Inventory Models

QM 265

Assignment 6

Inventory Models

Table of Contents

Base case linear programming model Page 3

Optimal plan and corresponding total gross margin Page 4

Constraints for scenarios with final values and shadow prices Page 5

Shadow prices for cattle and summer casual labour Page 5-6

Changes in the optimal plan between scenarios A and C Page 6

Binding and upper and lower limits on resources Page 6-7

References Page 8

Question 2) a)

Table 1. Optimal plan and corresponding total gross margin.

Activity Gross Margin Change (Plan B)

Forage Oats (ha) 3.45

Improved Pasture (ha) 55.87

Native Pasture (ha) 150

Fallow (ha) 0

Merino Ewes (hd) 400

Xbred Ewes (hd) 910.88

Cattle (hd) 20

Spring Supplementary Feed (kg) 0

Summer Supplementary Feed (kg) 0

Autumn Supplementary Feed (kg) 0

Winter Supplementary Feed (kg) 0

Spring Casual Labour (hrs) 115

Summer Casual Labour (hrs) 115

Autumn Casual Labour (hrs) 0

Winter Casual Labour (hrs) 99.96

Total Gross Margin 80221.48

b)

Table 2. Constraints for the three scenarios with final values and shadow prices.

Constraints Base Case Labour Change GM Change

Final Values Shadow Prices Final Value Shadow Price Final Value Shadow Price

Merino Ewes (minimum) -400.00 24.49 -400.00 14.49 -400.00 24.49

Xbred Ewes (minimum) -910.88 0.00 -910.88 0.00 -912.57 0.00

Cattle (minimum) -20.00 411.97 -20.00 411.97 -20.00 412.78

Total Sheep (maximum) 1310.88 0.00 1310.88 0.00 1312.57 0.00

Arable (ha) 3.45 0.00 3.45 0.00 0.22 0.00

Fallen Timber (ha) 150.00 3.78 150.00 3.78 37.43 0.00

Crop Rotation (ha) 3.45 0.00 3.45 0.00 0.22 0.00

Spring Labour (hrs) 220.00 180.65 220.00 180.65 220.00 259.33

Summer Labour (hrs) 220.00 101.56 220.00 101.56 220.00 23.26

Autumn Labour (hrs) 151.18 0.00 151.18 0.00 147.45 0.00

Winter Labour (hrs) 180.00 17.00 180.00 17.00 180.00 17.00

Spring Feed (kg/ha) -151016.12 0.00 -151044.06 0.00 -131942.93 0.00

Summer Feed (kg/ha) -134868.66 0.00 -134857.49 0.00 -114012.79 0.00

Autumn Feed (kg/ha) 0.00 0.11 0.00 0.11 0.00 0.10

Winter Feed (kg/ha) -17335.15 0.00 -17363.09 0.00 0.00 0.00

Spring Grain (t) 0.00 0.00 0.00 0.00 0.00 0.00

Summer Grain (t) 0.00 0.00 0.00 0.00 0.00 0.00

Autumn Grain (t) 0.00 0.00 0.00 0.00 0.00 0.00

Winter Grain (t) 0.00 0.00 0.00 0.00 0.00 0.00

Spring Casual Labour (hrs) 115.00 163.65 115.00 163.65 115.00 242.33

Summer Casual Labour (hrs) 115.00 84.56 115.00 84.56 115.00 6.26

Autumn Casual Labour (hrs) 0.00 0.00 0.00 0.00 0.00 0.00

Winter Casual Labour (hrs) 66.96 0.00 66.96 0.00 67.26 0.00

Non Arable (ha) 55.87 0.00 55.87 0.00 137.75 0.00

Total Gross Margin 76221.48 80221.48 75765.69

c)

The shadow price of a resource, such as labour or hectares, is the effect an increase or decrease of one unit of a resource has on total gross margin (TGM). Therefore it