The Distribution Model, Resources, and Costs 



The Model 



Each hand in the producing area of a firm has a requirement for a 

 specific numher of chicks from each hatch. The objective is to organize 

 chick distribution in such a manner as to derive the lowest possible cost. 

 This is accomplished by using the resources, coefficients, assumptions, 

 and cost relationships previously developed. 



Since the marginal productivity of labor is constant, the man-hours 

 of labor for placing a given quantity of chicks at a broiler producing 

 unit is also always constant. Consequently, the problem is one of deter- 

 mining what combinations of vehicles and labor will minimize the num- 

 ber of trips into the producing area, and then determining which com- 

 bination performs the operation at the lowest cost. This is accomplished 

 once for each density level for each of the six hatcheries. 



For each hatchery, the trip alternatives are established by arranging 

 the individual bands into the maxinmm number of unlike groups. Some 

 groups contain as few as a single band while the largest contains all the 

 bands. The groups are then arranged into the maximum numlier of com- 

 binations each of which is equivalent in sum and identify to the bands in 

 the producing area. The comliinations represent the various alternatives 

 for distributing the chicks by each distribution model. 



The sequence for analysing these various combinations is to proceed 

 with the combination consisting of a single group. This group represents 

 a single trip which minimizes the number of vehicles and miles travelled 

 as well as man-hours of driver time expended in transit. In addition, this 

 alternative requires the largest capacity vehicles that would be used re- 

 sulting in the lowest possible vehicle cost per chick distributed. If this 

 complement fails to meet the restrictions, the analysis is shifted to com- 

 Ijinations consisting of two groups and so on until satisfactory solution? 

 are found. Once a combination with a particular number of groups 

 proves satisfactory, all other combinations with the same numlier of 

 groups are analysed and the physical inputs determined for those that 

 satisfy the restrictions. The inputs are converted into costs, and the least 

 cost method is found. Combinations consisting of larger numbers of 

 groups do not require calculation since they would involve additional 

 trips and inputs and result in higher cost operations. 



As an example of the al)ove procedure, hatchery F has to distriljute 

 34,800 chicks a day, six days a week into four liands: I, II, III, and IV. 

 The first combination tested to determine whether one complement can 

 service the Ijands in one trip consists of one group containing all four 

 bands. This alternative requires a type Q vehicle which has a load capa- 

 city of 34,800 chicks. At the density level of 1,491 chicks per square mile 

 per year, a round trip through the bands is 114.4 miles and requires 

 4.06 hours of travel time. Placing of chicks in the broiler houses requires 

 6.96 hours utilizing the smallest crew, a driver. This alternative requires 

 a total of 11.02 hours which exceeds the 10 hour work day restriction. 

 The addition of a helper to the distribution complement then reduces 

 the time spent in placing chicks at the farms to 3.48 hours. This reduces 

 the duration of the entire operation to 7.54 hours which is a satisfactory 

 solution. 



