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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
http://indusedu.org
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.
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 174
http://indusedu.org
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
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 175
http://indusedu.org
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:
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 176
http://indusedu.org
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:
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 177
http://indusedu.org
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
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 178
http://indusedu.org
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
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 179
http://indusedu.org
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.
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 180
http://indusedu.org
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
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 181
http://indusedu.org
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.
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 182
http://indusedu.org
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
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 183
http://indusedu.org
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
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 184
http://indusedu.org
Production
Run When
the End
Inventory
Fall Below
Minimum
Inventory
Production
Peaks
Demand
Assumed
to be
Constant
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