary compliance regimes. Numerical results are presented to provide more insights into the models developed and the mechanisms proposed.     

Managing the order pipeline to reduce supply chain volatility

The bullwhip effect in particular, and supply chain volatility in general, has been the subject of much analytical and empirical investigation by researchers. One goal of this work has been to determine supply chain designs and policies that minimize volatility. Using a system dynamics approach, we use three distinct supply chain volatility metrics to compare the ability of two alternative pipeline inventory management policies to respond to a demand shock. The results indicate that no one policy dominates on all three metrics of supply chain volatility. A simplistic static pipeline policy minimizes the bullwhip effect and lessens the likelihood of on-hand inventory oscillations, while a more sophisticated dynamic pipeline policy may converge more rapidly to the new equilibrium. In addition, simulation results suggest that the dynamic policy provides better customer service through fewer stockouts and backorders.     

Analysis of supply contracts with quantity flexibility

This paper explores a class of supply contracts under which a buyer receives discounts for committing to purchases in advance. The further in advance the commitment is made, the larger the discount. As time rolls forward, the buyer can increase the order quantities for future periods of the rolling horizon based on updated demand forecast information and inventory status. However, the buyer pays a higher per-unit cost for the incremental units. Such contracts are used by automobile and contract manufacturers, and are quite common in fuel oil and natural gas delivery markets. We develop a finite-horizon dynamic programming model to characterize the structure of the optimal replenishment strategy for the buyer. We present heuristic approaches to calculate the order volume in each period of the rolling horizon. Finally, we numerically evaluate the heuristic approaches and draw some managerial insights based on the findings.     

A lexicographic approach to bi-objective scheduling of single-period orders in make-to-order manufacturing

This paper presents a lexicographic approach and integer programming formulations for a dual-objective, long-term production scheduling in make-to-order manufacturing environment. The problem objective is to assign single-period customer orders for various product types to planning periods to complete all the orders with minimum number of tardy orders as a primary criterion and to level the aggregate production or the total capacity utilization over a planning horizon as a secondary criterion. Each order must be completed during one planning period. The basic integer programming formulation has been strengthened by the addition of some cutting constraints derived by relating the demand on required capacity to available capacity for each subset of orders with the same due date. The approach has been applied to optimize production schedules in a flexible flowshop made up of several processing stages in series, with identical, parallel machines, and an output buffer of limited capacity for holding completed products before delivery to the customers. Numerical examples modeled after a real-world make-to-order flexible assembly line in the electronics industry are provided and some computational results are reported.     

Proactive data envelopment analysis: Effective production and capacity expansion in stochastic environments

Demand fluctuations that cause variations in output levels will affect a firm’s technical inefficiency. To assess this demand effect, a demand-truncated production function is developed and an “effectiveness” measure is proposed. Often a firm can adjust some input resources influencing the output level in an attempt to match demand. We propose a short-run capacity planning method, termed proactive data envelopment analysis, which quantifies the effectiveness of a firm’s production system under demand uncertainty. Using a stochastic programming DEA approach, we improve upon short-run capacity expansion planning models by accounting for the decreasing marginal benefit of inputs and estimating the expected value of effectiveness, given demand. The law of diminishing marginal returns is an important property of production function; however, constant marginal productivity is usually assumed for capacity expansion problems resulting in biased capacity estimates. Applying the proposed model in an empirical study of convenience stores in Japan demonstrates the actionable advice the model provides about the levels of variable inputs in uncertain demand environments. We conclude that the method is most suitable for characterizing production systems with perishable goods or service systems that cannot store inventories.     

Wholesale price rebate vs. capacity expansion: The optimal strategy for seasonal products in a supply chain

We consider a supply chain in which one manufacturer sells a seasonal product to the end market through a retailer. Faced with uncertain market demand and limited capacity, the manufacturer can maximize its profits by adopting one of two strategies, namely, wholesale price rebate or capacity expansion. In the former, the manufacturer provides the retailer with a discount for accepting early delivery in an earlier period. In the latter, the production capacity of the manufacturer in the second period can be raised so that production is delayed until in the period close to the selling season to avoid holding costs. Our research shows that the best strategy for the manufacturer is determined by three driving forces: the unit cost of holding inventory for the manufacturer, the unit cost of holding inventory for the retailer, and the unit cost of capacity expansion. When the single period capacity is low, adopting the capacity expansion strategy dominates as both parties can improve their profits compared to the wholesale price rebate strategy. When the single period capacity is high, on the other hand, the equilibrium outcome is the wholesale price rebate strategy.     

Integrating effective flexibility measures into a strategic supply chain planning model

This paper develops models for capacity, product mix, distribution and input supply flexibility and integrates them in a strategic level, mixed integer supply chain (SC) planning model as a way of addressing demand and supply uncertainty, as well as improving market responsiveness. Capacity flexibility is modeled via the SC’s production capacity planning to address budgeted demand and ensure the fulfillment of prospective demand increases when considering various market scenarios. This model selects an optimal number of products from fast moving and extended product range options—based on the product mix flexibility. The model confirms a quick response to a changing marketplace by considering elements like transportation and supply lead time along with the probabilities of stock out options when addressing input supply and distribution flexibility. This paper proposes a solution procedure to solve the model for real world problems, and investigates the sensitivity of the model outputs with respect to changes in flexibility measures.     

Collaborative production planning of supply chain under price and demand uncertainty

This research is motivated by an automobile manufacturing supply chain network. It involves a multi-echelon production system with material supply, component fabrication, manufacturing, and final product distribution activities. We address the production planning issue by considering bill of materials and the trade-offs between inventories, production costs and customer service level. Due to its complexity, an integrated solution framework which combines scatter evolutionary algorithm, fuzzy programming and stochastic chance-constrained programming are combined to jointly take up the issue. We conduct a computational study to evaluate the model. Numerical results using the proposed algorithm confirm the advantage of the integrated planning approach. Compared with other solution methodologies, the supply chain profits from the proposed approach consistently outperform, in some cases up to 13% better. The impacts of uncertainty in demand, material price, and other parameters on the performance of the supply chain are studied through sensitivity analysis. We found the proposed model is effective in developing robust production plans under various market conditions.     

Managing a dual-channel supply chain under price and delivery-time dependent stochastic demand

Several leading manufacturers recently combined the traditional retail channel with a direct online channel to reach a wider range of customers. We examine such a dual-channel supply chain under price and delivery-time dependent stochastic customer demand. We consider five decision variables, the price and order quantity for both the retail and the online channels and the delivery time for the online channel. Uncertainty frequently arises in both retail and online channels and so additional inventory management is required to control shortage or overstock and that has an effect on the optimal order quantity, price, and lead time. We developed mathematical models with the profit maximization motive. We analyze both centralized and decentralized systems for unknown distribution function of the random variables through a distribution-free approach and also for known distribution function. We examine the effect of delivery lead time and customers’ channel preference on the optimal operation. For supply chain coordination a hybrid all-unit quantity discount along a franchise fee contract is used. Moreover, we use the generalized asymmetric Nash bargaining for surplus profit distribution. A numerical example illustrates the findings of the model and the managerial insights are summarized for centralized, decentralized, and coordinated scenarios.