A strategic model for exact supply chain network design and its application to a global manufacturer

This paper presents a comprehensive model that captures significant strategic decisions involved in designing or redesigning high-performance supply chains from the perspective of the manufacturer. The problem considers deterministic demand by multiple clients, for multiple products, over the periods of a long-term horizon. The design decisions involve selection of suppliers, establishment or resizing of production facilities and distribution centres, possible subcontracting of related activities, and selection of transportation modes and routes. The problem is formulated by a Mixed Integer Linear Programming model. Its objective is to minimise the overall costs associated with procurement, production, inventory, warehousing, and transportation over the design horizon. Appropriate constraints model the complex relationships among the links of the supply chain. The proposed model has been applied to a large case study of a global manufacturing firm, providing valuable insights into the transformation of the firm’s current supply chain network, as well as into the potential of the proposed approach.     

Setting safety stocks in multi-stage inventory systems under rolling horizon mathematical programming models

This paper considers the problem of determining safety stocks in multi-item multi-stage inventory systems that face demand uncertainties. Safety stocks are necessary to make the supply chain, which is driven by forecasts of customer orders, responsive to (demand) uncertainties and to achieve predefined target service levels. Although there exists a large body of literature on determining safety stock levels, this literature does not provide an effective methodology that can address complex multi-constrained supply chains. In this paper, the problem of determining safety stocks is addressed by a simulation based approach, where the simulation studies are based on solving the supply chain planning problem (formulated as a mathematical programming model) in a rolling horizon setting. To demonstrate the utility of the proposed approach, an application of the approach at Organon, a worldwide operating biopharmaceutical company, will be discussed.     

Configuring a manufacturing firm's supply network with multiple suppliers

Consider a supply network consisting of a manufacturer and its suppliers. The manufacturer produces different types of products, using a common set of inputs (e.g., raw materials and/or component parts) from the suppliers: but, each product needs a different mix of these inputs. The manufacturer sells its finished products to the market at the end of the current decision horizon, facing an uncertain market demand. In situations where a manufacturer has outsourced its parts production to contract manufacturers, the contract manufacturer's capacity available for the given manufacturer in a particular time period may be limited by “capacity reservation” agreements made in advance. Thus, in making production mix decisions for the current planning horizon, the manufacturer has to take into account both its own and the component suppliers' capacity restrictions. We develop a mathematical model and an iterative algorithm that helps the manufacturer solve its supply configuration problem, that is, how much of each raw material and/or component part to order from which supplier, given capacity limits of suppliers as well as the manufacturer. The model takes into account such factors as market demand uncertainty, costs and product characteristics. We present an numerical example to illustrate the interacting effects among critical parameters in the model, and apply the model to a real-world case of a computer manufacturer.     

All-unit discounts,multi-item inventory model with stochastic demand,service level constraints and finite horizon

Inventory systems are typically described as deterministic or stochastic, single, or multi-item, etc. The model reported in this research combines several such dichotomies, into a single model. It has the objective of deciding the optimal order quantities for a multi-item inventory system over a finite horizon. The demand is probabilistic with service level constraints, and there is an all-unit price break, for orders that exceed a given size. The solution approach uses a goal programming technique, in a mixed integer linear programming formulation. The model is analysed for sensitivity to deviations from the optimal policy, and inaccurate parameter estimation, including the demand distribution. In addition the optimal multi-item policy is compared to an optimal solution derived for each part type separately. Simulation experiments reveal that the model is not sensitive to inaccurate parameters nor to exact estimation of the demand distribution, thus aiding in reducing the control cost. It is also shown that in spite of the computational cost, it is preferable to apply the model as is, instead of dealing with each unit type separately.     

Forecasting and maintenance problem under subcontracting constraint with transportation delay

In this paper, a forecasting production/maintenance optimization problem has been proposed with a random demand and single machine M₁ on a finite horizon. The function rate of the machine M₁ is depending on the production rate for each period of the forecasting horizon. In order to satisfy the customer, a subcontracting assures the rest of the production through machine M₂ with transportation delay. An analytic formulation of the problem has been proposed using a sequential computation of the optimal production plan for which an optimal preventive maintenance policy has been calculated based on minimal repair. Firstly, we find, the optimal production plans of principal and subcontracting machines, which minimises the total production and inventory cost for the cases without and with returned products under service level and subcontracting transportation delay. Secondly, we determine a joint effective maintenance policy with the optimal production plan, which integrates the various constraints for the production rates, the transportation delay and the returned production deadline. Numerical results are presented to highlight the application of the developed approach and sensitivity analysis shows the robustness of the model.     

A gradient search and column generation approach for the build–pack planning problem with approved vendor matrices and stochastic demand

We study a production planning problem of product assembly with random demand, where the customers choose their preferred suppliers for pairs of inter-dependent components through the approved vendor matrix. The problem is to develop production plans that minimise the expected total shortage and holding costs while observing the matrix restrictions and limited component supplies. We provide a mathematical programming formulation of the problem with a large number of decision variables, whose cost function is the solution of a parametric stochastic transportation problem. We present a gradient-based interior-point approach to solve this problem where the gradient is estimated by the shadow price from the solution of such a transportation problem. A column generation scheme is integrated into the approach to handle the large problem issue. Computational results show that our algorithm significantly improves the computational time when compared with the approach without column generation. In addition, we also discuss some extensions of the basic problem to the multi-period rolling horizon case.     

Simulation and performance evaluation of partially and fully integrated sales and operations planning

This article presents rolling horizon simulation models and performance analysis of partially and fully integrated sales and operations planning (S&OP) against traditional decoupled planning in a multi-site make-to-order (MTO) based manufacturing supply chain. Three simulation models are developed illustrating, respectively, the fully integrated S&OP model, which integrates cross-functional planning of sales, production, distribution, and procurement centrally; the partially integrated S&OP model, in which the joint sales and production planning is performed centrally while distribution and procurement are planned separately at each site; and the decoupled planning model, in which sales planning is carried out centrally while production, distribution, and procurement are planned separately and locally. A solution procedure is provided for each model so that a more realistic planning process can be simulated. Performances of rolling horizon simulation models are evaluated against those of the fixed horizon deterministic models. The results demonstrate that while deterministic models are important for theoretical studies, they are insufficient for decision support and performance evaluations in a real business environment. A rolling horizon simulation model is required to provide more realistic solutions. The effects of demand uncertainties and forecast inaccuracies are incorporated in the evaluation. The study is carried out based on a real industrial case of a Canadian-based oriented strand board (OSB) manufacturing company.     

Incorporating risk aversion and fairness considerations into procurement and distribution decisions in a supply chain

This paper considers a three-tier supply chain in which a manufacturer uses raw materials sourced from multiple suppliers to produce an item and sells it through multiple distributors. We develop an integrated optimisation model to study supply chain procurement and distribution decisions incorporating the manufacturer’s aversion to risk and the distributors’ concern for fairness in a climate of uncertain supply and demand. Resilient strategies, such as alternative sourcing and transshipment, are also considered when optimising the supply chain cost and service level. To solve the problem, a Monte Carlo simulation-based multi-objective stochastic programming model is built. It uses the CVaR (Conditional Value-at-Risk) and unfairness aversion utility function to reflect the decision maker’s risk aversion and the customer’s concern for fairness, respectively. A Normalised Normal Constraint based algorithm is adopted to obtain the Pareto Frontier. In addition, the numerical analysis provides some valuable insights for supply chain managers.     

Dynamic pricing for remanufacturing within socially environmental incentives

We study a dual-product dynamic pricing problem for a remanufacturing system in which a manufacturer makes new and remanufactured products competing for a certain market share. The socially environmental incentives, consisting of consumers' environmentally conscious demand and governments' subsidy on remanufactured products, are considered in this study, which encourage the manufacturer to exert production effort toward environmentally friendly remanufacturing. Three models, namely, two-period, multi-period, and infinite-period scenarios, are formulated to investigate the dynamic pricing problem. Analytical results show that the government's subsidy policies, which provide subsidies to consumers or firms, have equivalent effects for the manufacturer in terms of production and profit. Consumers' environmental consciousness and government subsidy are effective incentives to induce the manufacturer to make more remanufactured products. Some threshold policies are proposed to provide decision supports for manufacturers to formulate pricing and production strategies. By comparing the pricing and production strategies of the three models, we find it interesting that the pricing and production strategies of the multi-period model can be ideally characterised by those of the two-period and infinite-period models. This managerial concept is valuable for manufacturers in formulating pricing and production strategies when the precise production planning horizon is unknown.     

Rolling-horizon lot-sizing when set-up times are sequence-dependent

The challenging problem of efficient lot sizing on parallel machines with sequence-dependent set-up times is modelled using a new mixed integer programming (MIP) formulation that permits multiple set-ups per planning period. The resulting model is generally too large to solve optimally and, given that it will be used on a rolling horizon basis with imperfect demand forecasts, approximate models that only generate exact schedules for the immediate periods are developed. Both static and rolling horizon snapshot tests are carried out. The approximate models are tested and found to be practical rolling horizon proxies for the exact model, reducing the dimensionality of the problem and allowing for faster solution by MIP and metaheuristic methods. However, for large problems the approximate models can also consume an impractical amount of computing time and so a rapid solution approach is presented to generate schedules by solving a succession of fast MIP models. Tests show that this approach is able to produce good solutions quickly.     

DISCRETE-TIME MINIMAX PRODUCTION PLANNING FOR MANUFACTURING SYSTEMS

This paper deals with the production planning problem for discrete-time manufacturing systems with deteriorating items. A minimax approach is presented throughout the paper for the case where the demand is unknown. Both the cases of finite horizon and infinite horizon are discussed. Moreover, the case of production planning for manufacturing systems with failure-prone machines is also considered. For this case, a stochastic approach is used in which the states of the machines are represented by a two-state Markov process with transition rates determined by the availability of the machines. Finally, a robust control policy to take care of plant uncertainties is developed. Simulation results are also presented to show the usefulness of the approaches.     

Production planning in automotive powertrain plants: a case study

Based on a real case study from the automotive industry, this paper deals with production planning in powertrain plants. We present an overview of the production planning process and propose a mixed integer linear programme to determine the production quantities of each product over a planning horizon of several days. Then, using real data of an engine assembly line, we simulate the performance obtained through the proposed model within a rolling horizon planning process. We perform multiple tests in order to evaluate the impact of two parameters involved in this process: planning frequency and frozen horizon length. Furthermore, in order to illustrate the value of improving coordination between engine plants and their customers, we evaluate the impact of the quality of demand information (orders and forecasts). We analyse the simulation results and provide insights and recommendations in order to achieve a good trade-off between service level, inventory, and planning stability.     

Dynamic pricing for multiple class deterministic demand fulfillment

We consider how a firm should allocate inventory to multiple customer classes that differ based on the price they pay and their willingness to incur delay in fulfillment of their demand. The problem is set in a deterministic demand, economic-order-quantity-like environment with holding, backorder, lost demand and setup costs. The firm either fulfills demand or offers a price discount to induce the demand to wait for fulfillment from the next reorder. We determine the optimal policy and discuss how changes in various parameters affect profitability, customer service, and operational measures such as order frequency and base stock levels. We compare the results to a policy that only rations inventory without dynamic discounting and to a policy that only provides discounts. Through the comparison, we observe that dynamic pricing can be seen as a combination of a pricing mechanism which determines demand and an allocation mechanism that differentiates between customer classes, serving each ones needs. We show that if lower-value customers are distinguished by accepting reduced service, it is possible that both high and low-value customer classes see better levels of service under the optimal policy than under a discounting only policy. In addition we demonstrate the applicability of the results to a stochastic version of the problem.     

Purchasing Policy of New Containers Considering the Random Returns of Previously Issued Containers

A number of organizations sell products in containers that can be reused. The time from issue to return of an individual container is usually not known with certainty and there is a chance that the container is never returned (because of loss or irrepairable damage). Consequently, even under a level demand pattern new containers must be acquired from time to time. In this paper a purchasing policy of these new containers is determined for a finite time horizon so as to minimize the total purchasing and expected carrying costs under a prescribed service level. The associated stochastic model is reduced to a deterministic, dynamic lot-sizing problem with possible occurrence of negative net demand (demand minus return). A transformation into the usual nonnegative demand case allows us to apply well-known deterministic lot-sizing procedures to obtain the solution.     

Comparative analysis of lot-sizing models for multi-stage systems: a simulation study

In the past few years researchers have given considerable attention to various aspects of lot-sizing for single-stage and multi-stage systems in material requirements planning (MRP). Numerous models have been developed and tested on problems with finite horizons and deterministic time-varying demand. A real production system is, however, so complex that no model can capture all the elements under consideration. Instead of the static horizon commonly assumed by researchers, real planning is usually carried out on rolling horizons with different lengths. Such performance measures may include minimization of the total cost, inventory level, and schedule instability caused by rolling horizon and the number of setups. For large and complex product structures, the conventional approach is to apply a single-stage lot-sizing rule once to every stage of the multi-stage system. The Wagner–Whitin (WW) algorithm does provide a solution to this problem, but the length of the necessary calculations precludes its use in practice. As a result, many researchers have proposed numerous other lot-sizing procedures. The purpose of this paper is to examine the performance of various multi-stage lot-sizing procedures under rolling horizon environment using simulation. Cost and schedule instability were used as the performance criteria and product structure, demand variabillity, cost structure and planning horizon were considered as independent variables. It has been shown that Silver–Meal (SM) procedure outperforms other procedures such as WW and incremental approach (ICA) in most of the cases. The performance of ICA and SM are better than their respective counterparts Gaither’s rule (GA) and modified Silver-Meal (MSM). The results also indicate that there are differences in the performance of various lot-sizing procedures when applied to two different product structures.     

Development and evaluation of a rolling horizon purchasing policy for cores

A number of companies utilise end-of-use products (i.e. cores) for remanufacturing or recycling. An adequate supply of cores is needed for such activities. Establishing a purchasing policy for cores, over a finite planning horizon, requires multi-step ahead forecasts. Such forecasts are complicated by the fact that the number of cores in any future period depends upon previous sales and recent returns of the product. Distributed lag models have been used to capture this dependency for single-period ahead forecasts. We develop an approach to use distributed lag models to make multi-period ahead forecasts of net demand (i.e. demand minus returns), and investigate the cost implications, at a prescribed service level, of using such forecasts to purchase cores on a rolling horizon basis. Our results indicate that the effects of errors in the sales forecasts are negligible if sales follow an autoregressive pattern but are substantial when sales are more random. Dynamic estimation of the parameters in a rolling horizon environment yielded the most cost savings at high prescribed service levels (i.e. >0.95). Collectively, our results demonstrate the conditions in which companies can best leverage the dynamic nature of distributed lag models to reduce the acquisition costs over a finite horizon.     

Solving the multiple platforms configuration problem

The focus of manufacturing has been shifting from mass production to mass customization and producers are seeking ways to reduce production costs, still offering a competitive basket of products. One approach for implementing mass customization is to develop or produce products based on platform architecture. Variant products make use of the product platform as the starting point and then add or remove components to change features of the base product. This allows the manufacturer to offer the variety of products that meet market demands without developing each product independently. In this paper, we propose multiple platforms for the production of a given product family while minimizing the overall production cost. The methodology considers the demand for each product variant, with the decision variables as the optimal number of platforms, optimal configuration of each platform, and assignment of the products to the platforms. The problem is formulated as a mixed integer program, and both the optimal formulation and an evolutionary strategy based on Genetic Algorithm are presented. The approach is illustrated with an example from a family of cordless drills.     

Capacity and material requirement planning modelling by comparing deterministic and fuzzy models

A model for the capacity and material requirement planning problem with uncertainty in a multi-product, multi-level and multi-period manufacturing environment is proposed. An optimization model is formulated which takes into account the uncertainty that exists in both the market demand and capacity data, and the uncertain costs for backlog. This work uses the concept of possibilistic programming by comparing trapezoidal fuzzy numbers. Such an approach makes it possible to model the ambiguity in market demand, capacity data, cost information, etc. that could be present in production planning systems. The main goal is to determine the master production schedule, stock levels, backlog, and capacity usage levels over a given planning horizon in such a way as to hedge against the uncertainty. Finally, the fuzzy model and the deterministic model adopted as the basis of this work are compared using real data from an automobile seat manufacturer. The paper concludes that fuzzy numbers could improve the solution of production planning problems.     

Chance-constrained formulations in rolling horizon production planning: an experimental study

Rolling horizon procedures, where an infinite horizon problem is approximated by the solution to a sequence of finite horizon problems, are common in production planning practice and research. However, these procedures also lead to frequent changes in planned release and production quantities, a phenomenon referred to as nervousness. We examine the performance of two chance-constrained production planning models developed for systems with stochastic demand in a rolling horizon environment, and find that these formulations significantly reduce planned release changes (nervousness) while also improving cost and service-level performance.     

A hybrid Benders approach for coordinated capacitated lot-sizing of multiple product families with set-up times

We examine a coordinated capacitated lot-sizing problem for multiple product families, where demand is deterministic and time-varying. The problem considers set-up and holding costs, where capacity constraints limit the number of individual item and family set-up times and the amount of production in each period. Using a strong reformulation and relaxing the demand constraints, we improve both the upper and lower bounds using a combination of Benders decomposition and an evolutionary algorithm, followed by subgradient optimisation. Through computational experiments, we show that our method consistently achieves better bounds, reducing the duality gap compared to other single-family methods studied in the literature.