Multi-product Multi-period Production Research Articles

Integrating Inventory-Based Financing in Production Planning Decisions

In this article, we study a multiproduct multiperiod production planning problem faced by a cash-strapped manufacturer, who utilizes inventory-based financing (IBF) to capture additional demand during peak season, which otherwise will not be met due to cash shortage. Each product has a unique selling season and its production incurs a significant setup cost. We formulate the problem as an integer program and show the special case with one product is NP-hard. By exploiting the inherent structure of three distinct but related decisions, i.e., the production, financing, and working capital allocation decisions, we develop a Lagrangian relaxation-based branch-and-bound procedure to solve the model. Through a series of numerical experiments using real data, this article presents managerial insights into how the manufacturer's optimal production plan could differ with and without IBF. In an optimal plan, we show the profit maximizing strategy for the cash-strapped manufacturer is to overstock and pledge inventories to secure more loans prior to peak demand periods.

Multi-stage multi-product multi-period production planning with sequence-dependent setups in closed-loop supply chain

A multi-stage lot sizing problem with remanufacturing is modelled.Sequence dependent setups and setup carry-over in a flow shop are considered.A mixed integer programming is introduced to formulate the problem.Rolling horizon heuristics and a SA algorithm are proposed to solve the model.For large size problems SA algorithm would have better solutions than heuristics. This paper studies multi-stage multi-product multi-period capacitated production planning problem with sequence dependent setups in closed-loop supply chain. In this problem, manufacturing and remanufacturing of each product is regarded consequently, and in addition to the setup for changing products, a setup while changing the processes is needed. To formulate the problem, a mixed-integer programming (MIP) model is presented. Four MIP-based heuristic named non-permutation and permutation heuristics, using rolling horizon are utilized to solve this model. Moreover, a simulated annealing algorithm using a heuristic to provide initial solution is developed to solve the problem. To calibrate the parameters of the proposed simulated annealing algorithm, Taguchi method is applied. The numerical results indicate the efficiency of the proposed meta-heuristic algorithm against MIP-based heuristic algorithms.

Tactical production planning in a hybrid Make-to-Stock–Make-to-Order environment under supply, process and demand uncertainties: a robust optimisation model

In this paper, we consider a hybrid ‘Make-to-Stock–Make-to-Order’ environment to develop a novel optimisation model for medium-term production planning of a typical multi-product firm based on the competencies of the robust optimisation methodology. Three types of uncertainties: suppliers, processes and customers, are incorporated into the model to construct a robust practical model in an uncertain business environment. The modelling procedure is started with applying deterministic linear programming to develop a new multi-objective approach for the combination of multi-product multi-period production planning and aggregate production planning problems. Then, the proposed deterministic model is transformed into a robust optimisation framework and the solution procedure is designed according to the Lp-Metric methodology. Next, using the IBM ILOG CPLEX optimisation software, the proposed model is evaluated by applying the data collected from an industrial case study. Final results illustrate the applicability of the proposed model.

Impact of price-adjustments costs on integration of pricing and production planning of multiple-products

Joint pricing and production decisions are crucial to the competitiveness of a manufacturing company. A common assumption in coordination of pricing and production planning decisions is that the price-adjustments are costless. However, those costs are not negligible, as they may take up a significant part of the firms’ reported profit. In this paper, we consider multi-product multi-period production planning systems with costly price-adjustments. A capacitated setting is investigated and a demand-based model where the demand is a function of the price is introduced. Effective computational models will be developed for both deterministic and stochastic price dependent demand. Both fixed and variable price-adjustment costs will be considered. The aim of the paper is to utilize the existing commercial packages for optimization and compare the effectiveness of various models for addressing realistic size problems. In the case of uncertain demand function, we focus on an additive demand model for which the underlying random variable is normally distributed. By using a chance constrained programming approach, we show that the model is still solvable for realistic size problems. We also develop a robust optimization model to fit in a scenario-based demand function. Computational results on a range of test problems support the effectiveness of our models.

Modelling of multi-period multi-product production planning considering production routes

The multi-period multi-product (MPMP) production planning problems, generally, deal with matching production levels of individual products with fluctuated demands over planning horizon. The conventional MPMP optimisation models suffer from insufficient utilisation of available capacity of machines. This fallacy is due to inappropriate formulation of machine capacity and material handling constraints. In this study, a novel mathematical model is proposed to simultaneously optimise production quantities and provide information about managerial decisions such as subcontracting, carrying inventory/backordering, and also hiring/layoff personnel. The problem is then formulated as a mixed integer linear programming (MILP) model by applying appropriate linearisation of non-linear components. The objective is to minimise production costs comprising of production, storage, shortage, subcontracting costs and costs associated with hiring/dismissing labourers. Superiority of the proposed model over existing ones, has been initially evaluated by solving the case presented by Byrne and Bakir [Byrne, M.D. and Bakir, M.A., 1999. Production planning using a hybrid simulation-analytical approach. International Journal of Production Economics, 59 (1), 305–311], and then evaluated by comparing the results obtained from solving both the proposed and the conventional MPMP production planning models using a 100-randomly-generated-test-problem.

A grid-based collaborative supply chain with multi-product multi-period production–distribution

A collaborative supply chain seeks to coordinate its members to produce and distribute products along the chain for minimum overall costs to satisfy customer demand. An integrated multi-period, multi-product and multi-stage supply chain model is developed. A collaborative supply chain grid (CSCG) system gathers necessary information on operations and resources from members of the supply chain. It then guides the members on ordering decisions for a minimum overall cost, while continuously re-directing them as new data becomes available. An actual CSCG system has been implemented in a collaborative auto industry with diverse and dynamic membership, yielding an approximately 26% reduction in total supply chain costs.

Capacitated production planning problem considering the detailed scheduling constraints in a flow shop environment

In this paper, a multi-product multi-period production system organized as a flow shop is considered. To overcome the shortcomings of hierarchical production planning, detailed production planning scheduling and sequencing constraints are integrated. A new integrated mixed-integer programming (MIP) model, capable of simultaneously performing production planning and nonpermutation scheduling, is proposed for the considered problem. For precise machine workload calculation, detailed scheduling constraints are used to determine a feasible production plan. The objective function includes production, inventory, backlog, set-up costs, and the costs associated with machine idle time and overtime. A hybrid simulated annealing (HSA) algorithm with dispatching rules and an exact solution method is proposed to solve the integrated model. The proposed algorithm searches the solution space for both problems and finds a combination of production planning and scheduling that is feasible and close to optimum. To evaluate the performance of the proposed model and solution method, problems of different scales are studied. The total costs of the proposed solution method are smaller than the results of hierarchical production planning.

Two-stage fuzzy production planning expected value model and its approximation method

This work develops a novel two-stage fuzzy optimization method for solving the multi-product multi-period (MPMP) production planning problem, in which the market demands and some of the inventory costs are assumed to be uncertainty and characterized by fuzzy variables with known possibility distributions. Some basic properties about the MPMP production planning problem are discussed. Since the fuzzy market demands and inventory costs usually have infinite supports, the proposed two-stage fuzzy MPMP production planning problem is an infinite-dimensional optimization problem that cannot be solved directly by conventional numerical solution methods. To overcome this difficulty, this paper adopts an approximation method (AM) to turn the original two-stage fuzzy MPMP production planning problem into a finite-dimensional optimization problem. The convergence about the AM is discussed to ensure the solution quality. After that, we design a heuristic algorithm, which combines the AM and simulated annealing (SA) algorithm, to solve the proposed two-stage fuzzy MPMP production planning problem. Finally, one real case study about a furniture manufacturing company is presented to illustrate the effectiveness and feasibility of the proposed modeling idea and designed algorithm.

Application of Fuzzy Multi-Objective Linear Programming Model in a Multi-Period Multi- Product Production Planning Problem

The Multi-Period Multi-Product (MPMP) production planning, as a well known problem in literature, attempts to match production rates of individual products with fluctuated market demand over planning horizon. This study, demonstrates how the conventional MPMP Linear Programming (LP) model may fail to utilize available capacity of machines, and also a novel Multi Objective Linear Programming (MOLP) model is developed to simultaneously minimize net present value of production costs and maximize machine utilization. The proposed model consists of production constraints such as available labor, inventory, maximum subcontracting levels and also forecasted demands. The proposed MOLP model is further converted to a Fuzzy Multi Objective Linear Programming (FMOLP) model utilizing piecewise linear membership functions. The model, accommodates the Decision Maker (DM) with a more systematic decision making approach enabling the DM to adjust the search direction during the solving procedure to achieve the most satisf...

A multi-objective production smoothing model with compressible operating times

Real life multi-product multi-period production planning often deals with several conflicting objectives while considering a set of technological constraints. The solutions of these problems can provide deeper insights to the decision makers/managers than those of single-objective problems. Some managers want to use from a production plan that is corresponding to minimum change in production policy along with minimum total cost simultaneously as possible. On the other hand, these two objectives have intrinsic conflicts such that producing in a fixed rate will cause huge costs than producing economically or according to JIT. So this paper presents a novel multi-objective model for the production smoothing problem on a single stage facility that some of the operating times could be determined in a time interval for. The model is to: ( a) smooth the variations of production volume, and ( b) minimize total cost of the corresponding production plan, while satisfying a set of technological constraints such as limited available time. The proposed model is developed in a real case study and is solved by a new genetic algorithm. The proposed genetic algorithm uses a novel achievement function for exploring the solution space, based on LP-metric concepts. Computational experiences reveal the sufficiency and efficiency of the proposed approach in contrast to previous researches.

On the noniterative multiproduct multiperiod production planning method

Bahl and Zionts [H.C. Bahl, S. Zionts, A noniterative multiproduct multiperiod production planning method, Operations Research Letters 1 (1982) 219–221] formulated a problem for planning multiproduct multiperiod production on a single facility. They developed a column-minima noniterative method and claimed that it gave an optimal solution. We show that the claim is incorrect.

A new project scheduling approach for improving multi-product multi-period production planning problems

The problem of matching production levels for individual products to demand fluctuations during multiple periods is known in the production planning literature as the multi-product multi-period (MPMP) problem. Linear programming (LP)-based solutions have been extensively reported in this respect. MPMP problems are commonly solved by using either analytic or simulation methods. More recently, hybrid solutions consisting of both analytical models and simulation analysis have been proposed where some operational criteria, e.g. the order of visit to machining centres, are taken into account. In this paper, results related to some of the literature based on hybrid solutions are used as the initial feasible solutions and then examined in the context of project scheduling by considering the influences of resource constraints. After converting the MPMP to a project network problem and assigning resources to activities and consequently levelling the resource profiles, it is discovered that machine utilization can be further improved by applying unused machine capacities. A LP model is therefore developed in order to maximize feasible production rates over all the production planning periods. The proposed approach results in improvements on the results of earlier hybrid solutions reported in the literature. Finally, three different planning problems are suggested for further applications of the proposed approach in the context of manufacturing environments.

Scenario aggregation in single-resource production planning models with uncertain demand

Abstract In this paper we present an application of the scenario aggregation approach proposed by Rockafellar and Wets to a simple standard multi-product multi-period production planning problem with uncertain demand and setup cost modelled by logical zero-one variables. The uncertainty in demand is expressed by a number of demand scenarios. As compared with more traditional approaches that require distributional assumptions and/or estimates of parameters from historical demand data, the scenario approach offers greater flexibility and makes it possible to take subjective information into account. The scenario aggregation principle and the corresponding progressive hedging algorithm offer a theoretically sound basis for generating consistent solutions for production planning models with uncertain demand. Since the production planning problem studied in this paper is of mixed-integer type the original scenario aggregation approach cannot be applied directly. However, since the integer variables in the prod...