How to Perform DIY Production Scheduling to Make the Most of Your Production Assets February 18, 2015by Hugh Walters

SHARE:

Useful ideas for maximizing the power of Microsoft Excel for Supply

Chain Analysis, Part II

This is the second post in a three-part series that describes how toperform desktop network

optimization, job scheduling and vehicle routing with nothing but Microsoft Excel.

Future posts will focus on forecasting and supply chain finance. We hope you find these topics

interesting and encourage you to reach out to Hugh with any questions.

Introduction

In my previous post, I talked about performing a desktop transportation/ network optimization.

This was an interesting class of problems that produced valuable information and insights

regarding the cost and service components of a distribution network. These problems require a

good bit of pre-work related to data gathering and analysis, but the worksheet setup is fairly

straightforward, perhaps even intuitive.

The job scheduling problem requires less pre-work, but the set-up is more complicated and less

intuitive. This makes it more difficult to explain…at least in my mind. However, the benefits are

much more tangible. If organized properly, the solution methodology can be used several times

per day to schedule and re-schedule work. Further, analyzing the results will reveal the location

of bottlenecks and opportunities to streamline operations.

At the simplest level, the objective of these problems is straightforward: schedule production to

get as much work done as possible in the shortest amount of time. However, we will modify the

objective slightly to make the problem more realistic. Production orders will be organized such

that groups are completed at approximately the same time. Think of this as a way to have specific

production orders completed by a certain cut-off time or cut-off date.

To solve this problem, I leverage the idea that solving an optimization problem consists of two

distinct but connected parts: problem set-up and solution search.

Like my other post, Microsoft Excel will be the tool for problem set-up and solution search.

However, since this class of program does not lend itself to searches based on linear

programming techniques, we will once again use the Evolutionary Solver in Excel (released in

version 2010) to search for the solution.

Characterizing the Problem

In this situation, pretend that you are the manager of a value-added service (VAS) operation. You

are responsible for scheduling the jobs through one of eight VAS processing lines. Your lines all

have the same capabilities. However, because of differences in equipment, space, experience, and

leadership, some of the lines can process work faster than others. You know what these process

speeds are and would like to include this information when developing schedules. The company

you work for has national contracts and every day you ship completed work all over the United

States. Lately, business has been good but this has resulted in a few problems:

A crowding problem where work sits on the floor waiting for a truckload quantity to be

assembled so that a truck can be brought in and loaded.

Carriers complaining that their drivers have to wait too long for a load and are starting to charge

penalties for the delay.

Work stoppages, re-sequencing, and expediting that contribute to inefficiencies.

Is there a way to find a daily job sequence that completes jobs in geography groups in the shortest

elapsed time while simultaneously minimizing the total time to complete all jobs?

Today, there are 75 jobs that will be distributed nationwide. These 75 jobs have been divided up

into 10 groups representing the major regions of the United States.

The job information is simple: it consists of the number of units and a group. The job index (idx)

is just used to keep track of the job. The line information shows the rate it takes to process one

unit in seconds. Thus, line 1 can process 1 unit in 1 second and line 8 can process one unit in .75

seconds.

Setting up the problem for the solution

The key to understanding the way this problem is set up is to understand one of the key

capabilities of the Evolutionary Solver in Excel. This key capability is the “All Different”

constraint. This constraint was designed to order a sequence of numbers to meet a specified

criteria. Since a scheduling problem is a sequencing problem, this is exactly what we need to do.

The completed table shows the SEQ number which determines the Line Number and the Line

Sequence of the job. The Excel formulae are provided below:

The Duration, in minutes, determines how long the job will take given its assignment to a

particular line. Since different lines have different processing speeds, the duration will vary based

on line assignment. Each job starts immediately after the previous job ends. Thus, the Start

Time for a particular job on a line is the cumulative time for all the previous jobs on that line.

This time is measured in elapsed time from a base of zero. The Finish Time is the sum of

the Start Time plus the Duration.

Setting up the Results Viewing Area

There are two key connected objectives for this problem: 1) Get the work done as quickly as

possible while 2) reducing the elapsed time to complete the jobs for each of the groups. The

tables that measure these objectives are below.

In each case,

measurement is the elapsed time between the first job and the last job. The smaller the elapsed

time the better.

Setting up the Solver

Setting up the solver requires five steps:

1. Determining the objective cell on the Excel spreadsheet

2. Selecting the type of problem

3. Detailing the cells that can change to solve the problem

4. Defining constraints on the changing cells or other values in the problem

5. Selecting the solver to use for the problem

This gives the following results:

This

represents over a 2000 minute improvement in aggregate waiting time and after the initial set up;

it took the solver less than three minutes to arrive at this answer.

The total time did not improve dramatically. This result is in line with expectations since the

“work is the work.” However, the total production time did not increase, meaning that as a

solution was generated for one problem, it also improved the other. At this point, it is worth

mentioning that using the Evolutionary Solver comes with some drawbacks. Indeed, it is

incredibly powerful, but as problem sizes get larger, the Evolutionary Solver has a harder and

harder time finding good answers. Also, since the solver is stochastic in nature, the same answer

will not be achieved on a subsequent run of the solver. The main reason for this is that the search

space for the Evolutionary Solver grows geometrically as jobs are added and the starting location

of the search can vary. Five jobs can be ordered 5! or 120 ways. 100 jobs can have 100! or

9.3E157. That’s a lot bigger than google (1E100). In fact, since there are 2.5E9 seconds in an

average lifetime and if we had a computer that could test 1E9 solutions every second, it would

still take more than 1E140 lifetimes to test all possible combinations. The galaxy would burn out

before that. With a search space that size it is worth wondering if there are better solutions and

how the problem can be formulated to reduce the size of the search space.

Improving the Solver Solution

Given that the size of the problem explodes geometrically as the number of jobs increases, it is

worth considering how to break up the problem so that it is not so big. One of the ways this can

be accomplished is by solving for the most efficient sequencing for each of the ten groups. This

would yield the set up below:

In this setup the problem has been changed from sequencing a single string of 75 numbers to

sequencing 10 strings of varying length. This is dramatically easier for the solver because

contained within the formulation is an assumption that Group 1 jobs will be scheduled before

Group 2 jobs and so on. This results in a better solution in a faster search time.

In addition, the overall production time decreased only slightly. Again showing that group

elapsed time could be reduced without increasing the total production time.

In this article you have learned how to set up a multi-line production sequencing problem in

Microsoft Excel and solve it using the Evolutionary Solver. These solutions are not always

available with ERP packages and need to be developed outside the system. Understanding how to

set up and solve these problems can boost productivity, reduce cost, and increase

competitiveness.

Good production scheduling is a foundational requirement for efficient operations and effective

asset utilization. Centric would like to help you make the most of your assets by developing new

approaches to solve these types of problems. For a discussion or consultation, please contact me.

In my next article, I will show you how to conduct DIY vehicle routing to minimize distance and

transportation expense.

How to Conduct a DIY Network Analysis to Understand How Location Impacts Service and Transportation Expense Submit

Useful ideas for maximizing the power of Microsoft Excel for supply

chain analysis, Part I

This is the first post in a three-part series that describes how to perform desktop network

optimization, job scheduling and vehicle routing with nothing but Microsoft Excel.

Future posts will focus on forecasting and supply chain finance. We hope you find these topics

interesting and encourage you to reach out to Hugh with any questions.

Introduction

Performing a network analysis is one of the bread and butter tasks for a supply chain consultant.

Typically, it takes specialized software, weeks of working with the data going into to the

software, and another couple of weeks working with the data that comes out of the software.

The most valuable pieces of information this analysis yields are warehouse locations and

approximate transportation spend. However, it can also be extended to understand the classic cost

– service tradeoff that results from the cost of placing and operating more warehouses closer to

customers and the service benefits they receive because of faster response times.

Given that warehousing and transportation typically accounts for 60 percent to 90 percent of

logistics cost, maintaining a solid understanding of the relationship between location and

transportation expense is always a valuable exercise.

The problem is that there is seldom the time or the budget to retain a consultancy to do even a

small network analysis. Instead, there may only be two weeks, between other duties, for an in-

house supply chain analyst to develop a directionally correct, 80 percent solution that could be

understood, vetted, and evaluated by a larger audience. This is really like asking if there is a way

to do this in Microsoft Excel.

Getting Started

As of Microsoft Office 2010, the answer is yes, this can be done in Microsoft Excel, because of

the inclusion of a new algorithm in the Solver: the Evolutionary Solver. Without going into too

much detail, this algorithm is excellent for finding solutions to non-smooth, non-continuous,

optimization problems. For those with experience using the Excel Solver, you know setting up a

problem is as much science as craft. This is no different. The data that is required to perform this

analysis is:

Ship from –An address for an existing warehouse location

Ship to – An address for a customer location

Transit time – Check-out to check-in

Weight – The weight of the order in lbs.

Distance – The distance

Cost – Shipping cost

Mode –Truckload (TL) versus Less-than Truckload (LTL)

Analyzing the raw data is a painstaking process, but it will facilitate an understanding of the

current operational baseline. This current state analysis should provide information about:

1. Total transportation cost, total transportation weight, total transportation mileage, total

TL mileage, total LTL mileage and intermodal, if it is in the data

2. Average shipment cost, average shipment mileage, average shipment time, TL average

for all three, LTL average for all three, and intermodal, if it is in the data

3. Average cost per mile for TL, average cost per mile for LTL, average distance traveled

per day Establishing the operational baseline will result in an understanding of the relationships between

delivery distance, time and cost for the current operation. Further, these same relationships will

be leveraged to develop a future state operation with re-located warehouses. One of the first

things that must be done is the conversion of all addresses to geocodes. Geocodes are the Latitude

and Longitude (lat/lon) of a point on the earth and there is an equation that provides the distance

between two points on the surface of the earth. Three relatively low-cost ways exist to convert an

address to lat/lon:

1. Purchase Microsoft MapPoint and write a Visual Basic for Applications (VBA)

program that leverages the MapPoint object model and enables a “lookup” from Excel.

2. Purchase a subscription to Google Maps ($5 per month) and upload the addresses directly

and get the lat/lon.

3. Download the latest Census Bureau data. This data contains lat/lon for U.S. zip codes and

these can be used as an estimate for the address.

With the customer and warehouse locations converted to geocodes, the shipping distance must

now be calculated and corrected because the distance we use is surface distance and this will

always be shorter than road distance. By comparing actual to calculated distance, we can develop

a multiplier to make a road distance correction. Typically, the multiplier is between 1.15 and

1.35. The steps to follow include:

1. Convert the warehouse addresses to geocodes.

2. Convert delivery destinations to geocodes.

3. Calculate the delivery distance using the geocodes. 4. Correct the distance using a multiplier.

Setting up the Spreadsheet

To calculate the distance between two points on the surface of the Earth, one can use the

spherical law of cosines or the Haversine formula. I prefer the spherical law of cosines for its

simplicity in Excel. It looks like:

The information is consolidated in the spreadsheet with:

Baseline Network Information

Network Service Performance Aggregator

Distance Calculation Table, Warehouse Selection Table, Network Cost Performance,

Customer. Location and Freight, and Warehouse Locations.

All of this information is organized to perform the optimization. In Excel, this uses the Solver

Optimization tool. Beginning with three warehouses located in Harrisburg, PA, Dallas, TX and

Las Vegas, NV, the annual shipping cost is just over $24M with more than 13M miles shipped.

Reviewing the Baseline and Network Performance

The activity profile is detailed below. This model establishes the baseline for our optimization

efforts since it represents the current state. Notice that with the warehouses in these locations,

fewer than half (7,456 of the 15,341) of the shipments are two days or less from the customer.

Running

the Optimization The solver is set to re-locate all three warehouses. Activating the solver finds three new

warehouse locations that eliminate about 4.5M miles and more than $8M in cost. Warehouse 1 is

close to Richmond, KS; Warehouse 2 is close to Pikeville, KY; Warehouse 3 is close to Pueblo,

CO.

The activity profile shows the most improvement. Now, more than 60 percent of the shipments

are within 1.5 days of the customer (9,300 of the 15,341).

In addition,

the number of customers that have been moved into the 1.5 day or less delivery lead time window

have increased from 752 to 1513. The number of shipments that can be delivered in 1.5 days or

less grew from 4,195 to 9,300.

Changing the Objective

The versatility and power of the Evolutionary Solver is that it can be used to optimize “non

traditional” objectives. For example, if the objective was not minimizing cost but increasing the

number of shipments that could be delivered in the 1.5 day delivery lead time window, different

warehouse locations would be generated.

In order to set up the parameters to maximize 1.5 day delivery lead time, the locations change to:

Warehouse 1 is close to Marshall, NC; Warehouse 2 is close to Matheson, CO; Warehouse 3 is

close to Greentop, MO. The warehouses have moved 100 to 200 miles from their previous

locations. This has added overall cost and distance, but it is less than 3 percent to the network.

However, the activity table reveals that a few more customers (14) and more than 600 additional

shipments are within 1.5 days of delivery—and example of the classic tradeoff between service

and cost.

Extending the Model

Thus far, three warehouses have been relocated to minimize transportation expense and maximize

shipments delivered in 1.5 days or less. How much does an additional warehouse impact our

transport cost and service performance? This is easily determined with a spreadsheet model that

is properly set up. Beginning with Warehouse 1 close to Colorado Springs, CO; Warehouse 2 is

close to Hugo, OK; Warehouse 3 is close to Boone, IA; and Warehouse 4 is close to South

Williamson, KY.

Locating four warehouses in the network and minimizing cost reduces the transportation expense

from the comparable three warehouse model by more than $2M.

In addition, the average delivery lead time is well below 1.5 days. The number of shipments that

can be delivered in 1.5 days or less has increased by more than 2,200 and the number of

customers served in 1.5 days or less has increased by 227.

The natural question at this point is, “can this be improved?” By setting the solver to maximize

the number of shipments that can be delivered n 1.5 days or less, a different set of locations are

generated. Warehouse 1 is close to Matheson, CO; Warehouse 2 is close to Lockesburg, AK;

warehouse 3 is close to Washington, IA; warehouse 4 is close to Flag Pond, TN.

Locating four warehouses in the network and maximizing the number of shipments that can be

delivered in 1.5 days or less reduces the transportation expense from the comparable three

warehouse model by more than $2M, but adds $300K to the lowest cost four warehouse solution.

In addition, the average delivery lead time is well below 1.5 days. The number of shipments that

can be delivered in 1.5 days or less has increased by 1,985 from the best three warehouse solution

and the number of customers served in 1.5 days or less has increased by 217.

Unfortunately, it seems that it would be difficult to reduce the average delivery time from two

days to one. However, by relocating the warehouses and adding one additional (bringing the total

to five), the average delivery lead time can be reduced to less than 1.5 days while saving several

million dollars.

Of course, adding warehouses to the network adds additional cost and the model must be

augmented to address this cost increase.

This represents a relatively straightforward way to conduct a network analysis. The supply chain

analyst should be comfortable providing fact-based answers to questions regarding the benefits of

warehouse location and number. There are other things that need to be considered, such as the

availability of warehouse space in the locations identified, the cost of operating a new warehouse

and the cost of moving warehouse operations from one location to another. These are all very

significant activities that impact the value proposition.

In my next article, I will show you how to develop a solution for job shop scheduling, another

difficult optimization problem that can be solved in Excel using the appropriate framework. Until

then, keep modeling.

How to Conduct DIY Vehicle Routing to Minimize Distance and Transportation Expense Useful ideas for maximizing the power of Microsoft Excel for Supply

Chain Analysis, Part III

This is the final post in a three-part series that describes how toperform desktop network

optimization, job scheduling and vehicle routing with nothing but Microsoft Excel.

Future posts will focus on forecasting and supply chain finance. We hope you find these topics

interesting and encourage you to reach out to Hugh with any questions.

Introduction

In the last two articles I’ve shown ways to develop solutions for some of the classic supply chain

problems. These problems can be characterized as facility location problems and production

scheduling problems.

This entry will follow that pattern leveraging the traveling salesman problem as an example.

However, we will call this the vehicle routing problem (VRP) to make it a bit more supply chain.

Fortunately, regardless of how you refer to it, people will know what you are talking about

because this is one of those classic problems in supply chain and operations research.

The idea is to create the shortest, closed-loop route, visiting each customer only once and

returning to the starting point. Many companies must solve this problem daily, and there are

multiple software providers that offer software solutions. Parcel delivery companies like UPS

have elevated this to an art form and even sell their own software. Unfortunately, this software is

expensive to license, expensive to set up and install, and expensive to operate. Thus, a business

case must be carefully constructed to justify the expense.

Constructing this business case should include a comparison to a reasonable alternative that

produces a satisfactory solution within a satisfactory timeframe at a satisfactory price point. By

developing a solution in Excel, the price point is free (assuming it was already purchased), the

length of time is 10 minutes and the solutions, while typically not optimal, are very reasonable.

If you have read the other blog entries you can probably guess that we will be using Microsoft

Excel and the Evolutionary Solver with the “AllDifferent” constraint. As in the other two blog

entries, we will extend the problem to make it a bit more realistic. The extension will result in

the three shortest routes, served by a single depot so that all the routes start and end at the depot.

Further, the routes need not have the same number of stops, but with each stop taking 10 minutes

and averaging a driving speed of 40 mph, each route should be close to the same duration.

Characterizing the Problem

The problem can be stated as “is it possible to create three short and time-balanced routes that

start and end at the same depot and visit all of the customers?”

Setting up the Problem for Solution

Like the problem from the previous blog post, this can be categorized as a sequencing problem.

Leveraging what was done before, stops will be sequenced on three routes just like allocating and

sequencing production jobs to production lines. However, in the production problem we found

that sorting by a particular grouping provided a very satisfactory simplification for the solution.

There is the possibility to do this for the VRP as well by evaluating the angular distribution of

customer locations and allocating stops to routes based on the angle from the starting location.

1. Customer locations

2. Depot location (starting point for all routes)

3. Distance matrix

4. Angular vector

For the sake of simplicity, the locations we will use fall on an xy coordinate plane. Therefore, we

will be using the Euclidean distance formula. We could use the Haversine formula from the first

article, but the distance formula is not the central issue. The route stop sequence is. Further, using

xy coordinates makes this very easy to graph in Excel.

For this problem we will sequence 37 customer stops into three routes. A snapshot of the data is

provided below:

The angular allocation results in a setup that places the cities in a numerically increasing order:

Solver Setup

The solver set up for sequencing a single route is straightforward.

Following the same procedure but combining all three routes in the solver simultaneously yields:

However, the best view of the solution is obtained by graphing it.

The solver has done an adequate job of producing the routes, but there is room for improvement.

To improve the results, a second optimization can be performed on the individual routes. Using

Route 1 it is possible to re-sequence the stops and reduce the distance by 80 units, a 20%

reduction. The results look like this:

Early in first article mentioned that there was a way to group the stops to speed up and simplify

the solver routine. One way to perform this grouping is to divide the stops into sections. One of

the simplest ways to do this is through an angular sweep of the stops produced by dividing the

graph into equal 120 deg sections. The stops that fall into each section can then be optimized

using the techniques similar to the ones discussed here to obtain faster solutions that are much

closer to optimal.

Vehicle routing is a core competency for many companies and improvements result in improved

asset efficiency, reduced cost, and improved customer deliveries. Some companies have produced

closed-loop routes over time, but never reviewed them in any systematic way to insure they

remain efficient as routes of deliveries are added or deleted. In some cases, these routes have

been run for years without a review to determine if there are opportunities to consolidate or

reorganize routes.

We believe this is a huge opportunity to save money and miles and would like to review the way

your organization performs its routing. Please contact me to discuss ways that Centric can help

you review your routes and determine opportunities for improvement.

Addressing uncertainty in sales plans with supply chain techniques can become a key differentiator and a competitive weapon. Our chief weapons are time and flexibility.

I love manufacturing. The idea of making something that people want to buy fills me with a sense of pride. It’s almost a patriotic passion, and it’s for this reason I lament manufacturing’s demise, especially here in Northeast Ohio, my home. I’ve wrestled with the reasons and realize they are many and complicated. I just can’t shake the feeling that we’ve lost our competitive spirit and a desire to win. For my part, I’ve tried to do what I can to promote a higher level of competiveness with the companies where I consult.

Offshore manufacturing is a reality, but the willy-nilly movement of production off our shores over the past two decades has seen a small turnaround in recent years. In my mind, this turnaround has been too slow and the opportunity to bring some of this manufacturing back to the U.S. has not been pursued as aggressively as it should.

One area that continues to astound me is our inability to mount a compelling business case that compares the onshore versus offshore costs of manufacturing, materials, logistics and labor as well as the components of time, return on inventory investment and the risk of the lost sale because inventory is moving in longer supply chains.

The idea of the lost sale is not a new or complicated one, but it is difficult to measure. The most effective means of measurement I’ve seen revolve around assessing sales velocity and understanding the likelihood of a sale. There is also the need to consider stockout situations and assess the likelihood of sales that would have happened.

Although this is a pretty straightforward explanation, it is still difficult to assess and isolate meaningful data. These measurements are still flawed because there is not an effective way to test stockout timing or the purchase of a substitutable item. It is absolutely necessary, however, that lost sales be measured and it is absolutely necessary that steps are taken to prevent lost sales and by extension, stockout situations.

Generally, manufacturers want to sell as much of their wares as possible since they generate profit from each sale. This reveals the nature of the problem: being able to anticipate how much will be sold and how much profit will be made requires knowledge of future events. There is no crystal ball to see into the future, and the farther we look, the more uncertain we become. We are left with making educated guesses about the future, and the only thing we know for sure is that more information results in better guesses. Therefore, addressing uncertainty in our sales plans with supply chain techniques can become a key differentiator and a competitive weapon. Our chief weapons are time and flexibility.

As a manufacturer and supplier, selling the benefits of additional planning and reaction time to a retailer is critical. What can be done with this additional time? Ideally it can be used to increase sales by focusing on activities related to adjusting and refining actions to meet future demand. Where does the time come from? When viewed within the context of an offshore import there are multiple time buckets including:

In host country

At port of embarkation (incl. customs clearance)

Transit

At port of debarkation (incl. customs clearance)

In destination country enroute to destination

This can easily take three to four weeks, a significant portion of a selling season. The example below may better illustrate the benefits of additional time:

A national retailer gets its house brand of snow shovels from an offshore supplier. The process

they follow includes reviewing historical data to forecast a sales quantity, placing an order in

March for delivery in September and distributing to retail locations throughout October for sale

throughout the winter season. Last year a sales executive at a Northeast Ohio (NEO) [PU1] manufacturing company noticed

that the shovels had been OOS (out-of-stock) at her local store. She inquired why the shovels had

been OOS so long and discovered that because the shovels had all been distributed in October, it

was difficult, if not impossible; to move products back through the network for redistribution. As part of the executive team at her company, the sales executive is very interested in finding

ways to consume her company’s winter production capacity as well as making inroads with a

large national retailer. She puts together some numbers to determine if there is a compelling

business case. She estimates that a winter storm gives a one-week warning and this becomes the order lead time

for new shovels. The shovels need to be the same and sold at the same price. She estimates that

the imported cost is $12, her company’s cost is $15 and the sales price is $24. She also believes

there is a 20 percent sales lift by having the shovels at the right place at the right time, a service

her company can offer because of the additional time and their flexibility. Here is the deal she proposes:

Instead of purchasing all 5,000 shovels offshore, purchase 80 percent (4,000) offshore and 2,000

from the NEO company, deferring distribution to the time of need. The result is a better in-stock position as products are distributed just before the time of need (a

weather forecast) and a 10 percent increase in gross margin dollars. Other intangible benefits

include happier customers and an increase in associated sales such as ice-melt. There is a way to leverage time and supply chain flexibility to bring manufacturing opportunities back to the U.S. Since this was a very simple example many costs were not included, making the actual opportunity potentially much larger.

By taking the time to measure lost sales and allowing for additional planning and reaction time, it IS possible for medium and small manufacturers to compete effectively with the offshore behemoths.