Total Setup Cost Research Articles

A genetic algorithm for multiple objective sequencing problems in mixed model assembly lines

Presented in this paper is a new genetic algorithm to solve multiple objective sequencing problems in mixed model assembly lines. Mixed model assembly lines are a type of production line where a variety of product models similar in product characteristics are assembled. Such an assembly line is increasingly accepted in industry to cope with the recently observed trend of diversification of customer demands. While several objectives have been investigated for an efficient use of the production line, they are usually dealt with independently in existing researches. Relatively little attention has been paid to multiple objective problems. A new genetic algorithm is developed and is applied to the multiple objective problems addressed in this paper. The problem simultaneously considers three objectives found often in literature and meaningful in reality. The proposed genetic algorithm places emphasis on seeking for a set of diverse non-dominated solutions. Extensive computational experiments are carried out to demonstrate the superiority of the algorithm.Sequencing problems are important for an efficient use of mixed model assembly lines. There is a rich set of criteria on which to judge sequences of product models in terms of line utilization. We consider three practically important objectives: minimizing total utility work, keeping a constant rate of part usage and minimizing total setup cost. A considerate line manager would like to take into account all these factors. The multiple objective sequencing problem is described and its mathematical formulation is provided. A genetic algorithm is designed for finding near-Pareto or Pareto optimal solutions for the problem. A new genetic evaluation and selection mechanism, called Pareto stratum–niche cubicle, is proposed. The performance comparison of the proposed genetic algorithm with three existing genetic algorithms is made for various test-bed problems in terms of solution quality and diversity. The results reveal that the proposed genetic algorithm outperforms the existing genetic algorithms, especially for problems that are large and involve great variation in setup cost.

From Wagner-Whitin's dynamic lot size model towards zero inventory

This article discusses the interface between zero inventory (ZI) and the dynamic lot size problem. The conventional Wagner-Whitin dynamic lot size model shows a good ffi computational e ciency when obtaining the optimal lot-sizing policy, but it ignores reduction of lot size and total cost. The 'zero inventory' philosophy strives for the goals of zero inventory at the end of each period and minimum total cost. The setup cost is fixed in the Wagner-Whitin model, but is considered as a parameter in zero inventory (ZI) philosophy: in general, the setup cost is treated as a policy variable in ZI. Zangwill examined the case of stationary setup cost reduction, but did not discuss the case of nonstationary setup cost reduction. This paper presents a new expression for total setup cost and total holding cost for the Wagner-Whitin model. By adopting this new expression, we obtain a sufficient and necessary con dition such that ZI is the optimal policy in the Wagner-Whitin model. Regardless of whether the setup cost reduction is stationary or nonstationary, the total setup cost reduction over all periods increases when the amount of setup cost reduction increases. This result suggests that the optimal policy for the Wagner-Whitin model is close to ZI. Most presentations of ZI have been descriptive with very few mathematical models. This paper seeks to demonstrate by a mathematical approach that reducing the setup cost can make the Wagner-Whitin model approach ZI.

Learning in Setups: Analysis, Minimal Forecast Horizons, and Algorithms

We analyze the dynamic lot-sizing model in which the cost of a setup depends on the number of setups that have occurred prior to it. This arises, for example, when there exist learning effects in setups. Our model is more general than most learning models in the literature since it allows the total setup cost to be a general nondecreasing (but not necessarily concave) function of the number of setups. We explore tight relationships between our model and special cases of the classical dynamic lot-sizing model. On the basis of these we find minimal forecast and planning horizons for our model, which determine the first decision when the model is solved on a rolling horizon basis. When a forecast horizon cannot be found, we provide guidelines regarding the optimal first decision. We also provide an algorithm to solve the finite horizon problem, which uses as sub-problems variations of the classical dynamic lot-sizing problem. The advantage of this approach is the ability to use the extensive literature available on the latter, to generalize the results of this paper. As many of our results are qualitative in nature, they provide insights which can be useful for other models with a similar setup cost behavior.

Optimal production control of a dynamic two-product manufacturing system with setup costs and setup times

This paper deals with the optimal control of a one-machine two-product manufacturing system with setup changes, operating in a continuous time dynamic environment. The system is deterministic. When production is switched from one product to the other, a known constant setup time and a setup cost are incurred. Each product has specified constant processing time and constant demand rate, as well as an infinite supply of raw material. The problem is formulated as a feedback control problem. The objective is to minimize the total backlog, inventory and setup costs incurred over a finite horizon. The optimal solution provides the optimal production rate and setup switching epochs as a function of the state of the system (backlog and inventory levels). For the steady state, the optimal cyclic schedule is determined. To solve the transient case, the system's state space is partitioned into mutually exclusive regions such that with each region, the optimal control policy is determined analytically.

Optimal inventories in group technology production systems for a continuous consumption pattern

In this paper, a mathematical model to determine the optimal lot size in group technology systems is developed, based on a continuous consumption pattern. The optimal lot size formula that minimizes total cost is then determined. This formula is found to be similar to the standard economic production quantity formula, except for the cost elements associated with items' production and the opportunity cost associated with total machines set-up time. However, it is shown that in practical situations, where machine set-up consumes a limited time, the difference between the two formulas is insignificant. A variant formula for the case where storage cost is based on a fixed charge in a random access storage is also derived. Sensitivity analysis with respect to annual demand rate, annual carrying cost rate, cost of raw material handling, total machine set-up time and cost per unit time is presented. Finally, an example is worked out to illustrate the analytical results.

Algorithms for real-time scheduling of jobs on mixed model assembly lines

The problem of how to sequence jobs with options on a mixed model assembly line without work-in-process storage has been well addressed in the literature. In almost all of the previously developed models, the common goal has been to generate schedules that would maximize the utilization of station capacities. However, the problem of setups and utility work, which is the uncompleted work on a job leaving the station, has not been studied in detail. In this paper, a generalized formulation of the sequencing problem is presented. A Branch and Bound procedure and two heuristic algorithms are developed to determine a sequence which minimizes total setup and utility work costs simultaneously. The Branch and Bound algorithm is restricted to small size problems, while the heuristics can be used to obtain a solution for any realistic problem within a very small amount of computation time. The algorithms are tested on real data and shown to be applicable to real-time scheduling of jobs on mixed model assembly lines.

Note: An Improvement to the Dynamic Cycle Lengths Heuristic for Scheduling the Multi-Item, Single-Machine

A heuristic scheduling policy for multi-item, single-machine scheduling systems facing stochastic, time-varying demands was previously introduced by Leachman and Gascon. In this technical note we provide an improvement to the calculations of the policy. Simulation tests of the revised version of the policy indicate that the improvements maintain or enhance customer service while reducing total inventory and setup costs on the order of 1–7%.

Design of manufacturing cells: Operation assignment in printed circuit board manufacturing

We consider an operation assignment problem that arose from a printed circuit (PC) board assembly process. Components can either be inserted on boards manually or by machine. The objective is to determine an assignment of components (operations) to a set of capacitated machines (with the remainder of the components inserted manually) to minimize the total set-up and processing cost for assembling all boards. The problem can be formulated as a mixed integer linear program, but is too large to be practically solved. For the case of one machine, we present two different solution heuristics. We show that while each can be arbitrarily bad, on average the algorithms perform quite well. For the case of multiple machines, we present four different solution heuristics. We discuss implementation of our results at Hewlett-Packard.

Hierarchical production planning at a multiproduct multiprocessor fibreglass manufacturing facility

Abstract Abstract. A hierarchical production planning model is developed for a forming facility of a major fibreglass manufacturer. The model establishes aggregate quarterly quantities for families of products, monthly disaggregate production quantities for end-items within these families, and a weekly sequencing schedule of end-items. A key feature of the planning system is its ability to decompose total set-up cost into primary and secondary components and to account appropriately for each component at a distinct level of the planning hierarchy. The mathematical programming formulations, the accompanying solution algorithms, and the results of their application to nine months of actual company demand and cost data are presented.

Variation in oil concentration and economic return from tea-tree (Melaleuca alternifolia Cheel) oil

The oil concentration in tea-tree (Melaleuca alternifolia Cheel) twigs was measured over 8 consecutive days during November 1987, and over 10 out of 12 consecutive days in January 1989. The oil concentration, measured in units of volume of oil per unit dry weight of twigs (v/DW), varied markedly between successive days, from 2.9-1.8% v/DW (a 38% decrease) to 1.8-3.4% v/DW (a 89% increase). The reason for such variation is unknown but it had a pronounced effect on the profitability of growing the crop. The profit, which was expressed as a return on the total set-up cost of $A17 2591ha, was estimated for each of the measured oil concentrations and fixed values of biomass yield, the price of oil and average production costs. The extreme daily variations in oil concentration mentioned above caused the return on investment to decline by 11 percentage points and increase by 16 points, respectively. When measured at the same site, the mean oil concentration increased from 3.1% vPW in November 1987 to 5.8% v/DW in January 1989. As a consequence, the respective mean returns on investment increased from 0 to 26%.

A strategic integrated marketing and production planning model

Abstract To develop a strategic integrated marketing and production planning model, the tradeoffs among the total selling income, the total processing cost, the total tardiness cost, the total earliness (e.g. short-term holding) cost, and the total setup cost of a manufacturing operation are considered in a quantitative decision-making model. Based on this model, an optimal marketing and manufacturing operational strategic plan for utilizing the available processing capabilities of an integrated manufacturing system will be developed such that the total production of each job type equals its corresponding total demand. Moreover, this model will assist the operations managers to select among the potential customer orders which orders to accept or reject such that the net operational profit during the planning time horizon will be maximized. This model, is developed based on the group technology concept and assumes that: (a) each job requires a finite aggregated stage of operation; (b) job splitting is permitted; (c) the planning time horizon is sufficiently short; and (d) the processing priorities of all the jobs during the planning time horizon is specified based on a priority dispatching rule.

O𝕡timal Run Quantities for an Assembly System with Random Yields

Abstract An assembly system consists of m production lines, each of which produces a certain type of component. The components are then fed into an assembly stage, where each set of m components, one unit from each different type, are assembled. Due to uncertainties involved in the production lines, the component yields are random. The optimization problem is to find the run quantities of the components, in order to minimize the total setup cost while guarantee at a certain level the probability of achieving a given target yield from the assembly stage. Solution procedures are developed that efficiently solve the problem under convex setup costs and increasing failure rate (IFR) component yield distributions. Also studied are the computation of the expected yield and the effect of variability.

Separate vs. joint replenishment policies with maximum storage requirement costs

Multi-item inventory problems give rise to the possibility of time-phasing the replenishments of different items over the inventory cycle. Such a policy reduces the peak storage requirement, compared to a policy of simultaneous replenishment. This, in turn, increases the amount of warehouse space which is permanently available for leasing throughout the cycle. However, where cost savings may be achieved through combining setups of different items, as in the well known joint replenishment problem, such a time-phasing policy may increase total setup costs. This paper considers the two item joint replenishment problem, where a cost (equivalent to the opportunity cost of warehouse space) attaches to the peak storage requirement which occurs within the inventory cycle. Existing joint replenishment models do not consider such costs, but their consideration suggests that joint replenishment is not always optimal. We analyze possible policies under both joint and separate replenishment, and provide optimal closed form solutions. A numerical example to illustrate the tradeoff between joint and separate replenishment is provided.

Production Lot Sizing with Material-Handling Cost Considerations

Abstract The determination of production lot sizes and the assignment of storage space in a warehouse for the produced items are usually treated as two separate problems, the former providing input (space needed) to the latter. In this paper, we treat the decision problems as one with the objective of minimizing total setup, inventory carrying, and warehouse material-handling costs. We treat the minimum material-handling cost as a continuous function of the lot sizes and develop an algorithm for finding locally optimal solutions of the derived optimization problem. Computational experience is provided and a special case of the problem is shown to be equivalent to a single-processor scheduling problem.

Optimal lot size determination of multistage production system

This paper deals with the optimization of total setup plus inventory cost of a certain class of the multistage inventory-production systems with the series arranged production stages having generally different production rates, separated by stores from each other. The optimization is made by the choice of lot sizes across an infinite time horizon. The exact cost-optimization algorithm based on the Bellman optimality principle is derived and applied for deriving two lower bounds of the optimal cost of the above class of systems. These lowe bounds improve that derived by Crowston, Wagner and Williams. Two numerical examples are given.

A Branch-and-Bound Algorithm for Two-Stage Production-Sequencing Problems

This paper presents an algorithm for determining an optimum solution to a two-stage production sequencing problem with these characteristics: There are n jobs to be sequenced in a two-stage production environment; each production stage is equipped with a single facility; jobs to be sequenced are subject to due-date constraints; facilities in both stages require setup prior to processing each job; setup times in both stages are sequence dependent, and setup cost is assumed to be directly proportional to setup time; and the optimal solution is one that minimizes the total setup cost (of stages I and II) without violating job-due dates. The algorithm employs controlled enumeration through branch-and-bound procedures, together with feasibility tests.

Optimal Inventory Policies under a Hierarchy of Setup Costs

This paper considers multi-product inventory problems which are subject to an order cost or setup cost hierarchy of the following form: all replenishment orders issued in any given scheduling period are filled in the next period, with the total setup cost of replenishing N different products in one period being S + sN. The values of N observed in the various periods, and therefore the expected setup cost per job, depend on the unknown lot sizes. This type of setup cost dependence can arise in simple inventory problems but is more commonly found in production environments in which the setup cost for a given job depends on the job immediately preceding it in the production schedule. Assuming demands to be random with known probability distributions, an iterative algorithm is presented for computing optimal lot sizes and reorder points for a set of heterogeneous products.

A Heuristic Production Lot Scheduling Model

Abstract This article describes a model which seeks to schedule the production of m products over the next n production planning periods in a manner which minimizes total setup, production, and inventory costs while observing all constraints imposed by the capacities of the productive resources. The model formulates this problem as a fixed charge problem, and then uses a modified version of the simplex method to locate optimal or near optimal solutions of this nonlinear programming problem. A discrete optimizing approach is used to estimate the effectiveness of the model.