1. A decision matrix that shows the payoffs arising from the three potential locations under the various states of nature. Assume

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1. A decision matrix that shows the payoffs arising from the three potential locations under the various states of nature. Assume that all three forecasts are equally likely. Using Laplace, Maximin and Maximax criteria put forward your recommendation as t

You are the operations manager of Broadstairs Belgian Chocolate (BBC). This organisation is seeking to open another production facility. Three potential sites have been identified in the area; at Cliffs End, Manston and Birchington. The fixed costs over five years at each site are £150,000, £170,000 and £185,000 respectively. The variable cost for each site would be: Cliffs End 48p/kg, Manston 45p/kg, and Birchington 43p/kg. The selling price will be £1/Kg.

Three forecasts have been put forward, all covering a five-year period starting in 2018. The first forecast is that demand in 2018 will be 100 tonnes increasing by 8% p.a. The second forecast is that demand in that year will be 120 tonnes and that this will increase by 8% p.a. The third forecast is that demand will be 140 tonnes in 2018 and this will increase by 5% p.a.   

A chocolate processing and enrobing machine will also be required and three have been shortlisted. It has been decided that initial cost, running costs, ease of maintenance, ease of operation and ease of installation are of the most importance. Ease of maintenance is of equal importance as ease of installation. Ease of operation is considered twice as important as ease of maintenance and initial cost is considered twice as important as ease of installation. Running costs are considered twice as important as initial costs. The three machines have been evaluated and have scored out of 10 as follows:

Once the new machine has been delivered and installed and the staff have been trained to operate it, you will have to devise a production schedule for the chocolate that will be used for the new product. There are five major ingredients, cocoa butter, cocoa liquor, emulsifier, lactose and sugar. The prices for these on the commodity markets are as follows: cocoa butter USD ($) 3180/tonne; cocoa liquor $3200/tonne; emulsifier $1200/tonne; lactose $2.0/Kg and sugar $600/tonne. The machine produces chocolate in batches of 1000Kgs. The requirement is that the chocolate must contain at least 10% of cocoa butter, at least 10% of cocoa liquor, between 1% and 2% of emulsifier, at least 12% of lactose, and between 50% and 55% of sugar.

In addition to the chocolate enrobing machinery you also have a machine to produce your specialised fillings. One of these fillings is passion fruit crème. This has three ingredients, sugar, gelatine and passion fruit essence.   The crème must contain at least 10% but no more than 15% gelatine and at least 2% but no more than 5% passion fruit essence.

Your new machine will produce the crème filling in batches of 200 litres. It is produced by blending ingredients that come from two different suppliers.

Supplier X sells a product which is 80% sugar and 20% gelatine. This costs £1.10 a litre.

Supplier Y sells a product that is 90% sugar, 5% gelatine and 5% passion fruit essence. This costs £1.35 a litre. You must of course minimise the cost of the fillings you produce. The company accountant has confirmed that as a result of your diligent management the only variable costs are those of the ingredients.

Prepare a report for the MD that includes:

1. a decision matrix that shows the payoffs arising from the three potential locations under the various states of nature. Assume that all three forecasts are equally likely. Using Laplace, Maximin and Maximax criteria put forward your recommendation as to which option is preferable based on the projected demand over the next five years. Discuss the implications of your findings (30%).

2. the use of a weighted factored scoring method to determine which of the three machines is most suitable. Discuss the issues that emerge from this (30%).

3. (a) The formulation of two linear programming models. The first to provide the optimum quantities of the ingredients for the chocolate and the second to provide the optimum quantities for preparing the crème filling. (30%)

(b) Calculate and explain your solutions. Please attach your calculations or printouts in respect of this. (10%)