Triangularity of the basis in linear programs for material requirements planning

It is shown that the basis in a class of linear programs arising from material requirements planning can be triangularized. This allows for efficient adaptation of the Simplex Method similar to those for network problems. It also suggests that for finite-loading (i.e. capacitated) MRP, a decomposition approach exploiting both subproblem structure and parallel processing can be effective for handling complex problems in multiproduct, multistage, multiperiod production systems.     

A multiperiod model for production planning and design in a multiproduct batch environment

A general multiperiod model to optimize simultaneously production planning and design decisions applied to multiproduct batch plants is proposed. This model includes deterministic seasonal variations of costs, prices, demands and supplies. The overall problem is formulated as a mixed-integer linear programming model by applying appropriate linearizations of non-linear terms. The performance criterion is to maximize the net present value of the profit, which comprises sales, investment, inventories, waste disposal and resources costs, and a penalty term accounting for late deliveries. A noteworthy feature of this approach is the selection of unit dimensions from the available discrete sizes, following the usual procurement policy in this area. The model simultaneously calculates the plant structure (parallel units in every stage, and allocation of intermediate storage tanks), and unit sizes, as well as the production planning decisions in each period (stocks of both product and raw materials, production plans, policies of sales and procurement, etc.).     

Multicut Benders decomposition algorithm for process supply chain planning under uncertainty

In this paper, we present a multicut version of the Benders decomposition method for solving two-stage stochastic linear programming problems, including stochastic mixed-integer programs with only continuous recourse (two-stage) variables. The main idea is to add one cut per realization of uncertainty to the master problem in each iteration, that is, as many Benders cuts as the number of scenarios added to the master problem in each iteration. Two examples are presented to illustrate the application of the proposed algorithm. One involves production-transportation planning under demand uncertainty, and the other one involves multiperiod planning of global, multiproduct chemical supply chains under demand and freight rate uncertainty. Computational studies show that while both the standard and the multicut versions of the Benders decomposition method can solve large-scale stochastic programming problems with reasonable computational effort, significant savings in CPU time can be achieved by using the proposed multicut algorithm.     

Schumann,a modeling framework for supply chain management under uncertainty

We present a modeling framework for the optimization of a manufacturing, assembly and distribution (MAD) supply chain planning problem under uncertainty in product demand and component supplying cost and delivery time, mainly. The automotive sector has been chosen as the pilot area for this type of multiperiod multiproduct multilevel problem, but the approach has a far more reaching application. A deterministic treatment of the problem provides unsatisfactory results. We use a 2-stage scenario analysis based on a partial recourse approach, where MAD supply chain policy can be implemented for a given set of initial time periods, such that the solution for the other periods does not need to be anticipated and, then, it depends on the scenario to occur. In any case, it takes into consideration all the given scenarios. Very useful schemes are used for modeling balance equations and multiperiod linking constraints. A dual approach splitting variable scheme is been used for dealing with the implementable time periods related variables, via a redundant circular linking representation.     

A noniterative multiproduct multiperiod production planning method

Production planning for multiple products on a single production facility over a time horizon requires minimizing the sum of production costs (regular time, overtime and subcontracting) and inventory carrying costs for meeting the known demands of the products. It is shown that the problem can be formulated and solved by a simple and noniterative method of ‘column minima’ even for multiple product situations.     

Tactical Planning for a Cutting Stock System

Wood processing on a centralized conversion site can be considered as a cutting stock problem. The multiperiod optimization of the production system is a very hard problem to solve. A balance has to be made between value recovery optimization and service rate maximization. In this research a decision support system was designed and built to support production planning. Strategic, tactical and operational planning are covered, but here the focus is primarily on tactical planning.     

Exact and hybrid methods for the multiperiod field service routing problem

This article deals with a particular class of routing problem, consisting of the planning and routing of technicians in the field. This problem has been identified as a multiperiod, multidepot uncapacitated vehicle routing problem with specific constraints that we call the multiperiod field service routing problem (MPFSRP). We propose a set covering formulation of the problem for the column generation technique and we develop an exact branch and price solution method for small-sized instances. We also propose several heuristic versions for larger instances. We present the results of experiments on realistic data adapted from an industrial application.     

Price-based planning and scheduling of multiproduct orders in symbiotic manufacturing networks

This paper addresses the problem of planning and scheduling operations when processing a multiproduct order in a Symbiotic Manufacturing Network (SMN). The order is characterized for each of its products, by linear routings of operations which can be performed in parallel by different contracting firms of the network. We first present a characterization of the decision process for planning and scheduling operations in SMN. Next, we propose a bidding scheme expressing pricetime trade-off and a multi-commodity network model that can be used to plan and schedule many types of order-based customized production. Finally, an illustrative example is detailed to permit full comprehension of the approach.     

On the Use of Pseudo Shadow Prices in a Multiperiod Formulation of the Production Planning Problem

A multiperiod linear programming model of the production planning problem is used to argue for a different costing, profit and resource-evaluation procedure in manufacturing. This procedure is based on the concept of ‘pseudo shadow prices’, and it avoids many of the pitfalls associated with the more traditional accounting methodologies. Conclusions are drawn which question the profit objectives used by many firms, as well as by those in academia.     

A principle of construction of an integrated machine manufacturing system

The problems arising in the automation of multiproduct small batch production in mechanical engineering due to necessity to ensure its high flexibility are indicated. It is shown that the automation level of such a production can be effectively increased by the organization of a group production and the part orientation of equipment. In so doing it is useful to group parts on the basis of their standard images and enrichment elements. The use of standard image concept promotes the integration of design and manufacturing and creates the prerequisites for the automation of design. The planning of group production organized on the basis of standard images and enrichment elements realizes by regrouping the parts-setting-ups matrix. The method of matrix regrouping facilitating the group production planning is proposed. The described principles of organizing the computer-aided design and manufacturing on the basis of standard images and enrichment elements have been used in constructing the integrated system KAPRI intended for pilot production with a variable range of parts.     

An Interactive Multiple Criteria Approach to Ranking Alternatives

In this paper we are concerned with ranking various orderings of a set of alternatives to a composite order as a multiple criteria problem. The orderings (called preference orderings) can be real preference orderings or any natural orderings. The objective is to find the most preferred order of the decision maker using the preference orderings as criteria.In principle, the problem can be formulated as a multiple objective linear programming problem using the model of Bowman and Colantoni and then solved with the interactive method proposed by Zionts and Wallenius. However, the fact that we are dealing with integer variables prohibits us from applying this approach as such. We discuss the problem formulation and propose a modified approach to that of Zionts and Wallenius for solving the problem.     

Integrated Production Inventory Policies for Multistage Multiproduct Batch Production Systems

An integrated production inventory model is considered in this paper, for a flow shop type multiproduct batch production system, with a multifacility structure. Instantaneous production is allowed in each facility. The model aims to determine simultaneously the optimal manufacturing cycle for the multiple products and the corresponding optimal procurement policies for the raw material. The cycle concept of multiproduct batch processing is extended to multifacility system and is integrated with the concept of production-inventory system for a single product, single facility system.     

Alternate approaches to solving the Holt et al. model and to performing sensitivity analysis

The staircase structure of the recurrence relations for the Holt et al. model can be used to develop simple and efficient computational approaches for obtaining the optimal solution. The computational approaches are noniterative. We deal with finite planning horizon cases in which one or more terminal boundary conditions are not specified. The computation time varies linearly with the number of periods in the planning horizon. A framework is also developed for sensitivity analysis on the terminal values and for generation of alternate production plans. The alternate plans provide considerable flexibility to the decision maker because they can be evaluated in the context of (a) constraints not included in the model, (b) plant capacity, (c) actual costs, and (d) implications beyond the planning horizon. The results should be of interest for real world applications as well as for research because the Holt et al. model continues to be used as a benchmark to evaluate the performance of other aggregate production planning models.     

Stochastic network optimization models for investment planning

We describe and compare stochastic network optimization models for investment planning under uncertainty. Emphasis is placed on multiperiod a sset allocation and active portfolio management problems. Myopic as well as multiple period models are considered. In the case of multiperiod models, the uncertainty in asset returns filters into the constraint coefficient matrix, yielding a multi-scenario program formulation. Different scenario generation procedures are examined. The use of utility functions to reflect risk bearing attitudes results in nonlinear stochastic network models. We adopt a newly proposed decomposition procedure for solving these multiperiod stochastic programs. The performance of the models in simulations based on historical data is discussed.Research partially supported by National Science Foundation Grant No. DCR-861-4057 and IBM Grant No. 5785. Also, support from Pacific Financial Companies is gratefully acknowledged.     

Probabilistic modeling of multiperiod service levels

This study investigates multiperiod service level (MSL) policies in supply chains facing a stochastic customer demand. The objective of the supply chains is to construct integrated replenishment plans that satisfy strict stockout-oriented performance measures which apply across a multiperiod planning horizon. We formulate the stochastic service level constraints for the fill rate, ready rate, and conditional expected stockout MSL policies. The modeling approach is based on the concept of service level trajectory and provides reformulations of the stochastic planning problems associated with each MSL policy that can be efficiently solved with off-the-shelf optimization solvers. The approach enables the handling of correlated and non-stationary random variables, and is flexible enough to accommodate the implementation of fair service level policies, the assignment of differentiated priority levels per products, or the introduction of response time requirements. We use an earthquake disaster management case study to show the applicability of the approach and derive practical implications about service level policies.     

3.1. OR in banking

In this paper, we describe a deterministic multiperiod capacity expansion model in which a single facility serves the demand for many products. Potential applications for the model can be found in the capacity expansion planning of communication systems as well as in the production planning of heavy process industries. The model assumes that each capacity unit simultaneously serves a prespecified (though not necessarily integer) number of demand units of each product. Costs considered include capacity expansion costs, idle capacity holding costs, and capacity shortage costs. All cost functions are assumed to be nondecreasing and concave. Given the demand for each product over the planning horizon, the objective is to find the capacity expansion policy that minimizes the total cost incurred. We develop a dynamic programming algorithm that finds optimal policies. The required computational effort is a polynomial function of the number of products and the number of time periods. When the number of products equals one, the algorithm reduces to the well-known algorithm for the classical dynamic lot size problem.     

Critical considerations concerning the multicriteria analysis by the method of Zionts and Wallenius

Lately many interactive methods to solve multiple objective problems were proposed. One of these, the method developed by S. Zionts and J. Wallenius, looks particularly interesting. This paper takes a closer look at this method and reports on the results of an experiment set up in order to test the method.     

Coordination of production planning and distribution

This is a summary of the main results presented in the author’s Ph.D thesis, supervised by C. Prins and defended at the Université de Technologie de Troyes in October 2006. The thesis, written in French, is available from the author upon request. It deals with the integrated optimization of production planning and distribution in supply chains. A single product case and a multiproduct case are investigated. Integer linear programming models are proposed and different approaches based on heuristics, metaheuristics and cooperative methods are developed. Significant savings are obtained, compared to classical decoupled methods. These results confirm both the interest of integrating production and distribution decisions and of using metaheuristics for the largest instances.      

Operations planning test bed under rolling horizons,multiproduct, multiechelon,multiprocess for capacitated production planning modelling with strokes

One of the problems when conducting research in mathematical programming models for operations planning is having an adequate database of experiments that can be used to verify advances and developments with enough factors to understand different consequences. This paper presents a test bed generator and instances database for a rolling horizons analysis for multiechelon planning, multiproduct with alternatives processes, multistroke, multicapacity with different stochastic demand patterns to be used with a stroke-like bill of materials considering production costs, setup, storage and delays for operations management. From the analysis of the operations planning obtained from this test bed, it is concluded that a product structure with an alternative process obtains the lowest total cost and the highest service level. In addition, decreasing seasonal demand could present a lower total cost than constant demand, but would generate a worse service level. This test bed will allow researchers further investigation so as to verify improvements in forecast methods, rolling horizons parameters, employed software, etc.

     

Capacity planning in manufacturing networks with discrete options

We consider multiproduct manufacturing systems modeled by open networks of queues with general distributions for arrival patterns and service times. Since exact solutions are not available for measuring mean number of jobs in these systems, we rely on approximate analyses based on the decomposition approach developed, among others, by Reiser and Kobayashi [16], Kuehn [14], Shanthikumar and Buzacott [19], Whitt [29], and extensions by Bitran and Tirupati [2]. The targeting problem (TP) presented in this paper addresses capacity planning issues in multiproduct manufacturing systems. Since TP is a nonlinear integer program that is not easy to solve, we present a heuristic to obtain an approximate solution. We also provide bounds on the performance of this heuristic and illustrate our approach by means of a numerical example.