International Business: Management Processes and Practices. Unit - Production Management and Logistics

 

https://egyankosh.ac.in/

Finite Capacity Scheduling

 

What are the benefits and challenges of using finite capacity scheduling (FCS)?

Finite capacity scheduling (FCS) is a method of planning and managing production processes that takes into account the actual capacity and availability of resources, such as machines, labor, materials, and time. FCS aims to optimize the utilization of resources, reduce lead times and inventory, and increase customer satisfaction. However, FCS also poses some challenges, such as complexity, uncertainty, and flexibility. In this article, you will learn about the benefits and challenges of using FCS in different types of production environments.

FCS vs. infinite capacity scheduling (ICS)

The main difference between FCS and ICS is that FCS considers the realistic constraints and limitations of the production system, while ICS assumes that there is unlimited capacity and resources to meet the demand. ICS is simpler and easier to implement, but it often leads to overloading, bottlenecks, delays, and waste. FCS is more realistic and accurate, but it requires more data, analysis, and coordination. FCS can also adapt to changes in demand, capacity, or priorities more effectively than ICS

Benefits of FCS

FCS offers several advantages for production managers and customers, such as improved resource utilization, reduced lead times and inventory, increased customer satisfaction, and enhanced visibility and control. FCS helps to allocate resources more efficiently and avoid idle time, overwork, or underutilization. It also helps to schedule production activities more accurately and minimize the waiting time between operations, which reduces the need for excess inventory and storage space. Moreover, FCS helps to meet customer expectations and deadlines more reliably and consistently, which enhances the quality and reputation of the products and services. Additionally, it helps to monitor and track the status and performance of the production processes and resources, which enables better decision making and problem solving

Challenges of FCS

FCS involves certain challenges and difficulties, such as the complexity and data requirements which necessitate a lot of information and calculations to determine the optimal production schedule. This process must integrate data from various sources and systems, such as sales, engineering, purchasing, and inventory. Additionally, FCS must take into account the uncertainty and variability of the production environment, such as demand fluctuations, capacity changes, quality issues, breakdowns, or disruptions. This requires adjusting and rescheduling the production plan accordingly. Finally, FCS must balance efficiency and flexibility with short-term and long-term goals while accommodating customer requests, special orders, or urgent orders without compromising the overall production schedule or performance

Types of FCS

When it comes to FCS methods and tools, the nature and characteristics of the production system determine the type used. Forward scheduling is best for make-to-stock or repetitive production processes with stable demand and capacity, while backward scheduling is better for make-to-order or customized production processes with variable demand and capacity. Mixed scheduling is ideal for hybrid or flexible production processes with diverse demand and capacity, and constraint-based scheduling works best for complex or interdependent production processes with multiple constraints or limitations.

Best practices for FCS

To implement FCS successfully and effectively, production managers should adhere to some best practices. This includes defining the objectives and parameters of the production schedule, such as demand forecast and capacity availability, as well as collecting and verifying data and information needed for FCS. It is also important to choose and apply the appropriate FCS method and tool for the production system. Furthermore, managers should monitor and evaluate the results of FCS, such as resource utilization, inventory levels, customer satisfaction, and profitability. Lastly, it is essential to review and update the production schedule regularly based on changes from the production environment.

Finite capacity scheduling is so-called because it takes capacity into account from the very outset. The schedule is based on the capacity available. Infinite capacity scheduling - the approach used in MRP II - schedules using the customers' order due date and then tries to reconcile the result with the capacity available. There is no single accepted way to carry out Finite Capacity Scheduling, and of the various approaches that exist, some are proprietary secrets.

It is however possible to define certain approaches, or types of scheduler:

 

Electronic scheduling board

The simplest scheduler is the electronic scheduling board, which mimics the old fashioned card-based loading boards, but the system calculates times automatically and will warn of any attempt to load two jobs on the same machine. There is no scheduling algorithm as such involved.

Order Based Scheduling

In Order Based Scheduling the tasks are scheduled on the basis of order priority. The sequence at individual resources is determined by the overall priority of the order for which the parts are destined. It is a distinct improvement on infinite capacity schedulers but its biggest drawback is that it allows gaps to appear on resources. Some schedulers allow the process to be iterated to try and reduce gaps and therefore reduce the time through the system. This iteration can be very time consuming.

Constraint based schedulers, Synchronised Manufacturing

With the Constraint based schedulers, also known as Synchronised Manufacturing, the idea is to locate the bottleneck in the line and ensure that it is always loaded. The assumption is that non-bottlenecks can take everything thrown at them, and this allows them to be synchronised to the bottleneck through the Master Production Schedule (MPS). The MPS is generated by loading the orders onto the bottleneck and thus determining when they will be ready. This system is inclined to produce gaps and is also very sensitive to small changes such as a customer wanting to reschedule an order.

Discrete Event Simulation

In Discrete Event Simulation the simulation loads all resources at a point of time. When all contentions and queues are resolved it moves on to the next set of events. Because the simulation moves from one set of events to the next, there are far fewer gaps in schedules produced this way and they are far more stable. The problems with simulations are that they are: laborious ;and also difficult to incorporate into other systems such as data feedback from the shop floor.

Algorithms, Genetic algorithms

Algorithms usually suffer from being highly mathematical and therefore user unfriendly, however more recently a new approach has emerged under the general title of `genetic algorithms'. These use a 'fitness' criterion. A typical example would be to minimise the total time for jobs to stay in production. The procedure starts with a schedule or family of schedules. The idea is to try and improve them using a selection mechanism akin to natural selection. 'Children' (new schedules) are bred using characteristics (such as sequences of work) from parent schedules. If the new child shows improved fitness i.e. is faster than the parents, it replaces the worst schedule. While the approach looks promising it is still in the early stages.

There remains the question of how these new approaches fit with existing schedulers, particularly MRP in which companies have invested vast sums. In the first three cases they tend to replace the scheduling heart of the MRP system while leaving the rest unchanged. To that extent the MRP system acts like a database manager.

 

References

• Harrison. M., "MRP II & Finite Capacity Scheduling - a combination for the 90's", Works Management, December 1991.
• Kirchmier. W., "Finite capacity Scheduling", Proceedings of the 37th International Conference APICS, Falls Road, VA, 1994

https://www.ifm.eng.cam.ac.uk/

Finite-Capacity Scheduling and Planning 

Priority‘s production planning facility includes a unique feature that performs forward scheduling followed by backwards scheduling (most other systems schedule backwards and then forwards). Forward scheduling not only ensures that no work is planned before materials are available, but also pinpoints the earliest possible completion date of any given order item.

Backwards scheduling enables production to follow the rules of JIT (just-in-time planning). That is, if it is clear that a component for a given assembly will not be available on time, the production (or purchase) of the remaining components of that assembly is likewise postponed to the latest possible start date (where the user can regulate the delay).

Preparation for Production Planning 

• Production planning and scheduling are carried out on the basis of:
• Open sales orders (grouped by user-designated priorities)
• The bill of materials of the ordered item, taking into account parent-child ratios and the routings of all parts in the BOM
• Available inventory, actual and planned
• Material constraints
• Tooling constraints
• Capacity constraints
• Labor constraints
• A wealth of parameters that determine the standard time a job will take, percentages of scrap, lot sizes and the like.

Before production planning is run, the planning data used by the program are updated and frozen. This prepares for a new planning cycle which wipes clean the results of the previous cycle and takes into account updated data (such as current balances, due dates of open purchase orders and the like).

Production Planning
Priority allows you to choose between three planning options (see below):

• Forward scheduling only
• Forward and backward scheduling
• Forward and backward JIT scheduling.

Once the option has been selected, planning is carried out separately for each group of orders, according to Priority. Planning for a given order group takes into account data from the previous planning session.

Forward Scheduling 

This option is recommended during initial planning simulations, as it provides a precise picture of planning results without any further manipulations. It therefore makes it easier to pinpoint the factors that might be leading to poor planning results (e.g., delayed materials).

Forward+Backward Scheduling 

This option offers forward scheduling followed by backward scheduling. The latter reduces slack between child and parent jobs wherever possible.

Forward+Bkward JIT Scheduling 

This option provides for just-in-time planning. Forward scheduling is followed by backward scheduling (slack reduction), and the planning of all order items is postponed to the latest possible start date. This option allows for a supply of goods to customers as close to the due date as possible.

Stages in Production Planning 

The following actions are performed by the production planning mechanism:

1. Determination of calendric capacity — construction or extension of each work cell’s calendar, including, if necessary, a calendar for each machine in the work cell.
2. Determination of lot size, taking into account process batch quantity, work order size, campaign size and minimum production size (as defined per part, per job or as a factory-wide constant).
3. Calculation of required quantities for production — This is achieved by “expanding” the BOM of each of the ordered parts in the current planning group, down to the level of raw materials, and then subtracting floor inventory not already destined for another job (whether existing at the time of planning or deriving from earlier production planning sessions). In addition, available and anticipated warehouse inventory is taken into account (based on purchase orders and compressed lead times).
4. Order splitting to distribute required quantities into lots, taking into consideration lot size, work order size, campaign size, and rounded quantities of excess inventory.
5. Calculation of set-up and processing times, estimating the time required, per work cell, to set up and process planned jobs (concurrent or sequential).
6. Workload balancing, utilizing, whenever available, processing alternatives to reduce the workload on the main work cell and main operation. For every job whose operation, work cell, part or tools has alternates, an attempt is made to distribute the workload as evenly as possible.
7. Job sequencing per work cell,with the aim of minimizing set-up times and smoothing production in those work cells that have a tendency to become bottlenecks. The fuller a given work cell’s calendar and the greater its workload, the higher its priority in terms of job sequencing and the higher the priority of its child jobs. The system attempts to begin production at the bottleneck work cell (and on its child jobs) as early as possible in order to take advantage of any idle time at the work cell before it comes under pressure of constant operation. You have the option of sequencing with the aim of optimizing adherence to due dates or optimizing usage of work-cell capacity.
8. Preparation of the issues plan.

Planning Simulations and their Implementation 

Before work orders and the issues plan are actually created, Priority generates a planning simulation for testing what-if scenarios based on the planning data.

Once production planning has been run, results may be viewed in various reports. A decision is then made as to whether to put the plan into action or to make certain modifications — reorganize order groups (add or delete order items, rearrange groups, re-prioritize them) or add a work shift — and then rerun the planning program.

Analysis of Results 

The system provides a broad spectrum of reports allowing you to examine and understand the factors underlying the results received from production planning. These reports can also be used as the basis for carrying out changes in preparation for an additional run of the planning simulation:

• Pre-planning reports help pinpoint problematic areas, such as unrealistic job sizes or too many lots, which can lead to undesirable planning results. The reports include: job times and quantities for planned order groups; the number of lots for an order group; plant-floor inventory; production demands for the order group; and work cell hours for the order group. These reports are normally run prior to the activation of production planning.

• Work plan reports display the work plan (Gantt chart), planned issues of materials from the warehouses, planned issues from one work cell to another and planned queue times. They include information on planned production times from a variety of perspectives (e.g., work cells, labor, production processes).

• Quantitative reports display planned quantities of parts to be processed over user-designated periods (a day, week, month), as well as the quantities planned to fill specific orders. The reports include: work cell quantities by period, periodic quantities per work cell and job quantities per order item.

• Period load reports display planned load distribution over the work cells. These reports can reveal those periods or work cells at which workloads are particularly heavy.

• Critical path reports analyze the critical path of designated ordered parts.

• Routing reports display the full routing of a given part and all its child parts or the routing of a given planned lot.

Lot Size Optimization 

As part of the Production Planning module, Priority offers a mechanism for optimizing lot sizes. This mechanism helps you handle a common dilemma encountered in work cells: on the one hand, a need to increase lot size as much as possible so as to save on set-up times; on the other hand, a need to decrease their size as much as possible in order to produce a smoother load distribution and to reduce cycle time and shipping costs.

Preparing Work Orders and an Issues Plan 

Once you are satisfied with the simulation results, you can run the Prepare Work Orders and Issues Plan program. This opens needed work orders and creates an issues plan for the designated period, serving as a basis for production control and purchase planning.

Scheduling data are translated into production data by opening work orders for goods that need to be manufactured. Such work orders can then be released for execution of the first operation in the part’s routing. For each work order (including those opened for sub-assemblies), you can view the sales order (or orders) it is intended to fill.

The resultant issues plan displays the quantities and dates on which issues are to be executed, based on anticipated shortages of the material on the plant floor.

The system provides an interface that can be used to download the work plan data so that it can be displayed graphically in MS-Project. Data can be displayed there by orders or work cells.

Production Planning Reports 

Planning Data Reports 

• Child-Parent Ratios (Planning)
• Work Cell Parameters
• Alternate Jobs
• Part Route Card
• Jobs
• Set-ups per Work Cell
• Set-ups per Job
• Tool Allocation

Pre-planning Reports 

• Job Times and Qtys for Group
• Number of Lots for Group
• Plant-floor Inventory
• WIP in Closed Work Orders
• Production Demands for Group
• Work Cell Hours for Group

Work Plan Reports 

• Work Plan
• Work Plan – Labor
• Issues Plan
• Issues to Work Cell
• Issues to Jobs
• Queue Time

Quantitative and Period Load Reports

• Work Cell Quantities by Period
• Periodic Quantities per Work
• Job Quantities per Order Item
• Work Cell Loads per Period
• Period Loads per Work Cell
• Work Cell Loads per Period & Group
• Period Lead by Jobs
• Manpower per Period
• Period Loads for Tools

Critical Path and Routing Reports 

• Critical Path
• Detailed Critical Path
• Routing by Part
• Routing by Lot

https://www.topprioritysystems.com/

Production I. Production duality

 

Production maximisation

Production maximisation must be seen as an optimisation problem regarding the production function, represented by isoquants, and a constraint regarding production costs, represented by an isocost line.

Producers are therefore faced with the following problem: faced with a set of possible production levels and a fixed budget, how to choose the level which maximises their production?

If we know the production function of a certain producer, and we know their budget, we have the two restrictions necessary to maximise their production. This can be done graphically, with the point where isocost and isoquant meet defining an optimum, as shown in the adjacent figure.

It can be also done mathematically, through a Lagrangian, where the first derivatives determine a system of equations that can be resolved by submitting our production function to the restriction presented by the budget:

Video – Production maximisation:

Cost minimisation

Cost minimisation tries to answer the fundamental question of how to select inputs in order to produce a given output at a minimum cost.

A firm’s isocost line shows the cost of hiring factor inputs. This line gives us all possible combinations of inputs (here labour and capital) that can be purchased at a given cost.

Assuming that a certain amount of output wants to be achieved, we have several possible combinations to achieve it, but only one that minimises costs. The isocost line tangent to the isoquant, which represents the amount of output targeted, will reveal the input combination that results in the lowest cost, for that given output.

We can also use the method of Lagrangian systems to analytically solve a constrained minimisation problem. The first derivatives determine a system of equations that can be resolved by submitting our sought output to the restriction presented by the minimisation of costs:

Video – Cost minimisation:

Production duality

As in consumer’s theory (where consumption duality is analysed), the firm´s input decision has a dual nature. Finding the optimum levels of inputs, can not only be seen as a question of choosing the lowest isocost line tangent to the production isoquant (as seen when minimising cost), but also as a question of choosing the highest production isoquant tangent to a given isocost line (maximising production). In other words, having a cost function that sets a budget constraint, solving for the inputs allocation that gives the highest output.

The way to solve either problem is very similar: we look for the Lagrangian function and obtain first order conditions, then solve the system.

Video – Production duality:

https://policonomics.com/lp-production1-production-duality/

Production I. Production and cost

 In this first LP on production, we will examine the decisions that lead to optimal levels of production. This is crucial, as it mirrors the same decisions that we saw consumers making: assigning our limited (and expensive!) resources in the best way possible in order to maintain optimal levels of production. This will ultimately lead us to the same dual problem: whether to minimise costs assuming an optimal, fixed level of production, or whether to hedge our bets and maximise production whilst fixing a budget for costs.

In order to do this, we will begin by looking at the basics, production and costs, with an entry on:

• Isoquants, or graphical representations of our production possibilities, and relate this to the
• MRTS, which shows the trade off between our inputs, and put all this together in our summary of the
• economic region of production, which represents our rational possibilities. We will then go on to examine
• production functions and their characteristics and finish this first section with
• isocosts, which closely relate to the concept of isoquants.

In the second half of this LP, we will go on to cover the problem of production duality, beginning with an entry on:

• Production maximisation, and then looking at the flip side of the coin with
• cost minimisation, before putting it together in
• production duality.

Production and cost. Isoquants

An isoquant shows the different combinations of K and L that produce a certain amount of a good or service. Mathematically, an isoquant shows:

f (K,L) = q0

Graphically, the shape of an isoquant will depend on the type of good or service we are looking at. The shape of isoquants is also in close relation with the terms marginal rate of technical substitution (MRTS) and returns to scale.

The first example of isoquant map showed in the adjacent graph is the most common representation. It shows four convex isoquants (green), showing each curve what amount of capital K the producer can stop applying when increasing the amount of labour L, while maintaining the quantity of output produced constant. This relation gives us the MRTS between these inputs, which is the slope of the curve in each of its points.

Our second example is an isoquant map with four parallel lines (cyan). This is the case for inputs which are perfect substitutes, since the lines are parallel and MRTS = 1, that is the slope has an angle of 45º with each axis. It can also be the case for inputs that are perfect substitutes but in different proportions. In that case, the slope will be different and the MRTS can be defined as a fraction, such as 1/2 ,1/3 , and so on. For perfect substitutes, the MRTS will remain constant.

Our third example shows an isoquants map with four isoquants (red) that represent perfect complementary inputs. This is, there will not be an increase on the amount produced unless both inputs increase in the required proportion. The best example of complementary inputs are shovels and diggers, since the amount of holes will not increase when there are extra shovels without diggers. Notice that the elbows are collinear, and the line crossing them defines the proportion in which each input needs to increase in order to have an increase in the production. In this case the horizontal fragment of each isoquant has a MRTS = 0 and the vertical fractions a MRTS = ∞.

Isoclines are lines which ‘join up’ the different production regions. Having defined  and decided the optimal levels of K and L we need to produce the different quantities, the line that passes through these optimal levels is an isocline (cyan). In other words, it is the line that joins points where the MRTS of each isoquant is constant:

Video – Isoquants:

s we all know, we need inputs in order to be able to produce goods and services. But how much of each? Let’s look at this in our entry on the MRTS, or Marginal Rate of Technical Substitution.

Production and cost. Marginal rate of technical substitution

The marginal rate of technical substitution (MRTS) can be defined as, keeping constant the total output, how much input 1 have to decrease if input 2 increases by one extra unit. In other words, it shows the relation between inputs, and the trade-offs amongst them, without changing the level of total output. When using common inputs such as capital (K) and labour (L), the MRTS can be obtained using the following formula:

The MRTS is equal to the slope of isoquants. In the adjacent figure you can see three of the most common kinds of isoquants.

The first one has a MRTS that changes along the curve, and will tend to zero when diminishing the quantity of L and to infinite when diminishing the quantity of K.

In the second graph, both inputs are perfect substitutes, since the lines are parallel and the MRTS = 1, that is the slope has an angle of 45º with each axis. When considering different substitutes inputs, the slope will be different and the MRTS can be defined as a fraction, such as  1/2 ,1/3, and so on. For perfect substitutes, the MRTS will remain constant.

Lastly, the third graph represents complementary inputs. In this case the horizontal fragment of each indifference curve has a  MRTS = 0 and the vertical fractions a MRTS = ∞.

Not to be confused with: marginal rate of substitution and marginal rate of transformation.

Video – Marginal rate of technical substitution:

We’re now in a position to study our production level possibilities globally, and determine which production regions make sense from an economic perspective. Understanding this is crucial if we don’t want to go bankrupt… This is what we’ll examine in our entry on the economic region of production.

Production and cost. Economic region of production

The economic region of production shows the combinations of factors at a certain cost that make economic sense. Areas outside the economic region of production mean that at least one of the inputs has negative marginal productivity. This region is marked by what are called ridge lines, which are simply the boundaries beyond which one of the two factors is being overused. Therefore, outside the economic region of production, there is clear inefficiency, and the company would be better off using less of one of the two factors, bringing costs down whilst maintaining equal production output. Graphically:

Video – Economic region of production:

In order to analyse these production possibilities, let’s have a look at production functions and their main characteristics.

Production and cost. Production function

A production function shows how much can be produced with a certain set of resources. Generally, when looking at production, we assume there are two factors involved in production: capital (K) and labour (L), as this allows us graphical representations of isoquants. However, any analysis made with 2 factors can mathematically be extended to n factors.

Therefore, a production function can be expressed as q = f(K,L), which simply means that q (quantity) is a function of the amount of capital and labour invested. In the adjacent figure, qx is function of only one factor, labour, and it can be graphically represented as shown (green).

It is well worth introducing here another concept: marginal productivity, which is how much more quantity we could produce by adding one unit more of a factor. As is logical, this will depend on how we are employing the factors we already have. The marginal product is the partial derivative of the production function with respect to the factor we are examining:

Marginal productivity decreases with each additional unit, as it can be seen in the above figure (cyan). At a certain point, the more workers we have, for example, the more each additional worker will be redundant if we do not invest in other necessary factors. This is the same as saying that the second derivative is negative. At that point, A, production is as efficient as possible.

Video – Production function:

And, to finish this first section, a quick mention on the subject of isocosts, which will tie in when we examine costs.

Production and cost. Isocosts

Isocost lines show combinations of productive inputs which cost the same amount. They are the same concept as budget restrictions when looking at consumer behaviour. Mathematically, they can be expressed as:

rK + wL = C

Where r is the cost of capital and w is the cost of labour. Generally, we think of r as the interest rate the financial markets offer, as capital requires investment. Even if the capital can be paid for using a company’s own resources, r is still equivalent to the opportunity cost of having the money tied up in investments rather than in liquid assets which offer a return (r) by lending it to the markets. The cost of labour (w) is the salary paid to employees per unit of time.

Isocosts are usually represented graphically together with isoquant lines (which are combinations of productive inputs which produce a fixed quantity of outputs). The two have a tangency point, which determines the optimal production (where production is maximised or cost minimised).

Video – Isocosts:

https://policonomics.com