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Product Mix &Master Production Scheduling

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Product Mix Problem

Quantity of Each of Multiple Products to Produce

- Example: How Much of Various Flavors of Ice Cream to Produce?

Solution Methods- Hueristics- Linear Programming

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Linear Programming (L.P.)

Continuous Decision Variables

Decision Variable Subject to Constraints

Objective Function that is Maximized or Minimized

Equations or Inequalities are Linear

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Consider the Following:

The businessperson, Cindy Light, publishes two magazines, Paygirl (for men) and Payboy (for women). Monthly sales average about 6,000 and 4,500 issues respectively for the publications. Paygirls contribute $.60 per issue to net profits; Payboys add about $.50 per issue. No left over magazines are desirable.

Each Paygirl requires two minutes of actual machine and labor time to produce. Payboys only require one minute. There are 10,000 total minutes per month of time available. Inventory storage space imposes another limitation. 48,000 cubic inches are available and each magazine uses up about 8.

Determine monthly production for each magazine.

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E.g. L.P. Formulation

X1: Issues of Paygirl X2: Issues of Payboy

Objective Function: Max. Z = .6 X1 + .5 X2

Subject to (s.t.): 2 X1 + X2 10,000 (Labor)

8 X1 + 8X2 48,000 (Inventory)

X1 6,000 (Demand)

X2 4,500 (Demand)

X1, X2, 0

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Linear Programming (L.P.)

We Can Use the Computer (Simplex Method Using POM for Windows) to Find the Answer.

The Answer Would Be Incorporated in the Master Production Schedule

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Master Production Scheduling (MPS)

Link between Production Planning and What is Built or What Service is Performed

Used for Calculating Resource and Capacity Needs

Drives Material Requirements Plan (MRP)

Keeps Priorities Valid – Is Negotiated Agreement

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MPS Differs from Production Plan

Shorter Time Buckets

Used for Each End Item Not Families of Items as in Production Plan

Generally More Detailed

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Items in MPS Must Add Upto What’s in Production Plan

WEEK 1 2 3 4 5 6

UNICYCLES   100 50   50 40

BICYCLES 100     100   40

TRICYCLES     50   50 20

TOTAL - Production Plan 100 100 100 100 100 100

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What “End Items” Go into MPS

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MPS Can Show Running Inventory

Made to Stock Only

WEEK 0 1 2 3 4 TOTAL

FORECAST   200 300 100 100 700

AVAILABLE 200 250 200 100 100  

MPS   250 250   100  

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Optimizing MPS

Develop Preliminary Plan Maintain Desired Customer Service by Optimizing

Available Goods Make Best Use of Resources (Materials, Labor,

Equipment) Check Preliminary Plan Against Capacity Resolve Differences Between MPS and Capacity

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MPS with Minimum Available of 100

WEEK 0 1 2 3 4 TOTAL

FORECAST   200 300 100 100 700

AVAILABLE 200 250 200 100 100  

MPS   250 250   100  

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MPS and Capacity

Made to Stock

(Two Hours per Bike; Three Hours per Trike)

WEEK 1 2 3 4 5 6

BIKES 10 20 30 20 40 0

TRIKES 20 10 20 10 0 30

TOTAL HOURS 80 70 120 70 80 90

CAPACITY 100 100 100 100 100 100

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ATP (Available to Promise)

Portion of Inventory Not Committed – Available to Customer

ATP = Scheduled Receipts + Beginning Inventory - Actual Orders Scheduled

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ATP Calculation

On Hand:100

ATP (1) = 100 – 80 = 20 ATP (2) = 100 – (10+10) = 80 ATP (4) = 100 – 30 = 70

WEEK 1 2 3 4 5 6

CUSTOMER ORDERS 80 10 10   30  

MPS   100   100    

ATP 20 80   70    

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