Niraj Kumar Mahapatraindusedu.org/pdfs/IJREISS/IJREISS_2504_32766.pdf · 2018. 11. 19. · Niraj Kumar Mahapatra (MS Global Supply Chain Management, USC Marshall School of Business,

Special Issue-2 for International Conference on Sustainability Development – A Value Chain Perspective,

Management Development Institute (MDI), Murshidabad, West Bangal, India.

International Journal of Research in Engineering, IT and Social Sciences Page 173

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Production Planning Optimization: Going One Step Ahead of

Economic Order Quantity Model

Niraj Kumar Mahapatra (MS Global Supply Chain Management, USC Marshall School of Business, USA)

Abstract: Economic Order Quantity employs higher order quantities which lead to surplus

inventory resulting in increased total cost. Due to this, there is a constraint that

manufacturing houses and production planners face, which somehow reduces their

competencies to respond to demand variability. In this case, one uses a powerful solver in an

Open Solver platform that utilizes Gurobi Engine for solving complex problems using the

Linear Optimization principle. The EOQ model uses higher total capacity than the Open

Solver which means that resource optimization is on the higher side with the production

planning optimization model. EOQ doesn’t consider seasonality factor as much as it is

anticipated in the production planning as the minimum inventory doesn’t consider

management of lot size as per the demand. The open solver model has the capability to

optimize not only the inventory handling costs but also the overtime cost of the labor which

drastically decreases the labor costs. To represent certain intricacies on how the model

provides an optimal output over EOQ with different scenarios based on a simple “What-if”

criteria will explain about the parameters ranging from the sourcing to the manufacturing of

two products as a pilot test. Also, the model will give the insight to inspect how certain

decision parameters have overarching effects on the entire production planning process.

Furthermore, it can be expected that the Forecast Accuracy can lead to the formulation of

this planning process by considering the minimum inventory WeeksCover (Weeks of Supply)

and calculating the total savings throughout the time.

Keywords: EOQ, Demand Variability, Linear Optimization, Forecast Accuracy, Inventory

WeeksCover.

I. INTRODUCTION

The goal of any company always revolves around profitability, especially in

manufacturing operational metrics also play a key role. The concept of the Theory of

Constraints governs the principles in an organization which has many moving parts,

irrespective of its industry type (Goldratt, 1984). The production management systems

need a dynamic change in operational style as the supply chain flow happens in the

forward direction only. What is Supply Planning? Experts focus on Inventory,

Manufacturing Capacity, Material Resource Planning, Distribution Storage Capacity based

on Long-Term (1-3 years), Mid-Term (12-18 months): Master Production Schedule

(MPS), and Short-Term (1 – 8 weeks): Detailed Production Scheduling.




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Inventory plays a key role in the planning process, and this is where one would start

discussing the multiperiod inventory systems. In this period, one would talk about the

fixed-order quantity models or most popularly known as Economic Order Quantity (EOQ)/

Economic Production Quantity (EPQ). The fundamental purpose of such systems in place

is to ensure the availability of a specific product throughout a period, say a year for

instance. So, in this system, an item is ordered multiple times in a year which is

determined by a logic that dictates the quantity ordered and the frequency of the order in

that year. The trigger event in this system is initiated when reaching a specific reorder

level. The occurrence of this event may take place at any point in time; be it daily or

weekly or monthly depending on the demand of the item. Since demand tends to be most

lumpy at the end item level, EOQ models tend to be less useful for end items than for

details and materials at the lowest levels (Stevenson, 2012).

It has been more than 100 years since the concept was introduced by Ford W. Harris

based on the continuity of supply and demand. As Bill Roach explains how the origin of

the Economic Order Quantity began in his article, “Origin of the Economic Order Quantity

formula; transcription or transformation?” published in 2005, the formula calculates the

optimal economic order quantity. The critical decisions one needs to consider is the Plan

Production Capacity, Inventory Min/Max Targets, Seasonal Build, Production Cycle, and

Batch Size.

The EOQ Model is used to identify a fixed order size that will minimize the sum of

the annual costs of holding inventory and ordering inventory. The unit purchase price of

items in inventory is not generally included in the total cost




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because the unit cost is unaffected by the order size unless quantity discounts are a factor.

If holding costs are specified as a percentage of unit cost, the unit cost is indirectly

included in the total cost as a part of holding costs.

Annualized Costs

Material cost, ordering cost, and Holding (Carrying) cost

Variables

= Annual Demand

= Fixed cost incurred per order

= Unit cost (COGS)

ℎ = Holding cost per year as a fraction of the product cost C

= Order Size

Total Annual Cost (TC) = Material Cost + Fixed Ordering Cost + Holding Cost

ℎ

Optimal Order Quantity:

Optimal Order Frequency:




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Figure 1 Total Cost Vs. Order Size Figure 2 Inventory Vs. Time

So, what’s wrong with the traditional EOQ model? EOQ is a well-recognized and accepted

approach to setting batch size our, but Supply/Demand environment routinely violates every

one of the necessary assumptions! For most business, EOQ typically suggests running with

too large batch size, creates surplus inventory, and increases overall cost.

II. OBJECTIVE

To start with the researcher develops a multi-product production planning model

using the MS Excel which runs on a powerful optimization solver engine Gurobi. In the

model, there are two products which share a production line resource. The production

capacity is limited. Line capacity, change-over time, setup cost, and other production-

related parameters are assumed to for this frame of reference.

The intended application of this model is to understand how various input parameters

can impact the optimized production plan and the sensitivity of the impact when we

change some of them. The following What-If analyses will determine the Model

performance:




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Scenario1: One product has a much higher frame of raw material cost than the

other

Scenario2: One product has a much high setup cost

Scenario3: One product has much lower change-over time

Scenario4: One product has a much lower inventory holding cost

Scenario5: One product has much higher run-rate

Scenario6: One production line has higher capacity

Scenario7: One production line has much higher overtime labor cost

The primary objective of this model minimizes the total cost at every scenario to

determine which pathway is a best possible method to make a business decision based on an

appropriate change in the input parameters.

III. METHODOLOGY

Input Parameters

There are two product lines to considered here with Product 1 & 2.

Minimum WeeksCover (WC) which is the Weeks of Supply of the inventory in the

given period based on the average sales part. Here one assumes a specific

minimum value for the ease of calculation and take that as 5.

Raw Material Cost Per Unit is $ 50 for sourcing part of the supply chain.

Setup Cost is $1000 for production per product.

Setup Time (Hr) is 5 hours is the time required per product.

Run Rate (Units/Hour) 130 is the number of units of each product produced by the

machinery in place.

Holding Cost is 20% of the Total Cost from an inventory standpoint.

Labor and Material Cost Per Unit $88




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Cost of Goods Sold $133

Regular Capacity 40 hours

Regular Labor ($/Hr) 5000, Overtime Labor ($/Hr) 10000

Measures

The demand is recorded weekly basis based on 52 weeks in a year with both the

demands as different to show randomness and variability of the demand.

A concept of linking constraint will be used to execute a decision to produce or not

where it is connected with a Very Large Number (VLN) will be used to ensure a

maximum cap in the production quantity. VLN is 99999. The outcome of the

decision is binary to formulate the ease of calculation.

Model Characteristics:

o Week

o Demand

o End Inventory

o Minimum Inventory

o Produce or Not

o Resource Consumed (in Hours)

o Set Up Cost

o Inventory Holding Cost

o Total Line Consumed is a Function of Regular Line Cap and Overtime Cap

o Labour Cost

o Total Cost inclusive of all the internal expenses

Model Configuration:

o Objective: Minimization of Total Costs

o Variables




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Produce or Not: 0 or 1 Binary

Production Qty

Overtime Hours

o Constraints

Production Qty < Maximum Qty

End Inventory >= Min. Inventory

Produce or Not: Binary

Total Cap >= Consumed

Procedure

Use the EOQ model to calculate the optimal order quantity Q* for the two

products.

Manually plan the productions, (i.e., Production Frequency, Inventory Holding

cost, Labour cost, and Setup/Change-Over cost.

The first analysis gives the Total Cost of the EOQ/EPQ model using the model

template in MS Excel.

Add Excel Add-in of the Open Solver and download Gurobi Optimization 32/64

bit from www.gurobi.com.

Solve the model and generate an optimized production plan.

Save each scenario to tabulate it, and we get to compare the optimized plan with

the EOQ/EPQ plan.

http://www.gurobi.com/




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IV. OBTAINED RESULTS

Table 1 A. Operational Metrics Abbreviation (For Reference Purpose Only)

B. Input Parameters based on the considered scenarios

C. Comparison of Total Costs at different What-if Scenarios (Baseline Calculation After Running the Optimization Model)

Note: Refer Input Parameters to understand the unit for each of the of the operational metrics formulated in the

optimization model.

Operational Paramters Abbreviation

Product 1 & 2 P1, P2

Minimum WeeksCover Min WC

Inventory Invt.

Change Over Time CO Time

Raw Material Raw

Over Time (Labor) OT

Scenarios Products Min WC

Raw

Material

Cost Per

Unit

Setup

Cost

Setup

Time (Hr)

Run Rate

(Units/H

our)

Holding

Cost

Labor

and

Material

Cost COGS

Regular

Capacity

Regular

Labor

$/Hr

Overtime

Labor

$/Hr

EPQ Product 1 3 100$ $1,000 5 130 20% 138$ $208 40 5000 10000

Product 2 3 100$ $1,000 5 130 20% 138$ $208 40 5000 10000

Baseline Product 1 3 100$ $1,000 5 130 20% 138$ $208 40 5000 10000

Product 2 3 100$ $1,000 5 130 20% 138$ $208 40 5000 10000

Product 1 3 25$ $1,000 5 130 20% 63$ $95 40 5000 10000

Product 2 3 100$ $1,000 5 130 20% 138$ $208 40 5000 10000

Product 1 3 100$ $10 5 130 20% 138$ $208 40 5000 10000

Product 2 3 100$ $1,000 5 130 20% 138$ $208 40 5000 10000

Product 1 3 100$ $1,000 0 130 20% 138$ $208 40 5000 10000

Product 2 3 100$ $1,000 0 130 20% 138$ $208 40 5000 10000

Product 1 3 100$ $1,000 5 130 5% 138$ $208 40 5000 10000

Product 2 3 100$ $1,000 5 130 20% 138$ $208 40 5000 10000

Product 1 3 100$ $1,000 5 260 20% 119$ $179 40 5000 10000

Product 2 3 100$ $1,000 5 130 20% 138$ $208 40 5000 10000

Product 1 3 100$ $1,000 5 130 20% 138$ $208 60 5000 10000

Product 2 3 100$ $1,000 5 130 20% 138$ $208 60 5000 10000

Product 1 3 100$ $1,000 5 130 20% 138$ $208 40 5000 5000

Product 2 3 100$ $1,000 5 130 20% 138$ $208 40 5000 5000

Product 1 Low

Raw Material Cost

Product 1 Low

SetupCost

Higher Line

Capacity

Higher OverTime

Cost

P1 Lower Change

Over Time

P1 has higher Run-

Rate

P1 has lower

Holding Cost




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Scenarios Results/Insights

EOQ/EPQ Model

Flaws No capacity constraints are equal to High OT labor cost

No consideration on the line resource sharing

Fixed order size

Doesn’t consider seasonality factor

Doesn’t consider shelf-life which directly affects the obsolescence cost

Doesn’t recognize the comparison of order quantities as well as the

production capacity

P1: Lower Raw

Material Cost P1: More Inventory Build

P2: Less Inventory Build

P1: Lower Carrying Cost

P1: Lower Setup Cost Would expect reduced cycle stock, and less Inventory

Setup Time penalty is much higher

P1: Lower Change

Over (CO) Time Implies more line capacity, therefore less overtime

P1: reduced cycle stock (more production frequency)

P1: reduced carrying cost

P2: reduced cycle stock due to increased line capacity

P2: increased Inventory build and carrying the cost

P1: Lower Holding

Cost Similar to P1 with lower Raw Cost

P1: Higher Run-Rate Implies more line capacity for P1/2, therefore Less overtime

P1: larger batch size, no more build, less total WeeksCover (WC)

Batch size is limited by capacity in a week

P1: less setup cost

P2: smaller batch size, less cycle, less total WC

Higher Line Capacity Implies more line capacity for P1/2, therefore Less overtime

P1: larger batch size, no more build, less total WeeksCover

Batch size is limited by capacity in a week

P1: less setup cost

P2: smaller batch size, less cycle, less total WeeksCover

Higher Over Time (OT)

Cost Reduced use of Over Time (only if possible)

The trade-off between Setup and Over Time costs

P2: Increased Inventory Build, and carrying the cost Table 2 Scenario Analysis

V. CONCLUSION & FUTURE SCOPE

The open solver model has optimized the overtime cost of the labor which drastically

decreases the labor costs by $ 12 M as obtained in the baseline.

Resource utilization is more prominent in the optimized model than in the EOQ

model.




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There is a lowest Total Cost for a scenario where there is a change in the CO time

which also gives rise to lower overall labor cost as there is a reduction of OT which

is at

Due to optimal order quantity, there is the same value of order every cycle which

doesn’t benefit if there is a discount for a large order. Also, it leads to an unnecessary

build of inventory.

As it doesn’t consider capacity constraints, the EOQ model can’t establish an optimal

material plan for production.

Consideration of the Forecast Accuracy can be an added advantage which can reduce

variability which can lead to the optimization in production planning by considering

the minimum WC and calculating the total savings throughout that time.

Short Warehouse Shelf life (WSL), using salvage of finished goods to find Max WC;

Addition of Max WC in the model

If Forecast Accuracy Had Decreased:

o Recalculate the Min WC in the model;

o One product will have higher Min WC

Line Capacity is not Adequate:

o Relax the Min Inventory constraint to allow dipping below average;

o Introduce a cost penalty for the amount below Min;

o The cost penalty needs reflect the cost of shortage:

Profit Margin

Cost of customer dissatisfaction




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VI. REFERENCES

1. Bassin, William M. (1990). Inventories. Journal of Small Business Management 28.1 Pg.48- 55. ABI/INFORM Global, ProQuest.

2. Cargal, James M. (2009).The EOQ Inventory Formula.Http://www.cargalmathbooks.com.<http://www.cargalmathbooks.com/The%20EOQ%20Formula.pdf>.

3. Jacobs, F. Robert. (2014). Operations and Supply Chain Management. New York, NY: The McGraw-Hill Irwin.

4. Mahapatra Niraj K. (2016) Globalization of Manufacturing a Viable Business Strategy. Industrial Engineering Journal, Vol. IX & Issue 11, Pg.42-46.

5. Stevenson, Willian J. (2015). Operations Management. New York, NY: The McGraw-Hill Irwin.

VII. LIST OF FIGURES & TABLES

Figure 1 Total Cost Vs. Order Size……………………………………………..…….3

Figure 2 Inventory Vs. Time……………………………………………..…………...3

Table 1 A, B, C Results……………………………………………..………………...5,6

Table 2 Scenario Analysis…………………………………………………………….7

VIII. APPENDIX

BFFB

MODEL OUTLOOK 2 GRAPHICALLY REPRESENTATION OF THE PRODUCTION CYCLE

MODEL OUTLOOK 1 REPRESENTATION OF THE MODEL




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Production

Run When

the End

Inventory

Fall Below

Minimum

Inventory

Production

Peaks

Demand

Assumed

to be

Constant

Documents

Niraj Kumar Mahapatraindusedu.org/pdfs/IJREISS/IJREISS_2504_32766.pdf · 2018. 11. 19. · Niraj Kumar Mahapatra (MS Global Supply Chain Management, USC Marshall School of Business,